'To forge' implies to create a lasting relationship based
on hard work. ‘forge ... links’ (smithy) makes better
engineering sense than ‘build links’ or ‘create links’.
‘Links’ also goes with the purpose - Aeroplanes.
Ans .
b
Explanation :
Bank deposits 'swelled' implies that they increased to
a great extent. The banking industry can flourish, not
the deposits. Bank deposits cannot be ‘enhanced’ or
‘flummoxed’.
Ans .
c
Explanation :
The original phrase is the best suited for the given
sentence. The ‘revival’ has taken place, hence (a) is
not true. (d) also cannot be true in light of the ‘revival’.
(c) is a more precise choice than (b).
Ans .
a
Explanation :
'At will' fits here perfectly in contrast to 'freely'.
‘umbrage’ can be given without intention, so (b) is not
right. (d) does not make sense. ‘scolding’ happens
spontaneously most of the times, hence it is unlikely
that it involves a decision-making process.
Ans .
a
Explanation :
'To write at random' is more concise than 'to write at a
random speed' and conveys the meaning perfectly.
‘writing without affectation’ in no sense means writing
‘fast’ or ‘with speed’. We choose (a) over (b) because
of the parallel construction with ‘write without
affectation’.
Ans .
b
Explanation :
'Lukewarm' fits in the first blank, and in the second,
we need a verb. So 'electrifies' is the best suited of all
the given choices. ‘boiling’ and ‘fascinating’ cannot
grammatically fit the second blank. ‘almost’ and
‘genuinely’ are unlikely to go together.
Ans .
d
Explanation :
Social studies, science matters of health and safety
and the atmosphere of the classroom, help in formation
of proper emotional responses. Hence these can be
referred to as the ‘important areas’. ‘things’ is too vague
a word to fill the first blank. Emotional reactions cannot
be ‘inculcated’. Given ‘basis’ and ‘formation’, the second
word is more appropriate to fill in the second blank.
Ans .
b
Explanation :
'Audilble' sounds as opposed to 'visual' symbols, fits
here. ‘without making intelligible sounds’ does not make
sense in the sentence. ‘aural’ and ‘vocal’ are technical
words that draw attention away from the crux of the
sentence i.e. one need not be heard all the time to gain
meaning.
Ans .
d
Explanation :
Learning is always more efficient when it is fun and
less efficient when it is drudgery (boring). Learning
need not be efficient when it is fast or rapid, this may
lead to loss of retention. Nor can learning be more
efficient when it is tedious.
Ans .
c
Explanation :
The rulers get too much power while those who are
ruled show passive obedience. (d) makes an
incomplete sentence with the second phrase. It is
unlikely that a crusade is pointless. (a) does not make
sense. (c) shows a proper parallel and logical
structure.
Ans .
a
Explanation :
(a) has the only pair of words that fits in without
creating any contradictions. When it comes to
arithmetic, you can count the number of copy cats
(imitation). This inference does not come across in
choices (b), (c) and (d).
Ans .
b
Explanation :
The farmers are protesting and want their voice to be
heard. (a) and (d) do not fit into the semantic context
of the sentence. The farmers, by themselves, cannot
curb the prices, so (c) is not right.
Ans .
b
Explanation :
In terms of general rules, science as a news agency
is comparable to other news agencies. ‘principal’
means ‘chief’ and this is not the meaning that the
sentence is trying to convey, so (a) and (c) are wrong.
‘in spirit and form’ also sounds directionless.
Ans .
a
Explanation :
'Actuated' means motivated. Leaders cannot be ‘led’.
One cannot categorise people ‘by’ desires. ‘convinced’
similarly sounds vague.
Ans .
c
Explanation :
'Buy cheap and sell dear' is the only option that will,
without any doubt, lead to commercial success. (d)
gives an unwarranted warning. (a) is not sound
commerce. (b) is needlessly verbose, as compared
to (c). (c) sounds like a formula, it is also the best
choice after the hyphen.
Ans .
b
Explanation :
After 1, (C) states a fact about salvation. (B) states
the Christian belief in that regard. (A) opposes it to
Buddhism, by using 'but'. (D) elaborates the fact.
Ans .
d
Explanation :
After the factors stated in 1, (A) states the relationship
between size of a state and development. (B) states
that the problems of agricultural sector will remain
with us in the next century. (C) emphasizes the need
to improve agriculture. (D) states that rural India has
to start moving, an idea that is continued in (6).
Ans .
b
Explanation :
(B) shows the relationship between a magazine and
its editor, ‘editors’ are referred to as ‘they’. (C) states
that the number of editors should be determined by
the contributions it gets. (D) continues with this fact.
(A) follows by using 'furthermore'.
Ans .
c
Explanation :
(B) follows (1) by using ‘especially’. (D) explains the
‘NRI phase'. (A) states that the East and the West
meet in the NRIs. (C) states a fact that has been
overlooked, and (6) tells us that the festival of feature
films and documentaries is trying to fill this gap.
Ans .
c
Explanation :
(C) gives a reason for a market for Indian art coming
into being. (B) states what simultaneously happened
in India. (A) states what happened as a fallout of the
festivals of India. (D) elaborates on it and leads to (6).
Ans .
b
Explanation :
(B) introduces a figure walking slowly, (A) describes
it. (D) states that Annete followed the figure with a
triumph of recognition, and (C) tells us the name of the
figure and states that 'she' followed him.
Ans .
a
Explanation :
(C) states that learning is important. (A) states that in
contrast today unlearning is the real challenge. (D)
followed by (B) states why unlearning is a real
challenge.
Ans .
b
Explanation :
(B) states that 'we' reached the field soaked. (D) states
that Claudius was standing there. (C) states the effect
of being wet on Claudius, and (A) elaborates on it.
Ans .
c
Explanation :
(A) states that Alex had never been happy with his
origins. (C) states what he would rather have been.
(B) states what he tries to do to rectify the facts, and
(D) shows his wife's reaction to his actions.
Ans .
a
Explanation :
(B) states the influence of Indian colours and cuts on
Western styles. (A) states that it is seen most on the
beaded evening wear. (D) tells us the most popular
colours and (C) states how the international fashion
scene has been affected by the Indian outfits.
Ans .
b
Explanation :
(D) introduces the point of emergence of theocratic
states. (B) states how it benefits the politicians. (C)
shows how the politicians act and (A) concludes the
paragraph.
Ans .
a
Explanation :
(C) introduces the subject of the passage. (A)
describes him. (B) shows why he was in that place,
and (D) describes his mental state.
Ans .
a
Explanation :
(A) shows the director walking into the room. (C) tells
us that the managers stared at him. (B) states Mitch's
reaction, and (D) states what he finally did.
Ans .
d
Explanation :
(A) states the influence of Third Reich. (D) elaborates
on the events that accompanied the Third Reich. (C)
states that while speaking out against Hitler, Americans
favoured isolationist policies, and (B) elaborates on
such policies.
Ans .
b
Explanation :
(A) introduces Of Studies as the main idea of the
passage. (B) states that the essay requires complete
attention of the reader. (C) states Bacon’s stand on
studies, and (D) continues with the same.
