The above formulae can be used for solving giant multiplication problems.
Sometimes we have to calculate the powers of very large numbers like 13^35 which looks impossible but the answer is quite simple .. Recognize the cycle.
Suppose we need to find last digit of 2^ ^{2012}
2^1 = 2
2^2= 4
2^3 = 8
2^4 = 16 = 6
2^ 5 = 32 = 2
2^ 6 = 64 =4
Hence there is a cycle of size 4 like 2-4-8-6-2-4-8-6... so all powers of 2 in multiples of 4 like 4,8,12,16... have last digit 6 since 2012 also satisfies this 2^2012 has last digit 6.
So generalizing for k > 4 if 2^^{k} = 2^^{(4n+1)} then last digit is 2, if 2^^{(4n+2)} = 4, 2^^{(4n+3)} = 8 , 2^^{(4n)} = 6.
Similarly we can solve for all digits:
For 3 cycle is: 3-9-7-1-3-9-7-1... here too the cycle is 4 and So generalizing for k > 4 if 3^^{k} = 3^^{(4n+1)} then last digit is 2, if 3^^{(4n+2)} = 4, 3^^{(4n+3)} = 8 , 3^^{(4n)} = 6.
For 4 cycle is: 4-6-4-6-4-6-... hence cycle is 2 So generalizing for k > 3 if 4^^{k} = 4^^{(2n+1)} then last digit is 6, if 4^^{(2n)} = 4.
Similarly we can obtain cycles for all digits till 9 any digit above this doesn't matter as 13^n is same as 3^n and 17^^{n} is same as 7^^{n} etc.
Dividend - Remainder = Divisor * Quotient.
Q. A number when divided by 342 gives a remainder 47 when the same number is divided by 19 what would be the remainder?
A.
Step 1: (number - 19) = 342 * k + 47 i.e. number = 19*18k + 19*2+9 = 19(18k+2)+9
if this number is divided by 19 then it gives 18k+2 as quotient and 9 as remainder.
Q. if f(x) = log (1+x/1-x) then f(x) + f(y) is
f(x + y)
$f\frac{x+y}{1+xy}$
$(x+y) f \frac{1}{1+xy}$
$\frac{f(x) + f(y)}{1+xy}$
Ans . B
$f(x) + f(y) = log \frac{1+x}{1-x}$ + $log \frac{1+y}{1-y}$
$log \frac{(1+x)(1+y)}{(1-x)(1-y)}$
$log \frac{(1+x+y+xy)}{(1-x-y+xy)}$
$log \frac{(1+x+y+xy)}{(1+xy-(x+y))}$
$log \frac{1+\frac{x+y}{1+xy}}{1-\frac{x+y}{1+xy}}$
$f \frac{x+y}{1+xy}$
Q. Number S is obtained by squaring the sum of digits of a two-digit number D. If difference between S and D is 27, then the two-digit number D is
24
54
34
45
Ans . B
check choices and only choice B satisfies the condition.
S = (5+4)^2 = 81
D – S = 81 – 54 = 27. Hence, the number = 54
Q. The nth element of a series is represented as $X_n = (-1)^n * X_{n-1}$ . If $X_0$ = x and x > 0, then which of the following is always true?
$X_n$ is positive if n is even
$X_n$ is positive if n is odd
$X_n$ is negative if n is even
None of these
Ans . D
$x_0 = x, x_1 = -x, x_2 = -x$
$x_3 = x, x_4 = x$
$x_5 = -x, x_6 = -x$
Choices (1), (2), (3) are incorrect.
Q. If x, y and z are real numbers such that x + y + z = 5 and xy + yz + zx = 3, what is the largest value that x can have?
