What is the value of xy? (1) x + y = 10 (2) x - y = 6

Solution:

We need to determine the value of xy. Notice that if we can determine the individual values of x and y, then we can determine the value of xy.

Statement One Alone:

Since we don’t know the individual values of x and y, we can’t determine the value of xy. For example, if x = 5 and y = 5, then xy = 25. However, if x = 6 and y = 4, then xy = 24. Statement one alone is not sufficient.

Statement Two Alone:

Since we don’t know the individual values of x and y, we can’t determine the value of xy. For example, if x = 7 and y = 1, then xy = 7. However, if x = 8 and y = 2, then xy = 16. Statement two alone is not sufficient.

Statements One and Two Together:

With the two statements, we have two independent linear equations with two variables, which means we can solve for both x and y. Here we see that x = 8 and y = 2 satisfies both equations. Thus, xy = 16. So both statements together are sufficient.

Answer: C

What if X=8.5 and Y=1.5, It still satisfies both the Eqn's but the product is 12.75.

________________________
8.5 - 1.5 = 7, not 6.

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