Bunuel wrote:
If x and y are positive integers, what is the greatest common factor of 11x and 22y?
(1) x is an odd integer.
(2) y = x + 22
The HCF of 11x and 22y is 11*(HCF(x, 2y))
The question is basically about finding a unique value for HCF(x, 2y)
Statement 1: x is an odd integer.
There are infinite possibilities.
Approach: Counter ExampleExample : x = 5 and y = 10. HCF(x, 2y) is HCF(5, 20) = 5
Counter example: x = 3 and y = 15. HCF(x, 2y) is HCF (3, 30) =3
No conclusive answer. Statement 1 alone is NOT sufficient.
Statement 2: y = x + 22
HCF (x, 2y) = HCF (x, 2x + 44)
Approach: Counter ExampleExample: x = 11; HCF (x, 2x + 44) is HCF (11, 22 + 44) = 11
Counter example: x = 5; HCF (x, 2x + 44) is HCF (5, 10 + 44) = 1
No conclusive answer. Statement 2 alone is NOT sufficient.
Combining the two statements: x is odd and y = x + 22
The example and counter example used in statement 2 satisfy both these conditions.
Despite combining the information in the two statements, we will have multiple answers for the HCF (x, 2y) and therefore, for HCF(11x, 22y)
Choice E is the answer
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