Mathematical Operations Questions and Answers

Q: If '+' means subtraction, '÷' means addition, '<' means multiplication and '>' means division, then find the value of the given statement, The value of 9 ÷ 7 (4>2) + 5 will be

Correct answer: 32Replace each symbol by the operation it means: \( + \to - \), \( \div \to + \), \( \lt \to \times \), \( \gt \to \div \). The expression \( 9 \div 7 \lt 8 \gt (4 \gt 2) + 5 \) therefore reads \( 9 + 7 \times 8 \div (4 \div 2) - 5 \).Working the bracket first, then BODMAS: \[ 9 + 7 \times 8 \div 2 - 5 = 9 + 28 - 5 = \mathbf{32} \]

Q: If Q means ‘add’ to; J means ‘Multiply by’, T means ‘subtract from’ and K means ‘divide by’ then 30 K 2 Q 3 J 6 T 5 = ?

Correct answer: 28Substituting gives \[ 30 \div 2 + 3 \times 6 - 5. \] Taking the division and multiplication first: \( 30\div2 = 15 \) and \( 3\times6 = 18 \). Then \( 15 + 18 - 5 = 28 \).

Q: If "K" denotes "multiplied by", "M" denotes "subtracted from", "J" denotes "added to" and "L" denotes "divided by", then 44 M 24 K 56 L 14 J 60 = ?

Correct answer: 8Replacing the letters gives \( 44 - 24 \times 56 \div 14 + 60 \), and by the usual order \[ 44 - 96 + 60 = \mathbf{8} \]

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: 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 \[ 15 + 18 - 5 = \mathbf{28} \]

Q: The following equation is incorrect. Which two signs should be interchanged to correct the equation? 15 x 12 + 40 ÷ 40 - 6 = 21

Correct answer: + and xExchanging + and × gives \( 15 + 12 \times 40 \div 40 - 6 \), which works out as \[ 15 + 12 - 6 = \mathbf{21} \]

Q: In the following question, correct the equation by interchanging two signs. 6 + 8 ÷ 4 - 4 = 8

Correct answer: + and -Exchanging + and − gives \( 6 - 8 \div 4 + 4 \), which works out as \[ 6 - 2 + 4 = \mathbf{8} \]

Q: 5068 / 37 x 4 = ?

Correct answer: 548Dividing first, \( 5068 \div 37 = 137 \), and then \[ 137 \times 4 = \mathbf{548} \]

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: \[ 20 + 8 - 4 = \mathbf{24} \]

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61.

If '+' means subtraction, '÷' means addition, '<' means multiplication and '>' means division, then find the value of the given statement,

The value of 9 ÷ 7 < 8> (4>2) + 5 will be

A.32
B.18
C.16
D.11

Answer: A

Correct answer: 32

Replace each symbol by the operation it means: \( + \to - \), \( \div \to + \), \( \lt \to \times \), \( \gt \to \div \). The expression \( 9 \div 7 \lt 8 \gt (4 \gt 2) + 5 \) therefore reads \( 9 + 7 \times 8 \div (4 \div 2) - 5 \).

Working the bracket first, then BODMAS: \[ 9 + 7 \times 8 \div 2 - 5 = 9 + 28 - 5 = \mathbf{32} \]

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62.

If Q means ‘add’ to; J means ‘Multiply by’, T means ‘subtract 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

Substituting gives \[ 30 \div 2 + 3 \times 6 - 5. \] Taking the division and multiplication first: \( 30\div2 = 15 \) and \( 3\times6 = 18 \). Then \( 15 + 18 - 5 = 28 \).

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63.

If "K" denotes "multiplied by", "M" denotes "subtracted from", "J" denotes "added to" and "L" denotes "divided by", then
44 M 24 K 56 L 14 J 60 = ?

A.16
B.72
C.8

Answer: C

Correct answer: 8

Replacing the letters gives \( 44 - 24 \times 56 \div 14 + 60 \), and by the usual order \[ 44 - 96 + 60 = \mathbf{8} \]

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64.

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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65.

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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66.

The following equation is incorrect. Which two signs should be interchanged to correct the equation? 15 x 12 + 40 ÷ 40 - 6 = 21

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

Answer: A

Correct answer: + and x

Exchanging + and × gives \( 15 + 12 \times 40 \div 40 - 6 \), which works out as \[ 15 + 12 - 6 = \mathbf{21} \]

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67.

In the following question, correct the equation by interchanging two signs.
6 + 8 ÷ 4 - 4 = 8

A.÷ and =
B.÷ and +
C.÷ and -
D.+ and -

Answer: D

Correct answer: + and -

Exchanging + and − gives \( 6 - 8 \div 4 + 4 \), which works out as \[ 6 - 2 + 4 = \mathbf{8} \]

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68.

5068 / 37 x 4 = ?

A.548
B.625
C.214
D.745

Answer: A

Correct answer: 548

Dividing first, \( 5068 \div 37 = 137 \), and then \[ 137 \times 4 = \mathbf{548} \]

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69.

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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70.

In a group of buffaloes and ducks the number of legs are 24 more than twice the number of heads. What is the number of buffaloes in the group ?

A.6
B.18
C.12
D.24

Answer: C

Let the number of buffaloes be x

and number of ducks be y.

Now, number of heads = x+y

Number of legs = 4x+2y .......(1)

But given that legs = 2(x+y)+24 ......(2)

solving (1) & (2),we get

4x+2y=2x+2y+24

--> x=12.

Therefore number of buffaloes =12

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