Ans .
b
Explanation :
(C) relates logic to reasoning. (A) states what
reasoning means. (B) states what logical reasoning
covers, and (D) states how we can understand
arguments and draw inferences correctly.
Ans .
b
Explanation :
If Sita is not sick, it follows that she is careless. One of
the either/or conditions hold good.
Ans .
d
Explanation :
Ram does not eat hamburgers, so it follows that he
does not get a swollen nose. When X, then Y. Not Y,
hence not X.
Ans .
b
Explanation :
If the employees have confidence in the management,
it follows that they are hostile. The first of the either/or
condition is false, so the second one has to be true.
Ans .
d
Explanation :
None of the given options relates logically to the given
statements.
Ans .
a
Explanation :
As all irresponsible parents do not shout, it follows
that the children cavort. When X, then Y. X, hence Y.
Ans .
b
Explanation :
If only strong have biceps and no faith is strong, it
follows that no faith has biceps. In A, X and Y need
not overlap. In B, the Sona and crazy set need not
overlap. In D there is no logical conclusion at all.
Ans .
b
Explanation :
In (C) and (D) the first two statements do not logically
lead to the third. In C, we do not know if the hand and
the head set overlap. D leads to an unpredictable
conclusion. The icicles which are cycles are at least
men. In B, if no teeth is yellow, no girl can be yellow,
since all girls are teeth.
Ans .
a
Explanation :
If no sun is not white, it implies that all sun is white. All
moon is sun, so it follows that all moon is white. B and
C lead to undefined conclusions. In D, there is a
possibility that X and Y sets can intersect.
Ans .
c
Explanation :
If all Ts are square and all squares are rectangular, it
follows that all Ts are rectangular. Also, if idiots are
bumblers and bumblers fumble, it follows that idiots
fumble. In B, there is a possibility that fat and huge
sets need not intersect. D plays with words and leads
to uncertain conclusion again.
Ans .
a
Explanation :
As the passage says that efficiency won't be content
to reign in the shop, but will follow us home, it implies
that efficiency can become all-pervading. (b) is not
the focus of the questions. (c) goes beyond the scope
of the argument.
Ans .
c
Explanation :
As each project is being stalled for some reason or
the other and no consensus has been reached on
any of the projects, we can infer that the projects will
be stalled for an indefinite period. (a) is stated in the
argument, and (b) is likely to be a conclusion.
Ans .
b
Explanation :
The passage states that designations are forgotten
during the meetings and even a sales engineer can
question the CEO on company policies. The company’s
ulterior motive is not the focus of the argument, so (a)
and (c) are ruled out.
Ans .
a
Explanation :
The passage states that the rape of Indian architectural
wealth can be attributed to the blend of activist disunity
and local indifference. (b) may not be true as Indians
may be gullible. (c) and (d) are stated in the passage.
Ans .
b
Explanation :
The moral police feel that Fire would influence the
Indian psyche and ruin the moral fabric of the nation,
which it should not be allowed to do. (a) is not true, as
Indian audiences may be discriminating. (c) is not an
inference, it is true to a certain extent.
Ans .
a
Explanation :
The passage states that the rich have never felt
secure against the poor and their aggressiveness
stemmed from fear of the poor. (b) refutes the
conclusion in the argument.
Ans .
c
Explanation :
The passage states that the second kind of traveller
visits only such monuments as the time at his disposal
allows him to contemplate without irreverent haste.
The preference of the writer is not the focus of the
argument. While (a) is wrong, (b) is too caustic.
Ans .
d
Explanation :
None of the given options is supported by the passage.
(c) may not be true in the immediate temporal context
of the argument. (b) is clear from the argument, it is
not an inference. (a) is, of course, wrong.
Ans .
d
Explanation :
The passage supports none of the given options.
(c)does not seem to be true in light of facts presented in
the passage. (b) is stated anyway in the passage.
What the director aimed at does not seem to be the
focus of the argument, which discusses a general
consequence.
Ans .
a
Explanation :
The Indian middle-class, what it wants and what it
buys has been the focus of economic policies since
the mid-80s. (b) infers far beyond what can be
reasonably inferred from the argument.
Ans .
b
Explanation :
In one day, A would do \( \frac{1}{3} \) of the job, B would do\( \frac{1}{4} \)of
the job and C would do \( \frac{1}{6} \)of the job.
Hence, if all three of them work simultaneously, in one
day they would do( \( \frac{1}{3} \) + \( \frac{1}{4} \) + \( \frac{1}{6} \)) = \( \frac{3}{4} \)of the job.
Hence, to complete the entire job together they would
take \( \frac{4}{3} \)days
Ans .
c
Explanation :
If n^3 is odd, then n should also be odd. Hence, n^2
should also be odd, not even. So only I and II are true.
Ans .
paste_right_option
Explanation :
We can see that there are two types of cost: (i)
Transportation cost (viz. hiring truck) and (ii) storing
cost. It can be seen that the daily production is far
less than the capacity of the truck. So a truck can be
hired to carry multiple days production at one go. So
as long as the storing cost is less than the cost of
hiring the truck (i.e. Rs. 1,000), it makes sense to
store the production. When the storing cost exceeds
Rs. 1,000, it is best that the entire lot be sent to the
market. The cost pattern is as given in the following
table:
* In spite of the fact that storing is cheaper than hiring
truck on the last day, we have to do with the latter
option because everything that is manufactured has
to be sent to the market.
So according to this table, if the truck is hired on 2nd,
4th, 6th and 7th days, total cost = Rs. 6,150. But is this
the most cost-effective scheme? It can be seen that
we are hiring truck on two consecutive days (6th and
7th). Hence, since everything that is manufactured
has to be sent to the market, we have yet another
option of hiring the truck on the 5th day and sending
the 6th and 7th days production together on the last
day. In that case, the cost on 5th day would be Rs.
1,000 (i.e. Rs. 200 more than the present cost), the
cost on the 6th day would be (120 × 5) = Rs. 600 (i.e.
Rs. 400 less than the present cost) and the cost on
the 7th day would be Rs. 1,000 (the same as the
present cost). Hence, we can say that the total cost
would actually come down by (+200 – 400 = – 200)
Rs. 200.
Hence, this becomes the most cost-effective scheme.
So we should hire trucks on 2nd, 4th, 5th and 7th
days.
Ans .
b
Explanation :
If the storage cost is reduced to Re. 0.8 per cubic
feet, then the cost pattern is as given in the following table.
** In spite of the fact that storing is cheaper than hiring
truck on the last day, we have to do with the latter
option because everything that is manufactured has
to be sent to the market.
Hence, the most cost-effective scheme would be
sending the entire production on the 7th day.
Ans .
a
Explanation :
Let there be x bacteria in the first generation i.e. n1 = x.
∴n2 = 8x, but only 50% survives
⇒ n_2,survived = \( \frac{8x}{2} \)= 4x
n3 = 8(4x), but only 50% survives
n_3,survived = 4^2 x
Similarly,
n_7survived = 4^7–1 x = 4096 million
∴ x = 1 million.
Ans .
c
Explanation :
PQ = PE + FQ – FE
= Radius of circle 1 + Radius of circle 2 – FE
= 20 + 20 – 12 = 28
Similarly, QR = 20 + 20 – CD = 40 – 10 = 30
and PR = 20 + 20 – AB = 40 – 5 = 35
So perimeter of ΔPQR = 28 + 30 + 35 = 93
Ans .
c
Explanation :
Since both 2 and 1 are positive, (2 # 1) = 2 + 1 = 3.