5/3
√ 19
13/3
none
Ans . C
$xy + yz + zx = 3$
$xy + (y + x)z = 3 $
$xy + (y + x)(5 + x + y)= 3$
$xy + 5y+xy+y^2+5x+x^2+xy = 3$
As it is given that y is a real number, the discriminant for above equation must be greater than or equal to zero. $(x - 5)^2 - 4(x^2 - 5x + 3) \geq 0$
$3x^2 - 10x + 13 \geq 0$
$x = 1, \frac{13}{3}$
Largest value that x can have is $\frac{13}{3}$
Q. Neeraj has agreed to mow a lawn, which is a 20 m × 40 m rectangle. He mows it with 1 m wide strip. If Neeraj starts at one corner and mows around the lawn toward the centre, about how many times would he go round before he has mowed half the lawn?
2.5
3.5
3.8
4
Ans . C
Area = 40 * 20 = 800 $m^2$
If 3 rounds are done, area = 34 × 14 = 476 $m^2$ ⇒ Area > 3 rounds
if 4 rounds ⇒ Area left = 32 × 12 = 347 $m^2$
Hence, area should be slightly less than 4 rounds.
Q. The owner of a local jewellery store hired three watchmen to guard his diamonds, but a thief still got in and stole some diamonds. On the way out, the thief met each watchman, one at a time. To each he gave 1/2 of the diamonds he had then, and 2 more besides. He escaped with one diamond. How many did he steal originally?
40
36
25
None of these
Ans . B
Since thief escaped with 1 diamond
Before 3 rd watchman he had (1 + 2) × 2 = 6 diamonds.
Before 2 nd watchman he had (6 + 2) × 2 = 16 diamonds
Before 1 st watchman he had (16 + 2) × 2 = 36 diamonds.
Q. Mayank, Mirza, Little and Jaspal bought a motorbike for Rs.60. Mayank paid one-half of the sum of the amounts paid by the other boys. Mirza paid one-third of the sum of the amounts paid by the other boys. Little paid one-fourth of the sum of the amounts paid by the other boys. How much did Jaspal have to pay?
Rs.15
Rs.13
Rs.17
None of these
Ans . B
Mayank paid 1/2 of the sum paid by other three.
Mayank paid 1/3 rd of the total amount = Rs.20
Similarly, Mirza paid Rs.15 and Little paid Rs.12. Remaining amount of Rs.60 – Rs.20 – Rs.15 – Rs.12 = Rs.13 is paid by Jaspal
Q. A rich merchant had collected many gold coins. He did not want anybody to know about him. One day, his wife asked, " How many gold coins do we have?" After a brief pause, he replied, "Well! if I divide the coins into two unequal numbers, then 48 times the difference between the two numbers equals the difference between the squares of the two numbers." The wife looked puzzled. Can you help the merchant's wife in finding out how many gold coins the merchant has?
96
53
43
None of these
Ans . D
Let the number of gold coins = x + y
48(x – y) = x^{2} - y^{2}
48(x – y) = (x – y)(x + y) ⇒ x + y = 48
Hence, the correct choice will be none of these.
Q. A car rental agency has the following terms. If a car is rented for 5 hr or less, then, the charge is Rs. 60 per hour or Rs. 12 per kilometre whichever is more. On the other hand, if the car is rented for more than 5 hr, the charge is Rs. 50 per hour or Rs. 7.50 per kilometre whichever is more. Akil rented a car from this agency, drove it for 30 km and ended up playing Rs. 300. For how many hours did he rent the car?
4 hr
5 hr
6 hr
None of these
Ans . C
By trial and error:
30 × 12 = 360 > 300
30 × 7.5 = 225 < 300
50 × 6 = 300. Hence, he rented the car for 6 hr.
Q. The number of non-negative real roots of 2^{x} – x – 1 = 0 equals
0
1
2
3
Ans . C
2^{x} – x – 1 = 0 and so 2^{x} – 1 = x
If we put x = 0, then this is satisfied and if we put x = 1, then also this is satisfied.
Now, if we put x = 2, the equation this is not valid.
Q. When the curves y = log_{10}x , y=x^{-1} are drawn in the x-y plane, how many times do they intersect for values x ≥ 1 ?
