8.Mathematical Operations

Questions on Mathematical operations will first start with either defining a new meaning to existing symbols or define a new symbol and its mathematical meaning.

You are then required to evaluate the value of an expression by assuming the meaning of the symbols as defined in the question. The following questions will make this question type clear to you.

Illustration 1:If '+' means '-', '-' means '¥', '¥' means 'Π', and 'Π' means '+' then which of the following will be the value of the expression?

32 + 8 ¥ 2 - 3 Π 4



Ans .

(d) 24


  1. Explanation :

    Putting the changed signs, the expression can be rewritten as
    32 - 8 Π 2 ¥ 3 + 4
    Using BODMAS rule, we have
    =32 - 4 ¥ 3 + 4
    =32 - 12 + 4 = 24
    Hence, the correct option is (d).



Illustration 2: If A implies '+', B implies '-', C implies '¥', D implies 'Π', then calculate the value of the expression 2A3B4C5D1.



Ans .

(c) -15


  1. Explanation :

    Using the proper signs, the above expression can be written as 2 + 3 - 4 ¥ 5 Π 1
    =5 - 20 = -15
    Hence, option (c) is correct



Illustration 3: Which of the following changes would make the given expression correct?

4 + 4 ¥ 4 - 4 #928 4 = 4



Ans .

(d) both 'b' and 'c


  1. Explanation :

    By making inter-changes given in 'a' we get the expression as:
    4 ¥ 4 + 4 - 4 #928 4 = 4 which is false.
    By making interchanges given in 'b', we get expression as
    4 + 4 ¥ 4 #928 4 - 4 = 4 which is true.
    By making interchanges given in option 'c', we get the expression as
    4 ? 4 ¥ 4 - 4 + 4 = 4 which is also true.
    Hence, option (d) is correct.



Illustration 4: If A"B means add B to A, A'B implies subtract B from A, A@ B implies divide A by B, A*B means multiply A with B.

If a train travels with a speed of S1 from point A to B and returns with a speed of S2. The average speed will be represented using the above explained notations?



Ans .

(b) (2*S1*S2)/(S1"S2)


  1. Explanation :

    We know that the formula for average speed is given by 2S1S2/(S1 + S2)
    Hence the correct option is (b).



Illustration 5: If (l, m, n) is represented as v [(l + 1)(m + 1)/(n + 1)]: What is the value of (48, 63, 80)?



Ans .

(a) 56/9


  1. Explanation :

    Putting the value in the above equation we get /[(48 + 1)(63 + 1)/(80 + 1)] =/(49 ¥ 64/81) = (7 ¥ 8)/9 = 56/9 Hence, the correct option is (a).



EXERCISE

Directions for Questions 1 to 5:

If a + b implies a - b

a - b implies a ¥ b,

a ¥ b implies a Π b

a Π b implies a + b



Ans .

(a) 5


  1. Explanation :

    The expression will become 5 -8 ¥ 25 Π 5 + 40.
    Using the BODMAS rule we will get:
    5 - 40 + 40 = 5. Hence, option (a) is correct





Ans .

(b) 1 - 2 + 6 ¥ 3 Π 8


  1. Explanation :

    Looking at option (b), we will get, 1- 2 + 6 ¥ 3 Π 8 becomes 1 ¥ 2 - 6 Π 3 + 8 = 8. Hence, option (b) is the correct answer.





Ans .

(c) 6 + 4 - 2 ¥ 2 Π 1 = 3


  1. Explanation :

    Option (c) gives us 6 - 4 ¥ 2 Π 2 + 1= 3. Hence, this is correct.





Ans .

(b) 1/5


  1. Explanation :

    (1 + 2 -3 ¥ 1 Π 4)/(4 + 5 - 4 ¥ 2 Π 1) ? (1- 2 ¥ 3 Π 1 + 4)/(4 - 5 ¥ 4Π 2 + 1) = -1/-5 =1/5. Hence, (b) is the answer





Ans .