(1∇2)= (1× 2)^1+2 = 2^3 = 8.
Thus, the given expression is equal to \( \frac{3}{8} \)
Ans .
a
Explanation :
Let us first simplify the numerator. Since 1 is positive,
(1 # 1) is 1 + 1 = 2 which again is positive. Then
(1 # 1) # 2 = 2 # 2 = 2 + 2 = 4
Now note that log_10 0.1
= log_10 10^–1 = –1
Then 10^1.3 log_10 0.1= 10^1.3 × (–1) is negative.
So 10^1.3 ∇ log_10 0.1 = 1
Hence, the numerator is equal to 4 –1 = 3
Since 1 × 2 = 2 is positive, (1∇2)= (1× 2)^1+2 = 2^3 = 8.
So the denominator = 8. Hence, the answer is \( \frac{3}{8} \)
Ans .
b
Explanation :
The best possible way to solve this is to check each
of the given answer choices. In options (a), (c) and
(d), either both X and Y are positive or both X and Y
are negative. Since we have (–Y) in the numerator of
our expression and (–X) in the denominator, X and Y
will never be both positive and neither will XY be
positive. Hence, both the numerator and the
denominator of our expression will be 1 and the value
will always be 1. Hence, the only possible answer
choice is (b).
Ans .
b
Explanation :
Since MPB is a three-digit number, and also the square
of a two-digit number, it can have a maximum value of
961 viz. 312. This means that the number BE should be
less than or equal to 31. ⇒ B can be 0, 1, 2 or 3.
Since the last digit of MPB is also B, it can only be 0 or
1 (as none of the squares end in 2 or 3). The only
squares that end in 0 are 100, 400 and 900. But for
this to occur the last digit of BE also has to be 0. Since
E and B are distinct integers, both of them cannot be 0.
Hence, B has to be 1. BE can be a number between 11
and 19 (as we have also ruled out 10), with its square
also ending in 1.
Hence, the number BE can only be 11 or 19. 112 = 121.
This is not possible as this will mean that M is also
equal to 1. Hence, our actual number is 192 = 361.
Hence, M = 3.
Ans .
c
Explanation :
The maximum and the minimum five-digit numbers that
can be formed using only 0, 1, 2, 3, 4 exactly once are
43210 and 10234 respectively. The difference
between them is 43210 – 10234 = 32976.
Ans .
b
Explanation :
Case (i): t = 1
u can be 2, 3, 4, 5 ⇒ 4 possibilities
So total possible number that can be formed
= 4 × 3 × 2 × 1
Case (ii): t = 2
u can be 3, 4, 5 ⇒ 3 possibilities
So total possible number that can be formed
= 3 × 3 × 2 × 1
Case (iii): t = 3
u can be 4, 5 ⇒ 2 possibilities
So total possible number that can be formed
= 2 × 3 × 2 × 1
Case (iv): t = 4
u can be 5 ⇒ 1 possibility
So total possible number that can be formed
= 1 × 3 × 2 × 1
Hence, total possible number = (4 + 3 + 2 + 1) 3 = 60
Ans .
d
Explanation :
Since A and B are moving in opposite directions, we
will add their speeds to calculate the effective speeds.
In other words, in the first hour they would effectively
cover a distance of (4 + 2) = 6 km towards each other.
In the second hours, they would effectively cover a
distance of (4 + 2.5) = 6.5 km towards each other.
In the third hour, (4 + 3) = 7 km.
In the fourth hour, (4 + 3.5) = 7.5 km and so on.
We can see that the distances that they cover in each
hour are in AP, viz. 6, 6.5, 7, 7.5, ... with a = 6 and d =
0.5. Since they have to effectively cover a distance of
72 km, the time taken to cover this much distance
would be the time taken to meet each other. So the
sum of the first n terms of our AP has to be 72.
If we are to express this in our equation of sum of first
n terms of the AP, we will get Sn =n/2 × [2a + (n – 1)d].
Substituting our values, we will get
72 =n/2 × [12 + 0.5(n – 1)]
Solving this, we get n = 9 hr. In 9 hr A would have
covered (9 × 4) = 36 km.
So B would also have covered (72 – 36) = 36 km.
Hence, they would meet mid-way between A and B.
Ans .
a
Explanation :
If P is true, then both Q and R have to be true. For S to
be true, either Q or R must be false. Hence, if P is true,
S cannot be true.
Ans .
d
Explanation :
It can be seen that if the length of the rope is 8 m, then
the cow will be able to graze an area equal to (the area of the circle with radius 8m) – (Area of the sector of the same circle with angle 30°)= π(8)^2 - 30/360 π(8)^2
= 64π - 1/12 (64π) = 64π (11/12)- (176π/12)sq.m Shortcut:
Area grazed without restriction is 64π m2 it should
be less than 64π sq.m. with restriction. So the correct
choice is (d).
Ans .
a
Explanation :
If the length of the rope is 12 m, then the total area that
can be grazed by the cow is as depicted in the diagram.
Area 1 is (the area of the circle with radius 12) –
(Area of the sector of the same circle with angle 30º).
So area 1 = π (12)^2 - 30/360π (12)^2 = 132 π sq.m.
Since the length of the rope is higher than the sides of
the triangle (viz. AB and AC), if the cow reaches point
B or C, there would still be a part of the rope (12 – 10)
= 2 m in length. With this extra length available the cow
can further graze an area equivalent to some part of
the circle with radius = 2 m from both points, i.e. B and
C. This is depicted as area 2 and area 3 in the diagram.
Hence, the actual area grazed will be slightly more
than 132π . The only answer choice that supports
this is (a).
Ans .
a
Explanation :
Since C and D cannot be together, they can occupy
either of the following seats: (1st and 3rd), (1st and
4th) or (2nd and 4th). In the last two cases, since B
cannot be in the 3rd place, A will have to be there.
Thus, we can see that A can never be in the 1st place.
Hence, statement (a) is false.
Ans .
c
Explanation :
Since neither A nor B can be at 3rd place, this place
has to be occupied by either D or C. And if either of
them occupies this place, the other one has to occupy
the 1st place (since D and C cannot be together).
Hence, C can only occupy either 1st or 3rd place.
Ans .
b
Explanation :
If A and B are together, but C and D are not, then the
only places that A and B can occupy are 2nd and 3rd.
And since B cannot be at 3rd place, A has to be at 3rd
place..
Ans .
a
Explanation :
Let the cost of the turban be T.
Total payment for one year = Rs. 90 + T. So the payment
for 9 months should be Rs.3/4 (90 + T). But this is equal
to (65 + T). Equating the two, we get T = Rs. 10.
Ans .
c
Explanation :
Let R be the radius of each circle. Then πR^2/2πR =2πR/πR^2
which implies that R/2 = 2/R = , i.e. R^2 = 4, i.e. R = 2.
Then the length of the square is 8. Thus, the area of
the square is 64, while the area covered by each coin
is π × 22 = 4π. Since there are four coins, the area
covered by coins is 4(4π ) = 16π.