Never
Once
Twice
More than twice
Ans . B
For the curves to intersect, log x = x
Thus log_{10}x = 1/x or x^{x}=10
This is possible for only one value of x such that 2 < x < 3.
Q. Which one of the following conditions must p, q and r satisfy so that the following system of linear
simultaneous equations has at least one solution, such that p + q + r ≠ 0?
x+ 2y – 3z = p
2x + 6y – 11z = q
x – 2y + 7z = r
5p –2q – r = 0
5p + 2q + r = 0
5p + 2q – r = 0
5p – 2q + r = 0
Ans . A
It is given that p+q+r≠0 , if we consider the first option, and multiply the first equation by 5, second by –2 and third by –1, we see that the coefficients of x, y and z all add up-to zero.
Thus, 5p – 2q – r = 0 No other option satisfies this.
Q. Let g(x) = max(5 – x, x + 2). The smallest possible value of g(x) is
4.0
4.5
1.5
None of the above
Ans . D
We can see that x + 2 is an increasing function and 5 – x is a decreasing function. This system of equation will have smallest value at the point of intersection of the two. i.e. 5 – x = x + 2 or x = 1.5.
Thus smallest value of g(x) = 3.5
Q. The function f(x) = |x – 2| + |2.5 – x| + |3.6 – x|, where x is a real number, attains a minimum at
x = 2.3
x = 2.5
x = 2.7
None of the above
Ans . B
At x = 2, f(x) = 2.1
At x = 2.5, f(x) = 1.6
At x = 3.6, f(x) = 2.7.Hence, at x = 2.5, f(x) will be minimum.
Q. How many three digit positive integers, with digits x, y and z in the hundred's, ten's and unit's place respectively exist such that x < y, z < y and x ≠ 0?
245
285
240
320
Ans . C
If y = 2 (it cannot be 0 or 1), then x can take 1 value and z can take 2 values.
Thus with y = 2, a total of 1 × 2 = 2 numbers can be formed. With y = 3, 2 × 3 = 6 numbers can be formed. Similarly checking for all values of y from 2 to 9 and adding up we get the answer as 240.
Q.
Ans:c
Q.
Ans:a
Q.Let a, b be any positive integers and x = 0 or 1, then
Ans:a
Q.If n is any positive integer, then (n^{3} – n) is divisible
Ans.c
Q.value of (1-d^{3})/(1-d)
Ans.b
Q.I brought 30 books on Mathematics, Physics, and Chemistry, priced at Rs.17, Rs.19, and Rs.23 per book respectively, for distribution among poor students of Standard X of a school. The physics books were more in number than the Mathematics books but less than the Chemistry books, the difference being more than one. The total cost amounted to Rs.620. How many books on Mathematics, Physics, and Chemistry could have been bought respectively?
Ans.c
Q.The last time Rahul bought Diwali cards, he found that the four types of cards that he liked were priced Rs.2.00, Rs.3.50, Rs.4.50 and Rs.5.00 each. As Rahul wanted 30 cards, he took five each of two kinds and ten each of the other two, putting down the exact number of 10 rupees notes on the payment counter. How many notes did Rahul give?
Ans.d
Q.A function can sometimes reflect on itself, i.e. if y = f(x), then x = f(y). Both of them retain the same structure and form. Which of the following functions has this property?
Ans.b
Q.What is the value of k for which the following system of equations has no solution: 2x – 8y = 3 and kx + 4y = 10
Ans.c
Q.How many 3-digit even numbers can you form such that if one of the digits is 5 then the following digit must be 7?
Ans.a
Q.A lord got an order from a garment manufacturer for 480 Denim Shirts. He brought 12 sewing machines and appointed some expert tailors to do the job. However, many didn’t report to duty. As a result, each of those who did, had to stitch 32 more shirts than originally planned by Alord, with equal distribution of work. How many tailors had been appointed earlier and how many had not reported for work?
