Sachin9 wrote:

For positive integers x and y, x^2 = 350y. Is y divisible by 28?

(1) x is divisible by 4

(2) x^2 is divisible by 28

Somebody please explain me why 2 is not sufficient.

From the statement we get that at least \(y = 2^a*7^b*z\)

where a,b are positive odd integers and z is a perfect square

1)x is divisible by 4. So x had at least two 2s and so \(x^2\) has at least four 2s. So y has at least three 2s. We know y also has a 7. So y is divisible by 28. Sufficient.

2)\(x^2\) is divisible by 28. This would be true even if y has only one 2. i.e, y = 2*7 = 14. In this case, x^2 is divisible by 28 but y is not divisible by 28. From the previous statement we can get a situation where x and y are both divisible by 28. Insufficient.

Answer is hence A.

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