Mathematical Operations Questions and Answers

Q: If '+' means '÷', '×' means '-', '÷' means '×' and '-' means '+', then the value of8 + 6 × 4 ÷ 3 - 4 is :

The value is \(-\frac{20}{3}\).Replace the symbols: + becomes ÷, × becomes -, ÷ becomes ×, and - becomes +.\[ \begin{aligned} 8 \div 6 - 4 \times 3 + 4 &= \frac{4}{3} - 12 + 4 \\ &= \frac{4}{3} - 8 = -\frac{20}{3} \end{aligned} \]Division and multiplication are done first. \(\frac{20}{3}\) drops the minus sign, and -12 or 12 result from ignoring the \(\frac{4}{3}\) or doing the operations left to right.

Q: If A + B = 2C and C + D = 2A, then

Correct answer: A + C = B + DFrom \( A+B = 2C \) we get \( B = 2C-A \), and from \( C+D = 2A \) we get \( D = 2A-C \). Adding those, \[ B + D = (2C-A) + (2A-C) = A + C \] so A + C = B + D.

Q: Given interchanges : Signs + and - , numbers 4 and 8.

Correct answer: 4 - 8 + 12 = 0Making both swaps - the signs + and −, and the numbers 4 and 8 - turns this into \( 8 + 4 - 12 \), which is \( \mathbf{0} \). None of the other equations balances after the same two exchanges.

Q: Find out the two signs to be interchanged for making following equation correct 5 + 3 x 8 - 12 / 4 =3

Correct answer: - and /Exchanging − and ÷ turns the equation into \( 5 + 3 \times 8 \div 12 - 4 \). Working by the usual order, \[ 5 + \frac{24}{12} - 4 = 5 + 2 - 4 = \mathbf{3} \]

Q: If × stands for 'addition', ÷ stands for 'subtraction', + stands for 'multiplication' and-stands for 'division', then 20 × 8 ÷ 8 - 4 + 2 = ?

Correct answer: 24Replacing each symbol by what it stands for gives \( 20 + 8 - 8 \div 4 \times 2 \). Division and multiplication first: \[ 20 + 8 - 4 = \mathbf{24} \]

Q: Select the correct set of symbols which will fit in the given equation? 5 0 3 5 = 20

Correct answer: -, +, xPutting the signs in as −, + and × gives \[ 5 - 0 + 3 \times 5 = 5 - 0 + 15 = \mathbf{20} \]

Q: 12:30 :: 14: ?

Correct answer: 35Each second number is two and a half times the first: \( 12 \times 2.5 = 30 \), so \[ 14 \times 2.5 = \mathbf{35} \]

Q: Given intercharges : Signs + and x and numbers 4 and 5.

Correct answer: 5 x 4 + 20 = 104Exchanging the signs + and ×, and the numbers 4 and 5, turns the left side into \( 4 + 5 \times 20 \), which is \[ 4 + 100 = \mathbf{104} \]

Q: If Q means 'add to', J means 'multiply by', T means 'substract from' and K means 'divide by' then 30 K 2 Q 3 J 6 T 5 = ?

Correct answer: 28Reading Q as +, J as ×, T as − and K as ÷ gives \( 30 \div 2 + 3 \times 6 - 5 \), and by the usual order \[ 15 + 18 - 5 = \mathbf{28} \]

Important Instructions

31.

If '+' means '÷', '×' means '-', '÷' means '×' and '-' means '+', then the value of
8 + 6 × 4 ÷ 3 - 4 is :

A.-12
B.12
C.\(-\frac{20}{3}\)
D.\(\frac{20}{3}\)

Exam Year(s)

UKPSC Lower PCS - 2025,

Answer: C

The value is \(-\frac{20}{3}\).

Replace the symbols: + becomes ÷, × becomes -, ÷ becomes ×, and - becomes +.

\[ \begin{aligned} 8 \div 6 - 4 \times 3 + 4 &= \frac{4}{3} - 12 + 4 \\ &= \frac{4}{3} - 8 = -\frac{20}{3} \end{aligned} \]

Division and multiplication are done first. \(\frac{20}{3}\) drops the minus sign, and -12 or 12 result from ignoring the \(\frac{4}{3}\) or doing the operations left to right.

