Mathematical Operations Questions and Answers

Answer: B

The signs in order are −, ÷, +, × and =. Put them in place: \[ 45 - 44 \div 22 + 17 \times 89 = 1556 \] By BODMAS, division and multiplication come first: \[ 44 \div 22 = 2,\quad 17 \times 89 = 1513 \] \[ 45 - 2 + 1513 = 1556 \] The left side equals the right side. Substituting the other three combinations does not give 1556: for example, the first reads 45 ÷ 44 + 22 × 17 − 89, which is about 286. As a check on the first option, 45 ÷ 44 + 22 × 17 − 89 does not come to 1556, and the third and fourth options fail in the same way.

Answer: A

The set with the same pattern is (19, 7, 133).

In (22, 8, 176) the third number is the product of the first two: \(22 \times 8 = 176\). The same holds for \(19 \times 7 = 133\).

The others fail: \(26 \times 5 = 130\), not 131; \(28 \times 7 = 196\), not 200; and \(17 \times 8 = 136\), not 157.

Answer: C

The signs to interchange are ÷ and ×.

Swap them and evaluate, doing division and multiplication before addition and subtraction:

\[ \begin{aligned} 28 \div 4 - 3 + 7 \times 5 &= 7 - 3 + 35 \\ &= 39 \end{aligned} \]

As printed the left side is \(112 - 3 + 1.4 = 110.4\). Swapping + and × gives \(28 + 4 - 3 \times 7 \div 5 = 27.8\), swapping - and + gives \(112 + 3 - 1.4 = 113.6\), and swapping × and - gives \(28 - 4 \times 3 + 1.4 = 17.4\).

Answer: C

The answer is 200.

Each result is the sum of the two numbers multiplied by their difference:

\[ \begin{aligned} (12+9)(12-9) &= 21 \times 3 = 63 \\ (10+7)(10-7) &= 17 \times 3 = 51 \\ (14+12)(14-12) &= 26 \times 2 = 52 \end{aligned} \]

\[ (15+5)(15-5) = 20 \times 10 = 200 \]

44, 100 and 625 do not fit the rule; 100 is just \(10^{2}\), the square of the difference.

Answer: C

The answer is 33.

Each result is the first number plus twice the second:

\[ \begin{aligned} 1 + 2 \times 5 &= 11 \\ 3 + 2 \times 7 &= 17 \\ 4 + 2 \times 9 &= 22 \end{aligned} \]

So \(9 + 2 \times 12 = 33\). 21 is the plain sum, 108 the product, and 26 does not fit.

Answer: B

The answer is 65.

Each result is the sum of the squares of the digits:

\[ \begin{aligned} 1^{2} + 3^{2} + 2^{2} &= 14 \\ 3^{2} + 4^{2} + 2^{2} &= 29 \\ 5^{2} + 2^{2} + 6^{2} &= 65 \end{aligned} \]

60 and 20 do not fit, and 3600 is the square of 60.

Answer: B

The combination is ÷, ×, +.

Replace the three signs in order:

\[ \begin{aligned} (50 \div 5) \times 4 + 16 &= 10 \times 4 + 16 \\ &= 56 \end{aligned} \]

The other combinations give \((50 + 5) \div 4 \times 16 = 220\), \((50 + 5) \times 4 \div 16 = 13.75\) and \((50 \times 5) \div 4 + 16 = 78.5\).

Answer: B

The right signs are −, ×, ÷, +.

Under the code, '−' means plus, '×' means divide, '÷' means multiply and '+' means minus. So the option −, ×, ÷, + becomes, in ordinary signs:

\[ \begin{aligned} 12 + 9 \div 6 \times 2 - 1 &= 12 + 3 - 1 \\ &= 14 \end{aligned} \]

which is correct, working division and multiplication from left to right before addition and subtraction.

The others fail: ×, −, ÷, + decodes to \(12 \div 9 + 6 \times 2 - 1\), which is not a whole number; +, ÷, ×, − decodes to \(12 - 9 \times 6 \div 2 + 1 = -14\); and ÷, +, ×, − decodes to \(12 \times 9 - 6 \div 2 + 1 = 106\).

Answer: C

Correct answer: 35

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

Answer: C

Correct answer: 8 R 8 P 8 S 8 Q 8 = 57

Substituting gives \[ 8 \times 8 + 8 \div 8 - 8 = 64 + 1 - 8 = 57. \] The multiplication and the division are evaluated before the addition and subtraction, which is what makes the middle term contribute 1 rather than being folded into a running total.