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Region A is defined by the equation 2x + y < 40. How many points (b, c) exist such that b is a natural number and c is a multiple of b?


1. 90
2. 89
3. 94
4. 92

1 Answer

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Correct Answer - Option 4 : 92

Calculation:

When b = 1, c can take 37 values [37/1]

When b = 2, c can take 17 values [35/2]

When b = 3, c can take 11 values [33/3]

When b = 4, c can take 7 values [31/4]

When b = 5, c can take 5 values [29/5]

When b = 6, c can take 4 values [27/6]

When b = 7, c can take 3 values [25/7]

When b = 8, c can take 2 values [23/8]

When b = 9, c can take 2 values [21/9]

When b = 10, c can take 1 value [19/10]

When b = 11, 12, 13 c can take one value each.

⇒ 37 + 17 + 11 + 7 + 5 + 4 + 3 + 2 + 2 + 1 + 1 + 1 + 1 = 92

∴ Total 92 such values are possible.

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