Hence, the area not covered by the coins is 64 – 16π= 16(4 – π ).
Ans .
*
Explanation :
The time taken by the red spots on all three wheels to
simultaneously touch the ground again will be equal to
the LCM of the times taken by the three wheels to
complete one revolution. The first wheel completes
60 revolutions per minute i.e., to complete one revolution, it takes (60/60)=1sec The second wheel completes 36 revolutions per
minute i.e., to complete one revolution, it takes (60/36) = (5/2) sec to complete one revoltion.=
Ans .
a
Explanation :
Since 899 is divisible by 29, so you can directly divide
the remainder of 63 by 29, so 63/29 will give 5 as a remainder, option (a).
Ans .
b
Explanation :
Note that the difference between the divisors and the
remainders is constant.
2 – 1 = 3 – 2 = 4 – 3 = 5 – 4 = 6 – 5 = 1
In such a case, the required number will always be
[a multiple of LCM of (2, 3, 4, 5, 6) – (The constant
difference)].
LCM of (2, 3, 4, 5, 6) = 60
Hence, the required number will be 60n – 1.
Thus, we can see that the smallest such number is
(60 × 1) – 1 = 59
The second smallest is (60 × 2) – 1 = 119
So between 1 and 100, there is only one such number,
viz. 59.
Ans .
a
Explanation :
For, if any one of them collects the maximum number
of coins, the remaining three should collect the
minimum number of coins. To have distinct, even, atleast
10 coins; they will have to collect 10, 12, 14 coins. So
if the three of them collect (10 + 12 + 14) = 36 coins,
the fourth one has to collect (100 – 36) = 64 coins
which has to be the maximum by any one person.
Ans .
c
Explanation :
Since A has collected 54 coins out of 100, he should
obviously be the person who collected the maximum
number of coins. For the difference between him and
the second highest person to be minimum, the second
highest person should collect the maximum number of
coins possible under the given conditions. And for
this to happen, the remaining two should collect the
minimum number of coins. So if the two of them collect
10 and 12 coins, i.e. 22 coins between themselves,
the third person would have to collect (100 – 54 – 22)
= 24 coins. Hence, the difference between him and
the highest person should at least be (54 – 24) = 30.
Ans .
d
Explanation :
If A has collected 54 coins, the remaining three of
them should collect (100 – 54) = 46 coins between
themselves.
Let us assume that C has collected 10 coins. So B will
collect (2 × 10) + 2 = 22. So A will collect (46 – 10 – 22)
= 14 coins, which is a possible combination.
Let us now assume that C picks up 12 coins. So B
should pick up (2 × 12) + 2 = 26. So A will have to
collect (46 – 12 – 26) = 8 coins.
This combination is not possible. It can be concluded
that C cannot pick up more than 10 coins and hence B
has to pick up 22 coins to satisfy the given condition.
Ans .
a
Explanation :
Amar does not wear red shirt.
Akbar does not wear green shirt.
Anthony does not wear blue shirt.
Since Akbar and Anthony wear same colour, it can
neither be green nor blue.
Hence, option (a) is false.
Ans .
b
Explanation :
If two of them wear the same colour, the following six
combinations will exist: since Amar does not wear
red, he can either wear blue or green. In either case,
the remaining two will have to wear red, Akbar does
not wear green, and Anthony does not wear blue.
This gives the combinations 1 and 2 below. Similarly,
the other combinations can be worked out.
Using this we can evaluate the statements. (I) is true
as we can see that in all the cases, if Amar wears
blue, Akbar does not wear green. (II) needs not be
false always, as in combination 4, we can see that
Amar does not wear blue but Akbar wears blue. (III) is
also not necessarily false as in combinations 1 and 3,
both Amar and Akbar do not wear blue. Statement (IV)
is necessarily false since if Amar wears green and
Akbar does not wear red, then combination 4 is the
only combination possible and hence Anthony should
wear green. So only one of the four statements must
always be false.
Ans .
d
Explanation :
HCF of 60, 84 and 108 is 12. Hence, 12 students
should be seated in each room. So for subject A we
would require \( \frac{60}{12} \) = 5 rooms, for subject B we
would require \( \frac{84}{12} \) = 7 rooms and for subject C we
would require \( \frac{84}{12} \) = 9 rooms. Hence, minimum
number of rooms required to satisfy our condition
= 5 + 7 + 9 = 21 rooms.
Ans .
c
Explanation :
Let us find some of the smaller multiples of 125. They
are 125, 250, 375, 500, 625, 750, 875, 1000, ...
A five-digit number is divisible by 125, if the last three
digits are divisible by 125. So the possibilities are 375
and 875, 5 should come in unit’s place, and 7 should
come in ten’s place. Thousand’s place should contain
3 or 8. We can do it in 2! ways. Remaining first two
digits, we can arrange in 2! ways. So we can have 2!
× 2! = 4 such numbers.
There are: 23875, 32875, 28375, 82375.
Ans .
b
Explanation :
To maximise the value of the wealth, we must carry
more of the one whose value per kilogram is more.
Value per kilogram of ruby = \( \frac{4}{0.3} \) = Rs. 13.33 crore,
and value per rupee of each emerald
= \( \frac{5}{0.4} \) = Rs. 12.5 crore.
It is obvious that we should carry entire 12 kg of ruby.
This would amount to \( \frac{12}{0.3} \) = 40 rubies.
Ans .
d
Explanation :
Since the number of coins are in the ratio 2.5 : 3 : 4,
the values of the coins will be in the ratio
(1 × 2.5) : (0.5 × 3) : (0.25 × 4)
= 2.5 : 1.5 : 1 or 5 : 3 : 2
Since they totally amount to Rs. 210, if the value of
each type of coins are assumed to be 5x, 3x and 2x,
the average value per coin will be \( \frac{210}{10x} \)
So the total value of one-rupee coins will be
5 = \( \frac{210}{10x} \)= Rs. 105
So the total number of one-rupee coins will be 105.
Ans .
a
Explanation :
Let the number of chocolates be c.
Number of apples has to be more than 3c, lets say
3c + k, k is a positive integer.
Total spend = 8c + 2k
for c = 4, k = 2
Total spend = 34
Hence, (a) is the answer.
The cost of each chocolate is Re. 1. So the cost of
apple should be Rs. 2 and that of one biscuit should be
Re. 0.5. Thus, if he eats x chocolates, he has to eat 2x
biscuits. Hence, the total value of chocolates will be
Rs. x and that of biscuits will be (0.5)(2x) = Rs. x.
Hence, we see that the value of chocolates is to the
value of biscuits will always be 1 : 1. As per our
assumption he will have to eat more than (x + 2x) = 3x
apples and hence the total value of the apples will be
more than (2)(3x) = 6x. In other words, the ratio of
value chocolates to apples or biscuits to apples will
be more than 1 : 6. In other words, if the value of
chocolates and biscuits is Re. 1 each, then the value
of apples has to be more than Rs. 6, or the combined
value will be more than Rs. 8. This means that the
value of apples will always constitute more than \( \frac{6}{8} \) or
\( \frac{3}{4} \)of the entire bill. It can further be observed that the
total value of chocolates and biscuits together will
always be an even integer and so will be the value of
apples. This means that the combined value of all three
of them has to be even and not odd. So Rs. 33 cannot
be the answer. Also Rs. 8 cannot be the answer as, if
we take the value of chocolates and biscuits to be
minimum, i.e. Re. 1 each, then the value of apples can
be a minimum of Rs. 8. Hence, the total value will
always be Rs. 10 or higher. The only option possible is
Rs. 34. To verify this let us find two even numbers
(one of them higher than \( \frac{3}{4} \)of 34) which adds 34.