Ans.c
Q.Iqbal dealt some cards to Mushtaq and himself from a full pack of playing cards and laid the rest aside. Iqbal then said to Mushtaq. “If you give me a certain number of your cards, I will have four times as many cards as you will have. If I give you the same number of cards, I will have thrice as many cards as you will have “. Of the given choices, which could represent the number of cards with Iqbal?
Ans.b
Q.Three times the first of three consecutive odd positive integers is 3 more than twice the third. What is the third integer?
Ans.a
Q.2^{73} – 2 ^{72} – 2 ^{71} is the same as
Ans.c
Q.The number of integers n satisfying –n + 2 ≥ 0 and 2n ≥ 4 is
Ans.b
Q.The sum of two integers is 10 and the sum of their reciprocals is 5/12. Then the larger of these integers is
Ans.c
Q.If y = f(x) and f(x) = (1–x) / (1 + x), which of the following is true?
Ans.d
Q.A player rolls a die and receives the same number of rupees as the number of dots on the face that turns up. What should the player pay for each roll if he wants to make a profit of one rupee per throw of the die in the long run?
Ans.a
Q.Let Y = minimum of {(x + 2), (3 – x)}. What is the maximum value of Y for 0≤x≤1?
Ans.d
Q.x, y and z are three positive integers such that x > y > z. Which of the following is closest to the product xyz?
Ans.a
Q.What is the greatest power of 5 which can divide 80! exactly.
Ans.c
Q.A third standard teacher gave a simple multiplication exercise to the kids. But one kid reversed the digits of both the numbers and carried out the multiplication and found that the product was exactly the same as the one expected by the teacher. Only one of the following pairs of numbers will fit in the description of the exercise. Which one is that?
Ans.b
Q.Find the minimum integral value of n such that the division 55n/124 leaves no remainder.
Ans.a
Q.Let k be a positive integer such that k + 4 is divisible by 7. Then the smallest positive integer n, greater than 2, such that k + 2n is divisible by 7 equals
Ans.a
Q.A calculator has two memory buttons, A and B. Value 1 is initially stored in both memory locations.
The following sequence of steps is carried out five times:
add 1 to B
multiply A to B
store the result in A
What is the value stored in memory location A after this procedure?
Ans.c
Q.A one rupee coin is placed on a table. The maximum number of similar one rupee coins which can be placed on the table, around it, with each one of them touching it and only two others is
Ans.b
Q.In Sivakasi, each boy’s quota of match sticks to fill into boxes is not more than 200 per session. If he reduces the number of sticks per box by 25, he can fill 3 more boxes with the total number of sticks assigned to him. Which of the following is the possible number of sticks assigned to each boy?
Ans.b
Q.In a six-node network, two nodes are connected to all the other nodes. Of the remaining four, each is connected to four nodes. What is the total number of links in the network?
Ans.a
Q.If x is a positive integer such that 2x + 12 is perfectly divisible by x, then the number of possible values of x is
Ans.c
Q.A man starting at a point walks one km east, then two km north, then one km east, then one km north, then one km east and then one km north to arrive at the destination. What is the shortest distance from the starting point to the destination?
Ans.d
Q.An outgoing batch of students wants to gift PA system worth Rs.4200 to their school. If the teachers offer to pay 50% more than the students, and an external benefactor gives three times teachers’ contribution, how much should the teachers donate?
Ans.c
Q.A positive integer is said to be a prime number if it is not divisible by any positive integer other than itself and 1. Let p be a prime number greater than 5. Then (p^{2} – 1) is
Ans.d
Q.If 8 + 12 = 2, 7 + 14 = 3, then 10 + 18 = ?
Ans.a
Q.What is the distance between the points A(3, 8) and B(–2, –7)?
Ans.c
Q.Two oranges, three bananas and four apples cost Rs.15. Three oranges, two bananas and one apple cost Rs 10. I bought 3 oranges, 3 bananas and 3 apples. How much did I pay?