(a) -7/3


  1. Explanation :

    (4 + 3 - 5 ¥ 1 Π 4) ¥ (5 + 2 - 3 ¥ 1 Π 4) = (4 - 3 ¥ 5 Π 1 + 4) Π (5 - 2 ¥ 3 Π 1 + 4) = -7/3. Hence, option (a) is the answer.



Directions for Questions 6 to 8: If 'a' means+, 'b' means -, 'c' means ¥ and 'd' means Π.


Ans .

(c) -19


  1. Explanation :

    6a7b8c8d2 = 6 + 7 - 8 ¥ 8 Π 2 = -19. Hence, (c) is the answer.





Ans .

(c) 670


  1. Explanation :

    (8c7)c(7a5)b(6d3)d(3b2) becomes 56 ¥ 12 - 2 Π 1 = 670. Option (c) is the answer.





Ans .

(d) undefined


  1. Explanation :

    The expression contains a division by 0, hence is undefined. Option (d) is the answer.



Directions for Questions 9 to 12:In each of the following questions if the given interchanges are made in signs and numbers, which one of the four equations would be correct?


Ans .

(d) none of these


  1. Explanation :

    None of these, i.e. option (d) is correct





Ans .

(b) 1 + 2 - 3 ¥ 8 Π 4 = 9


  1. Explanation :

    The given expression will become 1 + 3 Π 2 ¥ 8 - 4 = 9. Option (b) is the answer





Ans .

(d) none of these


  1. Explanation :

    Checking each of the four options we will get none of these the answer. Hence, option (d) is the answer.





Ans .

(d) 3 + 4 - 12 ¥ 1 Π 10 = 10


  1. Explanation :

    Option (d) becomes correct.





Ans .

(a) ¥ and -


  1. Explanation :

    If the signs are changed according to the first option the equation is satisfied. Hence, option (a) is correct





Ans .

(b) Π and +


  1. Explanation :

    If the signs are changed according to the second option the equation is satisfied. Hence, option (b) is correct.





Ans .

(b)¥, Π, ¥


  1. Explanation :

    Insertion of ¥, Π, ¥ in that order will make 12 ¥ 4 Π 2 ¥ 1 = 24. Hence, option (b) is correct





Ans .

(c) a, b, d


  1. Explanation :

    40 + 20 - 30 Π 6 = 60 - 5 = 55. Hence, a, b, d. Option (c) is correct.





Ans .

(a) Π, ¥, -, +


  1. Explanation :

    12 Π 8 ¥ 4 - 2 + 1 would mean 12 + 8 Π 4 ¥ 2 - 1 = 12 + 4 - 1 = 15. Hence, the order given in option (a) is correct





Ans .

(b) a, b, g, d


  1. Explanation :

    Option (b) is correct.



Directions for Questions 19 to 21:

If 12 + 2 = 6
27 + 9 = 3
and 15 + 5 = 3.



Ans .

(a) 14


  1. Explanation :

    It is clear that the + sign means Π. Hence

    182 + 13 would give us a value of 14. Hence, (a) is the answer




Ans .

(a) 10


  1. Explanation :

    50/5 = 10. Hence, (a) is the answer.





Ans .

(a) 4


  1. Explanation :

    10/2.5 = 4. Hence, correct option is (a).



Directions for Questions 22 to 25:

If 3 ¥ 4 = 5
5 ¥ 12 = 13
Then solve the following question.



Ans .

(a) 4


  1. Explanation :


    7 ¥ 24 = = 25. Hence, option (d) is the answer.





Ans .

(b) 12.041


  1. Explanation :

    8 ¥ 9 = = 12.041. Hence, option (b) is the answer.





Ans .

(c) 40


  1. Explanation :

    The required value will be got by the square root of the difference between 412 and 92 Æ 1681 - 81 = 1600. Hence, the required answer is 40. Correct answer is option (c).





Ans .

(b) 8.366


  1. Explanation :

    The required value would be square root of 61 + 9 = 8.366. Hence, option (b) is the answer


Directions for Questions 26 to 30:

If M means greater than
N means equal to
O means not less than
P means less than
Q means not equal to
and R means not greater than



Ans .