We can find many such numbers E.g. 32 + 2, 30 + 4,
28 + 6 and 26 + 8. All of these could be a possible
combination.
For questions 85 and 86:
Let CP = 100
Current gain = 20
⇒ SP = 120
CP = Cost of A + Cost of B + Other
= 30% + 50% + 20%
Ans .
a
Explanation :
Since cost of German mark (A) increase by 30%
New cost of A = 30 + 30% of 30 = 39
Similarly,
New cost of B = 50 + 22% of 50 = 61
New CP = 39 + 61 + 20 = 120
New SP = 120 + 10% of 120 = 132
Maximum profit = \( \frac{12}{120} \) = 10%
Ans .
b
Explanation :
New cost of A = 30 + 20% of 30 = 36
New cost of B = 50 – 12% of 50 = 44
New CP = 36 = 44 + 20 = 100
Gain = 20%.
Ans .
b
Explanation :
For questions 87 to 90:
Ms Maharashtra was wearing white. Since Ms West Bengal
was not the runner-up, she was not wearing green and neither
was Ms Andhra Pradesh. Hence, it was Ms Uttar Pradesh
who was wearing green saree. So red could have either be
worn by Ms West Bengal or by Ms Andhra Pradesh. Now
participants wearing yellow saree and white saree were at
the ends, but Ms West Bengal did not occupy any of these
positions. Hence, it can be concluded that Ms Andhra Pradesh
sat at one of the ends and wore yellow, while Ms West Bengal
wore red.
Ans .
c
Explanation :
Ans .
a
Explanation :
Ans .
c
Explanation :
Since the runner-up was wearing the green saree.
Hence, Ms UP was runner up.
Ans .
c
Explanation :
Since the distance travelled was the same both ways
and also it was covered in the same time, the average
speed will be the same uphill and downhill. Hence,
statement (a) is false. Statement (b) need not be true.
It would be true and had the speeds (and not average
speed) been the same both ways. But it is clearly
indicated that he varied his pace throughout. Now it
has to be noted that the journey uphill and the journey
downhill started at the same time, i.e. 6 a.m. and also
ended at the same time 6 p.m. (though on different
days). So if we were to assume a hypothetical case
in which one person starts downhill at 6 a.m. and
other one starts uphill at 6 a.m., along the same path,
then there would be a point on the path where they
would meet (i.e. they would reach at the same time),
irrespective of their speeds. Our case is similar to
that, except for the fact that here, we have only one
person moving both ways. So there has to be a point
on the path, where he reached at the same time on
both days.
Ans .
b
Explanation :
Since 2 has a cyclicity of 4,
i.e. 2^1 = 2, 2^2 = 4, 2^3 = 8, 2^4 = 16, 2^5 = 32, 2^6 = 64, ..., the
last digits (2, 4, 8, 6) are in four cycles.
∴ On dividing \( \frac{51}{4} \), we get the remainder as 3.
∴ The last digit has to be 2^3 = 8
Ans .
c
Explanation :
Let the capacity of each cup be 100 ml. So 300 ml of
alcohol is taken out from the first container and poured
into the second one. So the first vessel will have
200 ml of alcohol and the second one will have 500 ml
of water and 300 ml of alcohol. So the ratio of water
to alcohol in the second vessel is 5 : 3.
Hence, proportion of alcohol in B = 3 : 8
Now if 300 ml of mixture is removed from the second
container, it will have 300 X \( \frac{5}{8} \) = 187.5 ml of water
and 300 X \( \frac{5}{8} \) = 112.5 ml of alcohol. Now if this mixture
is poured in the second vessel, that vessel would
have (200 + 112.5) = 312.5 ml of alcohol and 187.5 ml
of water. Hence, ratio of alcohol to water in this
container = 312.5 : 187.5 = 5 : 3
Hence, proportion of water = A = 3 : 8
Hence, we find that A = B
Note: This result will be independent of the capacity
of the cup.
Ans .
c
Explanation :
The number formed by the last 3 digits of the main
number is 354. The remainder is 2 if we divide 354 by
8. So the remainder of the main number is also 2 if we
divide it by 8.
Ans .
a
Explanation :
It can be seen that each of the 26 players played 25
matches. Since none of the matches ended in a draw,
the scores for each of the players has to be even
(since a win gives 2 points). So the highest score
possible for a player would be 50 and the lowest
would be 0. Since all 26 of them had different scores
varying between 0 and 50, the scores should indeed
be all the even numbers between 0 and 50. And since
the ranks obtained by players are in alphabetical
order, it can be concluded that A scored 50, B scored
48, C scored 46 and so on and Z scored 0. Now the
only way A can score 50 is, if he wins all his matches,
i.e. he defeats all other players. Now B has scored
48. So he has lost only one of his matches, which
incidentally is against A. He must have defeated all
other players. Similarly, C has scored 46 matches. So
he must have lost two matches, (i.e. to A and B) and
defeated all other players. So we conclude that a
player whose name appears alphabetically higher up
in the order has defeated all the players whose name
appear alphabetically lower down.
Hence, M should win over N.
Ans .
b
Explanation :
The Nehru-Gandhi ideologies led to the formation of
the idea of India that inspired the writer's generation.
This answer is given in the tenth paragraph. Don’t be
misled by (c); the writer mentions ‘formative ideas’,
not ‘formative years’. (a) and (d) are again imprecise
answers.
Ans .
c
Explanation :
The writer agrees that the 50th anniversary is a great
moment, but does not share Naipaul's conclusions
about it. Refer to the tenth paragraph. Hence, (a), (b)
and (d) are not correct.
Ans .
b
Explanation :
The writer believes that India will come back and does
not feel that India's loss is forever. Refer to the last
paragraph. (a), (c) and (d) are inaccurate
observations.
Ans .
c
Explanation :
The writer feels that the politicians incite the general
public to demonstrate against writers and also that it
does not reflect the people's will. Refer to the
penultimate paragraph.
Ans .
a
Explanation :
Whatever he says about India is based on his
experience, as is shown by the last line of the
passage. There is insufficient evidence in the passage
to support (b), (c) and (d) as the answer.
Ans .
c
Explanation :
The writer's friend says that we can move beyond
things only after we know we are capable of those
things. The answer is given vividly in the sixth
paragraph. (a) and (b) are not mentioned in the
passage. (d) is not an exact representation of the
writer’s views.
Ans .
d
Explanation :
The passage states that the civilizing influence
prevents us from giving in to violent, terrible urges. (d)
is again stated explicitly in the sixth paragraph. (a),
(b) and (c) may be partially true.
Ans .
b
Explanation :
The writer fears the long-term damage to democracy
that the corruption can bring about, as it is a subversion
of democracy, and says that it will harm India too as
corruption is everywhere in India. The answer is given
in the seventh paragraph. Hence, (a) and (c) are
imperfect answers.