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32.

If A + B = 2C and C + D = 2A, then

A.A + C = B + D
B.A + C = 2D
C.A + D = B + C
D.A + C = 2B

Answer: A

Correct answer: A + C = B + D

From \( A+B = 2C \) we get \( B = 2C-A \), and from \( C+D = 2A \) we get \( D = 2A-C \). Adding those, \[ B + D = (2C-A) + (2A-C) = A + C \] so A + C = B + D.

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33.

Given interchanges :

Signs + and - , numbers 4 and 8.

A.4 + 8 - 12 = 12
B.4 - 8 + 12 = 0
C.8 + 4 - 12 = 24
D.8 - 4 + 12 = 8

Answer: B

Correct answer: 4 - 8 + 12 = 0

Making both swaps - the signs + and −, and the numbers 4 and 8 - turns this into \( 8 + 4 - 12 \), which is \( \mathbf{0} \). None of the other equations balances after the same two exchanges.

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34.

Find out the two signs to be interchanged for making following equation correct

5 + 3 x 8 - 12 / 4 =3

A.+ and -
B.- and /
C.+ and x
D.+ and /

Answer: B

Correct answer: - and /

Exchanging − and ÷ turns the equation into \( 5 + 3 \times 8 \div 12 - 4 \). Working by the usual order, \[ 5 + \frac{24}{12} - 4 = 5 + 2 - 4 = \mathbf{3} \]

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35.

If × stands for 'addition', ÷ stands for 'subtraction', + stands for 'multiplication' and-stands for 'division', then 20 × 8 ÷ 8 - 4 + 2 = ?

A.80
B.25
C.24
D.5

Answer: C

Correct answer: 24

Replacing each symbol by what it stands for gives \( 20 + 8 - 8 \div 4 \times 2 \). Division and multiplication first: \[ 20 + 8 - 4 = \mathbf{24} \]

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36.

Select the correct set of symbols which will fit in the given equation?

5 0 3 5 = 20

A.x, x, x
B.-, +, x
C.x, +, x
D.+, -, x

Answer: B

Correct answer: -, +, x

Putting the signs in as −, + and × gives \[ 5 - 0 + 3 \times 5 = 5 - 0 + 15 = \mathbf{20} \]

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37.

12:30 :: 14: ?

A.36
B.28
C.35
D.42

Answer: C

Correct answer: 35

Each second number is two and a half times the first: \( 12 \times 2.5 = 30 \), so \[ 14 \times 2.5 = \mathbf{35} \]

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38.

Given intercharges :

Signs + and x and numbers 4 and 5.

A.5 x 4 + 20 = 40
B.5 x 4 + 20 = 85
C.5 x 4 + 20 = 104
D.5 x 4 + 20 = 95

Answer: C

Correct answer: 5 x 4 + 20 = 104

Exchanging the signs + and ×, and the numbers 4 and 5, turns the left side into \( 4 + 5 \times 20 \), which is \[ 4 + 100 = \mathbf{104} \]

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39.

If Q means 'add to', J means 'multiply by', T means 'substract from' and K means 'divide by' then 30 K 2 Q 3 J 6 T 5 = ?

A.18
B.28
C.31
D.103

Answer: B

Correct answer: 28

Reading Q as +, J as ×, T as − and K as ÷ gives \( 30 \div 2 + 3 \times 6 - 5 \), and by the usual order \[ 15 + 18 - 5 = \mathbf{28} \]

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40.

In a cricket match, five batsmen P, Q, R, S and T scored an average of 36 runs. S Scored 5 more than T; T scored 8 fewer than P; Q scored as many as S and T combined; and Q and R scored 107 between them. How many runs did T score ?

A.20
B.29
C.28
D.24

Answer: A

Let the runs scored by P, Q, R, S and T be a, b, c, d and e

From given data,

a + b + c + d + e = 36 x 5 = 180
b + c = 107
Let a = x
e = x-8
d = x-3
now 3x - 11 + 107 = 180
3x = 84
x = 28
e's score = 28-8 = 20

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Mathematical Operations Questions and Answers

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