Ans.c
Q.From each of the two given numbers, half the smaller number is subtracted. Of the resulting numbers the larger one is three times as large as the smaller. What is the ratio of the two numbers?
Ans.a
Q.Eighty five children went to an amusement park where they could ride on the merry – go round, roller coaster, and Ferris wheel. It was known that 20 of them took all three rides, and 55 of them took at least two of the three rides. Each ride cost Re.1, and the total receipt of the amusement park was Rs.145.How many children did not try any of the rides?
Ans.c
Q.Eighty five children went to an amusement park where they could ride on the merry – go round, roller coaster, and Ferris wheel. It was known that 20 of them took all three rides, and 55 of them took at least two of the three rides. Each ride cost Re.1, and the total receipt of the amusement park was Rs.145.How many children took exactly one ride?
Ans.c
Q.John bought five mangoes and ten oranges together for forty rupees. Subsequently, he returned one mango and got two oranges in exchange. The price of an orange would be
Ans.b
Q.The number of positive integers not greater than 100, which are not divisible by 2, 3 or 5 is
Ans.a
Q.let u_{n+1} = 2u_{n}+1 (n=0,1,2) and u_{0}=0. then u_{10} is nearest to
Ans.a
Q.Let x < 0.50, 0 < y < 1, z > 1. Given a set of numbers, the middle number, when they are arranged in ascending order, is called the median. So the median of the numbers x, y and z would be
Ans.b
Q.If log_{7} log_{5} ( √x+5 + √x ) = 0 ; find x
Ans.d
Q.if a+b+c=0 where a≠b≠c then a^{2}/(2a^{2}+bc) + b^{2}/(2b^{2}+ac) + c^{2}/(2c^{2}+ab) is equal to
Ans.b
Q.If one root of x^{2}+px+12=0 is 4, while the equation x^{2} - 7x+q = 0 has equal roots, then the value of q is
Ans.a
If md (x) = | x |,
mn (x, y) = minimum of x and y and
Ma( a, b, c, ...)= maximum of (a, b, c)
Q.Value of Ma ( md(a) , mn (md(b),a), mn (ab , md(ac)) ) where a = -2, b = -3, c = 4 is
Ans.b
Q.Given that a > b then the relation Ma[md(a), mn(a,b)] = mn[a,md(Ma(a,b))]does not hold if
Ans.a
Q.It takes the pendulum of a clock 7 seconds to strike 4 o’clock. How much time will it take to strike 11 o’clock?
Ans.d
Q.What is the smallest number which when increased by 5 is completely divisible by 8, 11 and 24?
Ans.b
Q.5^{6}-1 is divisible by
Ans.b
Four sisters — Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs.32.
Q.How many rupees did Suvarna start with?
Ans.c
Q.Who started with the lowest amount?
Ans.d
Q.Who started with the highest amount?
Ans.a
Q.What was the amount with Uma at the end of the second round?
Ans.b
Q.72 hens cost Rs.__ 96.7__. Then what does each hen cost, where two digits in place of ‘__’ are not visible or are written in illegible hand?
Ans.c
Q.A person who has a certain amount with him goes to market. He can buy 50 oranges or 40 mangoes. He retains 10% of the amount for taxi fares and buys 20 mangoes and of the balance he purchases oranges. Number of oranges he can purchase is
Ans.d
Q.The value of (55^{3} + 45^{3}) / (55^{2} - 55 * 45 + 45^{2})
Ans.a
Q.For the product n(n + 1)(2n + 1), n ∈ N, which one of the following is not necessarily true?
Ans.d
Q.One root of x^{2} + kx – 8 = 0 is square of the other. Then the value of k is
Ans.d
Q.Two positive integers differ by 4 and sum of their reciprocals is 10/21. Then one of the numbers is
Ans.a
Q.What is the value of m which satisfies 3m^{2} – 21m + 30 < 0?
