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(1) x is an integer divisible by 7 (2) x*y is an integer divisible by 49.

I think this is E.

St1: Clearly INSUFF. We don't knwo value of y

St2: INSUFF. We don't knwo about y. x*y divisible by 49 does not say about value of y.

Combined:

Take examples which satisfies both the statements
(St2 can be written as (x*y)^2 * y^2)
1. x = 98, y =1/2 then Ans to main stem is NO
2. x = 98, y = 2 then ans to main stem is YES
_________________

If x = 7, x^2*y^4 is divisible by 49.
If x = 14, x^2*y^4 = (2*7)^2*y^4 = 49(4)(y^4) -> divisible 49
If x = 21, x^2*y^4 = (3*7)^2*y^4 = 48(9)(y^4) -> divisible by 49

You can see that a 7 can always be extracted and once sqaured will cancel out the 49 that is in the denominator. Sufficient.

(2) x*y = 49 -> can only be x=7 and y=7. Sufficient.

If x = 7, x^2*y^4 is divisible by 49. If x = 14, x^2*y^4 = (2*7)^2*y^4 = 49(4)(y^4) -> divisible 49 If x = 21, x^2*y^4 = (3*7)^2*y^4 = 48(9)(y^4) -> divisible by 49

You can see that a 7 can always be extracted and once sqaured will cancel out the 49 that is in the denominator. Sufficient.

(2) x*y = 49 -> can only be x=7 and y=7. Sufficient.

Ans D

I think you are assuming that y is also integer. But there is no such thing mentioned.
_________________

1) x = 7k (k - integer)
=> x^2*y^4 = 49k^2 * y^4 -- depends on value of y (ycould be fraction also) INSUFF.

2) x*y = 7m (m integer)
=> x^2*y^4 = (xy)^2*y^2 = 49*m^2*y^2 -- again depends on the value of y. INSUFF.

(1) & (2)
No additional conclusion can be drawn. Hence E!
_________________

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