Ans .
b
Explanation :
The writer says that no one is an objective observer.
The answer is given in the eighth paragraph. Hence,
(a), (c) and (d) are imperfect answers.
Ans .
a
Explanation :
The writer says that there never had been a political
entity called India prior to 1947. (a) is the best
representation of the writer’s views. (b), (c) and (d)
do not give the exact picture.
Ans .
d
Explanation :
The writer feels that the difference lies in the fact that
Pakistan was under-imagined. The answer is given in
the second paragraph. (a), (b) and (c) are not
substantiated by the passage.
Ans .
d
Explanation :
The writer feels that the strength of the nationalist
idea is shown by its ability to survive great stress that
it is placed under and in the sense of belonging that
the people feel for it. Refer to the third paragraph. (b)
has not been stated in the passage.
Ans .
a
Explanation :
The writer says that if Western civilisation is in a state
of a permanent crisis, something is wrong with its
education. The opening statement confirms (a). There
is insufficient
Ans .
c
Explanation :
Lord Snow seems to see the intellectual life of the
Western society as split between scientists and
literary intellectuals. The answer is given in the second
paragraph. (a), (b) and (d) are not stated in the
passage.
Ans .
b
Explanation :
The writer does not agree that education can help in
tackling all new problems and complexities. The
answer is given in the penultimate paragraph. The
views expressed in (a) and (c) find no mention in the
passage.
Ans .
b
Explanation :
He defines prejudice as fixed ideas with which people
think, without being aware of doing so. Refer to the
ninth paragraph. (a), (c) and (d) are imprecise
definitions of prejudice.
Ans .
a
Explanation :
Lord Snow says that the politicians, administrators
and the entire community needs to be educated to
understand the works of scientists and engineers.
Refer to the second paragraph. (b) and (c) are partially
correct answers.
Ans .
c
Explanation :
The writer does not agree with the scientists' stand
on the neutrality of their labours. (c) can be amply
inferred from the third paragraph. (a), (b) and (d) are
imprecise answers.
Ans .
a
Explanation :
The author feels that the main purpose of education is
to transmit ideas of value. (a) is clearly given in the
fifth paragraph. (b) and (d) are not supported by the
passage.
Ans .
d
Explanation :
(a) is not stated anywhere in the passage. (b) and (c)
also find no explicit mention in the passage.
Ans .
b
Explanation :
The author says that values are more than mere
dogmatic assertions. Refer to paragraph 6, line 3. (a),
(c) and (d) are stated in the same paragraph.
Ans .
c
Explanation :
According to the passage, thinking is application of
pre-existing ideas to a situation. Refer to paragraph
10, line 2. In light of (c), it will be a folly to mark (a), (b)
or (d).
Ans .
b
Explanation :
The writer says that a large part of the American
population indulges in word trade. Refer to the second
paragraph. (a), (c) and (d) cannot be even remotely
inferred from the passage.
Ans .
b
Explanation :
The hallmark of gag writers is that they have fun with
words. Refer to paragraph 4, line 1. (a), (c) and (d)
are not stated in the passage.
Ans .
a
Explanation :
The second level of language is important if one wants
to be comfortable listening and reading. (a) is stated
in the third paragraph. (b) and (c) are not stated in the
passage.
Ans .
a
Explanation :
The writer says that the gag writers thrive on the
double layered aspect of the language. The middle
portion of the passage amply demonstrates (a). (b),
(c) and (d) may be isolated aspects of the trade.
Ans .
d
Explanation :
In gag writing, both, long words as well as combining
of parts of words to produce a hilarious effect are
important. (a) cannot be inferred from the passage.
(b) and (c) can be inferred from the fourth paragraph
as well as various examples in the passage.
Ans .
c
Explanation :
Gag writers simulate ignorance. The answer is given
in the fifth paragraph. (b) is an isolated observation
and (a) is not true.
Ans .
b
Explanation :
According to the passage, radio artistes have taken
advantage of the techniques of gag writers. (a) and
(c) are not mentioned in the passage.
Ans .
c
Explanation :
The theory has been suggested to be an attempt at
appeasing the religious psyche of that time by stating
that God indirectly created life. (c) is stated in the
second paragraph. (a) and (b) are misleading
answers.
Ans .
b
Explanation :
All four have been referred to as working or writing at
the same time. This is evident in the second paragraph.
(a) is only partially right. (c) is not true.
Ans .
b
Explanation :
Pasteur did not work on arbitrary or spontaneous
discoveries. He worked on logical premises. This is
evident in the fourth paragraph. (a) is certainly not
true, considerable differences of opinion existed even
then. (c) and (d) are nor true either.
Ans .
a
Explanation :
Pasteur based his work on the belief that either air
contained a factor necessary for the spontaneous
generation of life or viable germs were borne in by the
air and seeded in the sterile nutrient broth. (b) is only
an observation, not the hypothesis. (a) is stated in the
fourth paragraph.
Ans .
b
Explanation :
The well water of Montanvert led to the discovery of
the porcelain filters. (a) is nowhere stated in the
paragraph. (b) is clear from the fourth paragraph.
Ans .
c
Explanation :
Pasteur declared that his experiments had dealt a
mortal blow to the spontaneous generation doctrine.
The conclusion of the fifth paragraph makes (c) a
clear choice. (a), (b) and (d) are rather extreme.
Ans .
b
Explanation :
The writer feels that the works of the proponents of
spontaneous generation was ruined by experimental
errors. (b) is mentioned in the seventh paragraph. (a)
is clearly not true.
Ans .
a
Explanation :
This cross fire ruled out the possibility of partial
sterilisation. (b) is clear from the penultimate
paragraph. (b) is not directly stated in the passage
and (c) sounds vague.
Ans .
b
Explanation :
Pasteur’s experiments supported the Biblical version
of creation of life, but denied many other philosophical
systems. (b) is explicitly given in the fifth paragraph.
Given (b), the other choices (a), (c) and (d) seem
extreme.
Ans .
d
Explanation :
The author says that the cell theory represents
biology's most significant and fruitful advance. Refer
last paragraph, line 1. (a) is thus wrong and (b) and
(c) are not supported by the passage.
Ans .
c
Explanation :
Rs. 85,000 crore has been entrusted to the care of
mutual funds. (c) is stated in the second paragraph..
Ans .
c
Explanation :
The individual investors led the move for the end of
mutual funds. Refer to the first paragraph. (a), (b) and
(d) are wrong choices.
Ans .
b
Explanation :
The mutual funds were flawed in their imprudent and
irresponsible handling. Refer to the end of the first
paragraph. (a) and (c) are not valid reasons.
Ans .
a
Explanation :
The indisciplined attitude of the mutual funds in their
approach to investment led to their fall. Refer to the
second paragraph. The claims in (b), (c) and (d) are
not completely substantiated by the passage.
Ans .
a
Explanation :
The passage states that at least 18 of the big schemes
due for redemption over the next 3 years will be unable
to service their investors. Refer to the fourth
paragraph. (b) plays with words ‘only very few’ and
(c) is not correct.
