Question : Directions: Which two signs and numbers need to be interchanged to make the following equation correct?
(31 × 3) – (27 × 4) + (81 ÷ 9) = 126
Option 1: 27 and 81, + and –
Option 2: 31 and 27, + and –
Option 3: 3 and 4, + and ÷
Option 4: 27 and 9, + and –
Correct Answer: 27 and 9, + and –
Solution :
Given:
(31 × 3) – (27 × 4) + (81 ÷ 9) = 126
Replace the original symbols and numbers given in the equation with the assigned symbols and numbers in the options one by one –
First option:
27 and 81, + and –
= (31 × 3) + (81 × 4) – (27 ÷ 9)
= (93) + (324) – (3)
= 414 ≠ 126
Second option:
31 and 27, + and –
= (27 × 3) + (31 × 4) – (81 ÷ 9)
= (81) + (124) – (9)
= 196 ≠ 126
Third option:
3 and 4, + and ÷
= (31 × 4) – (27 × 3) ÷ (81 + 9)
= (124) – (81) ÷ (90)
= 124 – 0.9
= 123.1 ≠ 126
Fourth option:
27 and 9, + and –
= (31 × 3) + (9 × 4) – (81 ÷ 27)
= (93) + (36) – (3)
= 126
So, only the fourth option satisfies the equation. Hence, the fourth option is correct.
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