If \(a\ \%\ b = 37\) , where \(a\ \%\ b = a + 2b\) , what is the value of a and b?

Question

If \(a\ \%\ b = 37\) , where \(a\ \%\ b = a + 2b\) , what is the value of a and b?

1. A. 25, 5
2. B. 27, 5 (Correct answer)
3. C. 16, 10
4. D. 27, 10

Correct Answer

Option B — 27, 5

Detailed Solution & Explanation

The correct answer is 27, 5.

Key Points

• The rule is given: a % b = a + 2b, and the result must be 37.
• Testing the options: 27 + 2(5) = 27 + 10 = 37 ✓.
• The others miss: 25 + 10 = 35, 16 + 20 = 36, 27 + 20 = 47.
• When the operation is defined explicitly, substitute the options straight into it — there is nothing to deduce.
• Because the operation is defined for you, substitution is faster than algebra — but if you prefer solving, a = 37 − 2b immediately shows b = 5 gives the whole-number pair 27, 5.
• Check every option rather than stopping at the first near-miss; 27 appears in two options, distinguished only by the value of b.

Additional Information

• Where the operation is defined explicitly, substituting the options is faster than algebra, since only four candidates exist.
• Check every option rather than stopping at the first near-miss; options are often built to share one value and differ in the other.
• If you prefer solving directly, rearranging to a = 37 − 2b and testing small whole numbers for b reaches the pair just as quickly.

प्रश्न (हिन्दी में)

यदि \(a\ \%\ b = 37\) है, जहाँ \(a\ \%\ b = a + 2b\) , तो a और b का मान क्या है?

1. A. 25, 5
2. B. 27, 5
3. C. 16, 10
4. D. 27, 10