Ans .
b
Explanation :
The passage shows the facts that lead to the inference
that many of the mutual funds offices indulged in
malpractices. Refer to the fifth and sixth paragraphs.
(a), (c) and (d) are not stated in the passage.
Ans .
c
Explanation :
Mutual fund industry ranks fourth on safety and fifth
in terms of returns on deposits. Refer to the seventh
paragraph. (a), (b) and (d) are thus wrong.
Ans .
a
Explanation :
More cellphones were subscribed as calls made on
them could not be lodged in the company records.
Refer to the fifth and sixth paragraphs. (b), (c) and (d)
are not stated in the passage.
Ans .
b
Explanation :
Mutual funds have caused a loss of Rs. 11,000 crore
of the investors' money. Refer to the tenth paragraph.
(a), (c) and (d) are wrong.
Ans .
a
Explanation :
Investors have the option of either exiting at a loss or
holding on in vain hope. Refer to the eleventh paragraph.
(b), (c) and (d) are not very perfect choices.
Ans .
a
Explanation :
The stock market boom in the late eighties and early
nineties led to the initial euphoria in the mutual funds
industry. Refer to the passage from the twelfth
paragraph onwards. (b) is clearly not true.
Ans .
a
Explanation :
If we were to take the highest quantity supplied from
various states in different months, we will get the
following table:
Hence, we find that the highest percentage of apples
supplied by any state is 99% (J & K in February).
Ans .
c
Explanation :
If we were to add the quantity of apples supplied by
various states, it can be found that HP supplied
2,31,028 tonnes, UP supplied 258 tonnes, and J & K
supplied 2,62,735 tonnes. Thus, it was J & K that
supplied the maximum number of apples.
Ans .
c
Explanation :
If J & K supplied the highest quantity of apples, it is
obvious that it would supply the highest percentage
of total apples supplied as well.
Ans .
c
Explanation :
It is given that in case demand is more than the supply,
additional demand is met by taking the stock from the
cold storage. So it can be figured out that in all those
months when supply was greater than the demand,
no stock would have been used from the cold storage.
Looking at the table, we can find that during the period
May to September, no stock was taken from the cold
storage, and hence supply should have been greater
than the demand.
Ans .
b
Explanation :
Total quantity of apples supplied to Delhi during the
year was (231028 + 258 + 262735)
= 494021 tonnes = 494021000 kg
If one tree yields 40 kg of apple, then the number of
trees required to yield 49,40,21,000 kg
=\( \frac{494021000}{40} \) = 1,23,50,525 trees
= 12.5 million trees (approximately)
Ans .
d
Explanation :
If there are 250 trees per hectare, then area required
to have 12350525 = \( \frac{12350525}{250} \) = 49402 = 49450 (approximately)
Ans .
b
Explanation :
It can be seen from the graph that the southern region
showed the highest growth in number of households
in all the income categories for the period.
Ans .
d
Explanation :
We only know the total number of households for all
four regions combined. Nowhere have they given the
region-wise break-up of this value. In the light of this,
the given question cannot be answered.
Ans .
b
Explanation :
It is very clear from the graph that the percentage
increase in total number of households for the northern
region for upper middle income category is 200%.
Ans .
a
Explanation :
As seen from the table, the average income of highincome
group in 1987-88 is Rs. 75,000.
Ans .
b
Explanation :
The total income of high income category in 1987-88 is
Rs. (5000 × 75000).
The total income of upper-middle class category in
1987-88 is Rs. (10000 × 50000).
Hence, the current ratio of their total incomes
= 3 : 4 = 0.75
Since the number of households in each category
were equally distributed in all regions, we can have
the following table for high income category.
The average household income for high-income
category increased by 90%. Hence, average
household income for this category in 1994-95
= (75000 × 1.9) = Rs. 1,42,500
Hence, the total income for high-income category in
1994-95 = (17375 × 142500) = Rs. 2,476 million
The same table can be drawn for upper-middle class
category as follows:
The average household income for upper-middle class
category increased by 60%. Hence, the average
household income for this category in 1994-95
= (50000 ×1.6) = Rs. 80,000
Hence, the total income for high-income category in
1994-95 = (30125 × 80000) = Rs. 2,410 million
Hence, the ratio of total income for these two
categories in 1994-95 = \( \frac{2476}{2410} \)= 1.02.
Hence, percentage increase in ratio
\( \frac{1.02 − 0.75}{0.75} \)= 36%
Ans .
a
Explanation :
For northern region, we can draw the following table
for 1987-88.
Hence, the average income for northern region
\( \frac{518.75}{13750} \)× 10^6 = Rs. 37,727
Ans .
b
Explanation :
It is said that Gopal and Ram invested equal amounts
initially. Let the amount paid by both of them to Krishna
be 2x and 3x respectively. Gopal further invested
Rs. 2 lakh. Hence, we can say (2x + 2) = 3x or x = 2
lakh. Hence, the initial amounts paid by Gopal and
Ram to Krishna is 4 lakh and 6 lakh. So Gopal and Ram
together put in (6 + 6) = 12 lakh initially (note that this
includes Rs. 2 lakh put in by Gopal later). The total
revenue generated is 25% of 12 lakh = 3 lakh.
The revenue from coconut and lemon trees are in the
ratio 3 : 2. Hence, 3 lakh when divided in the ratio
3 : 2 gives Rs. 1,80,000 from coconut and Rs. 1,20,000
from lemons. And since each coconut costs Rs. 5,
the total output of coconut would be
\( \frac{18000}{5} \)= 36000
Ans .
a
Explanation :
Lemon and coconut trees were planted on equal
areas of land, viz. 5 acres each. The value of lemon
output per acre of land =\( \frac{120000}{5} \)= 0.24 lakh per
acre.
Ans .
a
Explanation :
The total revenue of Rs. 3,00,000 was divided equally
by Gopal and Ram. Hence, the amount received by
Gopal in 1997 =\( \frac{1}{2} \) × = Rs. 1.5 lakh
Ans .
b
Explanation :
The ratio of the number of trees of coconut and lemon
was 5 : 1. Since the number of lemon trees is 100, the
number of coconut trees is 500. So they totally
obtained a revenue of Rs. 1,80,000 from 500 coconut
trees.
Hence, the value per tree =\( \frac{180000}{500} \)= Rs. 360.
Ans .
d
Explanation :
We have not been given the cost of one lemon. In the
light of this fact, we cannot find the number of lemons
produced and hence the required ratio cannot be
determined.
Ans .
b
Explanation :
Profit = Revenue – Variable Cost – Fixed Cost
= Revenue – (Variable Cost + Fixed Cost). If we
consider (Fixed Cost + Variable cost) as total cost,
then as long as the revenue is higher than the total
cost, there is a profit. In case the revenue is less than
the total cost there would be a loss. If we are to
compile the data given in the question it would be as
follows:
Thus, we can say that at a production of 12 units,
there is a profit of Rs. 2. Above 12 units there is
always a profit and below 12 units there is loss.
Hence, to make sure there is no loss, one has to
manufacture a minimum of 12 units.
* The answer is clearly not indeterminable, it should
be 12 units, but among the options given the one
closest to it is 10 units.
