Data Sufficiency

WHAt is the value of (x-y)^4

(1) The product of x and y is 7.
(2) x and y are integers.

1) Without further information x and y could be 1 and 7 or they could be 49 and 1/7, or any other combination of fractions and integers whose product is seven. We don't know that there integers so we cannot answer the question. Insufficient.

2) This only tell us that x and y could be any possible combination of integers. Clearly its insufficient.


Because 7 is prime, 1) and 2) together tells us that x=7 and y=1 or x=1 and y=7.

7-1=6 and 1-7=-6. Because we're raising 6 or -6 to a even power the result of 6^4 or -6^4 will be the same. You could calculate it out but it just knowing that they will result in the same is enough to conclude C is the answer.

jeevan.Gk wrote:WHAt is the value of (x-y)^4

(1) The product of x and y is 7.
(2) x and y are integers.

(x-y)^4

(1) The product of x and y is 7.
xy=7. 7 is a prime number and the only two factors of it are 1,7. But we can have +1,+7 or -1,-1 --> the product of both = 7. Also, the values can change between the 2 different variables. x=1 or y=1, x=7 or y=7.

So 1 is insuff.

(2) x and y are integers.
This is clearly insufficient.

Together:
We are at the same dilemma. +1,+7 or -1,-7. However, since its being raised to even power, the result will be the same for the 2.

So (C)

jeevan.Gk wrote:WHAt is the value of (x-y)^4
(1) The product of x and y is 7.
(2) x and y are integers.

Stmt1: X and Y can be any number,integer or fraction as sufficient info is unavailable.So,I is insufficient.
Stmt2: X and Y can be any integer.Value of (x-y)^4 can not be uniquely determined.

Consider Stmt1 and Stmt2 together, For XY=7
Possible values of (X,Y)=(-7,-1);(7,1);Resulting value of x-y=+/- 6.
Since a negative number raised to an even power shall lead to a positive result,The value is 6*6*6*6.
Thus,IMO:C