If 17 + 17 = 2895 18 + 18 = 3245 19 + 19 = 3615 then 23 + 23 = ?
Answer: D
Correct answer: 5295
Each answer is the square of the number written down and followed by a 5: \( 17^2 = 289 \) gives 2895, \( 18^2 = 324 \) gives 3245, \( 19^2 = 361 \) gives 3615. Since \( 23^2 = 529 \), the answer is 5295.
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Which of the following interchanges in signs and numbers will make the given equation correct?
8 x 9 + 2 = 74
Answer: B
Correct answer: x and +, 8 and 2
Making both exchanges - the signs × and +, and the numbers 8 and 2 - turns the left side into \( 2 + 9 \times 8 \), which is \[ 2 + 72 = \mathbf{74} \]
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If ‘+’ stands for ‘multiplication’, ‘<’ stands for ‘division’, ‘÷’ stands for ‘subtraction’, ‘-‘ stand for ‘addition’ and ‘×’ stands for ‘greater’ than. Identify which expression is correct?
Answer: C
Correct answer: 20 < 2 + 10 ÷ 4 – 6 × 100
Substituting gives \( 20 \div 2 \times 10 - 4 + 6 \) on the left, and the final symbol means greater than. Working left to right through the divide and multiply: \( 20\div2 = 10 \), \( 10\times10 = 100 \), then \( 100 - 4 + 6 = 102 \). Since 102 exceeds 100 the statement holds.
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If × stands for ‘addition’, ÷ stands for ‘subtraction’, + stands for ‘multiplication’ and – stands for ‘division’, then 20 × 8 ÷ 8 – 4 + 2 = ?
Answer: C
Correct answer: 24
Substituting gives \[ 20 + 8 - 8 \div 4 \times 2. \] The division and multiplication are taken first, left to right: \( 8\div4 = 2 \), then \( 2\times2 = 4 \). What remains is \( 20 + 8 - 4 = 24 \). Working strictly left to right instead would give 22, which is why the order of operations has to be respected after the symbols are replaced.
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If 13*45 = 29 ,
24*58 = 41 ,
74*32 = 53 ,
what should 97*47 be?
Answer: B
Correct answer: 72
Each answer is the average of the two numbers: \( \tfrac{13+45}{2} = 29 \), \( \tfrac{24+58}{2} = 41 \), \( \tfrac{74+32}{2} = 53 \). So \[ \frac{97+47}{2} = \mathbf{72} \]
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In a certain code language, '÷' represents '+', '-' represents 'x', '+' represents '÷' and 'x' represents '-'. Find out the answer to the followingquestion. 8 ÷ 14 - 20 + 5 x 2 = ?
Answer: B
Correct answer: 62
Replacing the symbols gives \( 8 + 14 \times 20 \div 5 - 2 \). Multiplication and division first: \[ 8 + 56 - 2 = \mathbf{62} \]
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1/2 - 1/8 =
Answer: B
Now to find the difference in the given fractions, 1/2 - 1/8
First take the LCM of 2 & 8
LCM of 2 & 8 is 8
Then,
1/2 - 1/8
= (4 - 1)/8
= 3/8
Hence, 1/2 - 1/8 = 3/8.
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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 ?
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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Given intercharges :
Signs + and x and numbers 4 and 5.
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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If ‘+’ means ‘divided by’, ‘-‘ means ‘added to’, ‘×’ means ‘subtracted from’ and ‘÷’ means ‘multiplied by’, then what is the value of 15 ÷ 12 - 36 + 3 ?
Answer: C
Correct answer: 192
Substituting gives \[ 15 \times 12 + 36 \div 3 = 180 + 12 = 192. \] Note that the two symbols are exchanged in an unexpected direction here - the divide sign means multiply and the plus means divide - so reading the expression at face value would give something quite different.
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