(b) yPa


  1. Explanation :

    yPz means that y is less than z and zNa means z = a. Thus, y is less than a Æ yPa. Option (b) is correct





Ans .

(d) none of these


  1. Explanation :

    10a is greater than 6b. and 12b is greater than 20c Æ 6n is greater than 10c. Thus 10a is greater than 10c or a is greater than c. Option (d) is correct




Ans .

(c) bP - 2


  1. Explanation :

    a is negative and b + 2 is less than a implies that b must be below -2. Hence, option (c) is correct




Ans .

(d) can`t be determined


  1. Explanation :

    Nothing can be said about the relationships between s, u or v or for that matter about u and v. Hence, cannot be determined. The correct answer is option (d).




Ans .

(d) (a), (b) and (c) could be true


  1. Explanation :

    Since the modulus value is always positive, all the three, i.e. the first, second and third relationships are possible. Hence, option (d) is correct.



Directions for Questions 31 to 33:

If aAb implies a + b
aMb implies a - b
aPb implies a ¥ b
aQb implies a Π b



Ans .

(b) 5P2A4Q2P2 = 14


  1. Explanation :

    Option (b) is correct since we will get 10 + 4 = 14.





Ans .

(c) 9.5


  1. Explanation :

    11 - 1.5 = 9.5. Option (c) is correct.





Ans .

(d) none of these


  1. Explanation :

    (-15)(-7) = 105. Hence, option (d) is correct.



Directions for Questions 34 to 36:

A"B implies A + B
A'b implies A - B
A@B implies A Π B
A*B implies A ¥ B



Ans .

(d) none of these


  1. Explanation :

    It can be seen that none of these is correct. Hence, (d) is the answer





Ans .

(b) 2[(x*a)"(a*c)"(x*c)]


  1. Explanation :

    The surface area of a cuboid box is equal to twice the areas of each of the sides. Hence, option (b) is correct.





Ans .

(c) (25*2)"(40*5)"(100*20)


  1. Explanation :

    The correct answer is option (c).



Directions for Questions 37 to 41:

If AXB implies A2 + B2
AYB implies A2 - B2
AZB implies (A + B)2
AMB implies (A - B)2



Ans .

(b) -5544


  1. Explanation :

    412 - 852 = 1681 - 7225 = -5544. Hence, option (b) is correct answer





Ans .

(a) 1600


  1. Explanation :

    (- 40)2 =1600. Hence, option (a) is correct answer





Ans .

(c) A.B = 0


  1. Explanation :

    The given expression tells us that (A - B)2 = (A + B)2. This can only occur when 2AB = - 2AB= 0. Hence, option (c) is correct.





Ans .

(a) 49


  1. Explanation :

    72 = 49. Hence, correct answer is option (a)





Ans .

(b) 256


  1. Explanation :

    162 = 256. Hence, correct answer is option (b).



Directions for Questions 42 and 43:

If '*' indicates either '+' or '¥', solve the following questions.



Ans .

(b) 5041


  1. Explanation :

    The maximum value will be obtained when we use multiplication between 2 to 7 and addition between 1 and 2. Hence, option (b) is the answer.





Ans .

(b) 9


  1. Explanation :

    The minimum value will be got if we use a multiplication between 1 and 2 and addition between 2, 3, and 4. The value will be 1 ¥ 2 + 3 + 4 = 9. Hence, option (b) is the answer



Directions for Questions 44 to 46:

If A indicates >
B indicates <
C indicates =
D indicates p
E indicates +
F indicates -
G indicates *
H indicates Π



Ans .

(b) (5E6)A(6E12)A(13E6)


  1. Explanation :

    It can be seen that options 1 and 3 are correct, but option (b) is wrong. Hence, option (b) is the correct answer





Ans .

(b) 32


  1. Explanation :

    32/1 = 32. Hence, option (b) is correct.





Ans .

(c) -4


  1. Explanation :

    5 + 3 12 = -4. Hence, option (c) is correct.