Ans.c
Q.Largest value of min(2 + x^{2} , 6 – 3x), when x > 0, i
Ans.c
le(x, y) = Least of (x, y)
mo(x) = |x|
me(x, y) = Maximum of (x, y)
Q.Find the value of me(a + mo(le(a, b)); mo(a + me(mo(a), mo(b))), at a = –2 and b = –3.
Ans.a
Q.Which of the following must always be correct for a, b > 0?
Ans.d
Q.For what values of 'a' is me(a^{2} – 3a, a – 3) > 0?
Ans.b
Q.For what values of 'a' is le(a^{2} – 3a, a – 3) > 0?
Ans.d
Q.If log_{2} log_{7} (x^{2}-x+37)= 1, then what could be the value of 'x'?
3
5
4
none
Ans.c
Q.If n is an integer, how many values of n will give an integral value of (16n^{2}+7n+6)/n ?
2
3
4
none
Ans.d
Q.A student instead of finding the value of 7/8 of a number, found the value of 7/18 of the number. If his answer differed from the actual one by 770, find the number.
1584
2520
1728
1656
Ans.a
Q.P and Q are two positive integers such that PQ = 64. Which of the following cannot be the value of P + Q?
20
65
16
35
Ans.d
Q.If the roots x_{1} and x_{2} of the quadratic equation x^{2} - 2x + c = 0 also satisfy the equation 7x_{2} - 4x_{1} = 47 then which of the following is true?
c=-15
x_{1} = -5, x_{2} = -3
x_{1} = 4.5, x_{2} = -2.5
none
Ans.a
Q.If m and n are integers divisible by 5, which of the following is not necessarily true?
m – n is divisible by 5
m^{2} – n^{2} is divisible by 25
m + n is divisible by 10
None of these
Ans.c
Q.Which of the following is true?
7^{32} = (7^{3})^{2}
7^{32} > (7^{3})^{2}
7^{32} < (7^{3})^{2}
none of these
Ans.b
Q.P, Q and R are three consecutive odd numbers in ascending order. If the value of three times P is 3 less than two times R, find the value of R.
5
7
9
11
Ans.c
For these questions the following functions have been defined.
la(x,y,z) = min (x+y,y+z)
le(x,y,z) = max (x-y,y-z)
ma(x,y,z) = 1/2 [la(x,y,z) + le(x,y,z)]
Q.Given that x > y > z > 0 Which of the following is necessarily true?
la(x,y,z) < le(x,y,z)
la(x,y,z) > ma(x,y,z)
le(x,y,z) > ma(x,y,z)
none
Ans.b
Q.what is the value of ma (10,4 , le ( la (10,5,3),5,3))
7
6.5
8
7.5
Ans.b
Q.ABC is a three-digit number in which A > 0. The value of ABC is equal to the sum of the factorials of its three digits. What is the value of B?
9
7
4
2
Ans.c
Q. n^{3} is odd. Which of the following statement(s) is(are) true? I. n is odd. II. n^{2} is odd. III. n is even.
I only
II only
I and II
I and III
Ans . c
Production pattern for number of units (in cubic feet) per day.For a truck that can carry 2,000 cubic ft, hiring cost per day is Rs. 1,000. Storing cost per cubic feet is Rs. 5 per day.
Q. If all the units should be sent to the market, then on which days should the trucks be hired to minimize the cost?
2nd, 4th, 6th, 7th
7th
2nd, 4th, 5th, 7th
None of these
Ans . c
Q. If the storage cost is reduced to Re. 0.80 per cubic feet per day, then on which day(s), should the truck be hired?
4th
7th
4th and 7th
None of these
Ans . b
Q. (BE)^{2} = MPB, where B, E, M and P are distinct integers. Then M =
2
3
9
none
Ans . b
Q. Five-digit numbers are formed using only 0, 1, 2, 3, 4 exactly once. What is the difference between the maximum and minimum number that can be formed?
