manik11 wrote:Is positive integer A greater than positive integer B?
(1) A has more factors than B does.
(2) Every prime factor of B is a factor of A.
Statements combined:
To make the math easier, let the only prime factor of B be 2.
Options for B:
2, 4, 8, 16, 32, 64...
To make it easier for A to be less than or greater than B, let B be equal to a medium-sized value in the list above:
Let B = 16.
Since B's one prime factor (2) must also be a factor of A, A must be EVEN.
Even values LESS THAN 16:
2, 4, 6, 8, 10, 12, 14
Even values GREATER THAN 16:
18, 20, 22...
Case 1: B = 16, A = 12
In this case:
B has 5 factors: 1, 2, 4, 8, 16
A has 6 factors: 1, 2, 3, 4, 6, 12
Since A is less than B, the answer to the question stem is NO.
Case 2: B = 16, A = 18
In this case:
B has 5 factors: 1, 2, 4, 8, 16
A has 6 factors: 1, 2, 3, 6, 9, 18
Since A is greater than B, the answer to the question stem is YES.
Since the answer is NO in Case 1 but YES in Case 2, the two statements combined are INSUFFICIENT.
The correct answer is
E.
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