Ans .
a
Explanation :
It can be seen that at 20 units there is a profit of
Rs. 50. Below this the profit will reduce. Hence, to
ensure that the profit is at least Rs. 50, then 20 units
have to be manufactured.
Ans .
b
Explanation :
Let us verify for the given options.
Hence, we can see that to maximise profit per unit,
we need to manufacture 34 units.
Ans .
b
Explanation :
Extending the above table for 45 units, we get
Thus, it can be figured out that still he has to
manufacture 34 units.
Ans .
b
Explanation :
Referring to the table in question 163, we can see that
if the fixed cost increases by Rs. 40, the profit will
reduce by Rs. 40. Hence, we can see that at 10 units
he will make a loss of Rs. 30 and at 20 units he will
make a profit of Rs. 10. Hence, the answer has to be
between (b) and (c). Let us verify for them:
Thus, we see that to make sure there is no loss, he
has to manufacture 19 units.
Ans .
c
Explanation :
The data can be represented in the following table.
Thus, we can see that the maximum increase is 50%.
Ans .
b
Explanation :
Thus, we see that the maximum percentage increase
over the period is shown by plywood.
Ans .
b
Explanation :
Since the price of saw timber is given in rupees per
tonne and that of log is given in rupees per cubic
metre, we cannot compare the two. Hence, using the
given conversion, let us convert the price of saw
timber in per cubic metre. The table will be as follows:
Thus, we see that the difference is least in the year
1990.
Ans .
d
Explanation :
As in the previous table, we can draw a similar table
for saw timber and logs.
cubic m and one tonne of saw timber =5/4 cubic m = 1.25 cubic m.
Hence, it can be seen that the difference is maximum
for 1992.
Ans .
d
Explanation :
Note that one tonne = \( \frac{4}{3} \)m^2= 1.33 m^3, for both plywood
and saw timber.
In 1993, price of logs = Rs. 20 per cubic metre.
Price of plywood = \( \frac{7}{1.33} \)= Rs. 5.26 per cubic metre.
And price of saw timber = \( \frac{19}{1.33} \)= 14.28 per cubic meter
Now the sales volume of plywood, saw timber and
logs are in the ratio 4 : 3 : 3. So the average realisation
per cubic metre of sales is indeed the weighted
average.
This is given as
\( \frac{[(4 * 5.26) + (3 * 14.28) + (3 * 20)]}{4 + 3 + 3} \)
= Rs. 12.4
= Rs. 13 (Approximately)
Ans .
c
Explanation :
The only change would be the accounting for price
increase. This is given as
\( \frac{(4 * 5.26 * 1.05) + (3 * 14.28 * 1.01) + (3 * 20 * 1.10)}{(4 + 3 + 3)} \)
= Rs. 13.15
Ans .
d
Explanation :
Do not make the mistake of assuming O to be the
centre of the circle. Since the centre is not known,
knowing radius is not of great help. It can be observed
that ∠BCA is also 90° , as in the quadrilateral OBCA,
the remaining three angles are 90° . So the quadrilateral
can either be a square or a rectangle. As we do not
know even this, we cannot make use of the second
statement as well. Hence, both the statements are not
sufficient to answer the question.
Ans .
c
Explanation :
LCM of 3, 5, 7, 9 = 315. Hence, all the multiples of 315
will be divisible by 3, 5, 7 and 9. These may be even or
odd. Hence, the statement I in itself is not sufficient to
answer the question.
The statement II however suggests that the number is
315 itself (as it is the only multiple that lies between 0
and 400). Hence, n is indeed odd. We require both the
statements together to answer this.
Ans .
a
Explanation :
It is clear that statement II alone is enough to answer
the question. This statement gives the value of the
function a ⊗b, so we can find the value of 2X3 .
So 2X3 = \( \frac{(2 + 3}{2} \) = 2.5
Ans .
d
Explanation :
Even by using both the statements, we can only find
out the proportion of the paper solved by Radha and
Rani. In the light of the fact that the number of questions
solved by either or both of them is not given, we
cannot answer the question asked.
Ans .
c
Explanation :
From the statement II, we can frame the equation that:
(Cold drink) = 3(Tea) and (Coffee) = (Cold drink) – 5
= 3(Tea) – 5. So we have one equation in terms of
be sufficient to answer the question, in the light of the
equation provided by the first statement, viz. (Coffee)
= (Tea) + 5, we can solve the two equations
simultaneously and get the price of tea.
Ans .
d
Explanation :
Note that both the statements give the same piece of
information that a : b = 3 : 5 and that a and b are both
positive. But none of the statements either in itself or
together can give the value of a.
Ans .
a
Explanation :
Using the first statement alone, we can use the rule of
alligations and find the ratio of boys to girls and hence
the number of girls, i.e. as shown in the adjacent
diagram, 150 students when divided in the ratio 115 :
260, give 46 girls and 104 boys. The second statement,
however, does not throw any further light on the data
given in the question as it simply suggests 0.3B + 0.3G
= 45 or B + G = 150, which is already known. Hence,
only statement I is required to answer the question.
Ans .
a
Explanation :
The issue at hand is to make C2 identify in which
envelope is the letter L2. The first statement actually
tells him this. Hence, it alone is sufficient to answer
the question. The second statement only implies that
his letter would be in either E1, E2 or E4 and hence is not
sufficient to answer the question.
Ans .
a
Explanation :
From the question itself, we can figure out that book 4
can either be in rack 1 or rack 3. The first statement
says that book 2 has been kept in rack 3. Hence, book
4 has to be kept in rack 1. So this statement is sufficient
to answer the question. The second statement,
however, does not add any additional information to
what we already know. As books 3 in rack 2 would
still imply book 4 can be in rack 1 or 3.
Ans .
a
Explanation :
Statement II is not required at all as no way can we
express X in terms of 'a'.
Statement I implies that X + Y = 2a and XY = a2.
Solving these two, we can say that X = a.
Hence, statement I alone is sufficient to answer the
question.
Ans .
c
Explanation :
The information given in the question implies that
r1 > r2.
Statement I suggests that (r1 – r2) = \( \frac{k}{2π} \)
Hence, this statement alone does not give the value of
r1.
Statement II implies that (r1^2 – r2^2) = \( \frac{m}{π} \)
Hence, again this statement alone is not sufficient to
answer the question. But in the second equation, we
simplify (r1^2 – r2^2) as (r1 + r2)(r1 – r2) and then substitute
the value of (r1 – r2) from the first equation, we will get
the value of (r1 + r2). Now we have two equations in r1
and r2, which can be solved simultaneously to get the
value of r1. Hence, both the statements when together
taken can answer the question.
Ans .
b
Explanation :
Statement I itself is sufficient to answer the question.
As, if we know the radius of the circle we can find out
the length of the diagonal of the square (which will be
the diameter) and if we know the diagonal of a square
we can find the length of its sides and hence the area.
Again the second statement in itself can answer the
question. As, from the data that is given we can find
the radius of the circle and hence the area of the
square (as given before). This can be explained from
the diagram given. Since the tangent makes a right
angle with the radius at the circumference, the triangle
is a right-angled triangle. Hence, A2 = 52 + r2. Hence,
knowing the value of A, we can find out r. Hence, both
statements in itself can answer the question.
Therefore, the answer is (b).