19800
41976
32976
None of these
Ans . c
Q. A certain number, when divided by 899, leaves a remainder 63. Find the remainder when the same number is divided by 29.
5
4
1
cant say
Ans . a
Q. A is the set of positive integers such that when divided by 2, 3, 4, 5, 6 leaves the remainders 1, 2, 3, 4, 5 respectively. How many integers between 0 and 100 belong to set A?
0
1
2
cant say
Ans . b
A, B, C and D collected one-rupee coins following the given pattern.
Together they collected 100 coins.
Each one of them collected even number of coins.
Each one of them collected at least 10 coins.
No two of them collected the same number of coins.
Q. The maximum number of coins collected by any one of them cannot exceed
64
36
54
None of these
Ans . a
Q. If A collected 54 coins, then the difference in the number of coins between the one who collected maximum number of coins and the one who collected the second highest number of coins must be at least
12
24
30
None of these
Ans . c
Q. If A collected 54 coins and B collected two more coins than twice the number of coins collected by C, then the number of coins collected by B could be
28
20
26
22
Ans . d
Q. The number of positive integer valued pairs (x, y) satisfying 4x – 17y = 1 and x ≤ 1000 is
59
57
55
58
Ans . A
Q. Let a, b, c be distinct digits. Consider a two-digit number 'ab' and a three-digit number 'ccb', both defined under the usual decimal number system, if (ab)^{2} = ccb > 300, then the value of b is
1
0
5
6
Ans . A
Q. The remainder when 7^{84} is divided by 342 is
0
1
49
341
Ans . B
Q. If |r-6| = 11 and |2q-12| = 8 what is the minimum possible value of q/r ?
-2/5
2/17
10/17
none of these
Ans . D
Q. If n = x + 1 where x is the product of four consecutive positive integers, then which of the following
is/are true?
A. n is odd
B. n is prime
C. n is a perfect square
A and C only
A and B only
A only
None of these
Ans . A
Q. If n^{2} = 12345678987654321, what is n?
12344321
1235789
111111111
11111111
Ans . C
Ten coins are distributed among four people P, Q, R and S such that one of them gets one coin, another gets two coins, the third gets three coins and the fourth gets four coins. It is known that Q gets more coins than P, and S gets fewer coins than R.
Q. If the number of coins distributed to Q is twice the number distributed to P, then which one of the following is necessarily true?
R gets an even number of coins.
R gets an odd number of coins.
S gets an even number of coins.
S gets an odd number of coins.
Ans . D
Q. If R gets at least two more coins than S, then which one of the following is necessarily true?
Q gets at least two more coins than S.
Q gets more coins than S.
P gets more coins than S.
P and Q together get at least five coins.
Ans . B
Q. If Q gets fewer coins than R, then which one of the following is not necessarily true?
P and Q together get at least four coins.
Q and S together get at least four coins.
R and S together get at least five coins.
P and R together get at least five coins.
Ans . A
A young girl Roopa leaves home with x flowers, goes to the bank of a nearby river. On the bank of the river, there are four places of worship, standing in a row. She dips all the x flowers into the river. The number of flowers doubles. Then she enters the first place of worship, offers y flowers to the deity. She dips the remaining flowers into the river, and again the number of flowers doubles. She goes to the second place of worship, offers y flowers to the deity. She dips the remaining flowers into the river, and again the number of flowers doubles. She goes to the third place of worship, offers y flowers to the deity. She dips the remaining flowers into the river, and again the number of flowers doubles. She goes to the fourth place of worship, offers y flowers to the deity. Now she is left with no flowers in hand.
Q. If Roopa leaves home with 30 flowers, the number of flowers she offers to each deity is
30
31
32
33
Ans . C
Q. The minimum number of flowers that could be offered to each deity is
0
15
16
CANT SAY
Ans . C
Q. The minimum number of flowers with which Roopa leaves home is
16
15
0
can't say
Ans . B
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