Is xy > 3 ?

[BTGmoderatorDC]

Is xy > 3 ?

(1) x + y > 3
(2) x - y > 3

How will i know if statement 1 is sufficient?

OA E

[GMATGuruNY]

Is xy > 3 ?

(1) x + y > 3
(2) x - y > 3

Statement 1: x+y > 3
Case 1: x=10 and y=0, with the result that x+y = 10+0 = 10
In this case, xy = 10*0 = 0, so the answer to the question stem is NO.
Case 2: x=10 and y=1, with the result that x+y = 10+1 = 11
In this case, xy = 10*1 = 10, so the answer to the question stem is YES.
Since the answer to the question stem is NO in Case 1 but YES in Case 2, INSUFFICIENT.

Cases 1 and 2 also satisfy Statement 2.
Since each case satisfies both statements -- and the answer to the question stem is NO in Case 1 but YES in Case 2 -- the two statements combined are INSUFFICIENT.

The correct answer is E.

[Scott@TargetTestPrep]

Is xy > 3 ?

(1) x + y > 3
(2) x - y > 3

We need to determine whether xy > 3.

Statement One Alone:

x + y > 3

Statement one alone is not sufficient to answer the question. For instance, if x = 1/2 and y = 3, then xy = 3/2 IS NOT greater than 3. However, if x = 2 and y = 3, then xy = 6 IS greater than 3.

Statement Two Alone:

x - y > 3

Statement two alone is not sufficient to answer the question. For instance, if x = 4 and y =1/2, then xy = 2 IS NOT greater than 3. However, if x = 5 and y = 1, then xy = 5 IS greater than 3.

Statements One and Two Together:

If we add the two inequalities from statements one and two, we will have:

(x + y > 3)

+ (x - y > 3)

2x > 6

x > 3

However, this still is not enough information to answer the question.

For instance, if if x = 4 and y =1/2, then xy IS NOT greater than 3. However, if x = 5 and y = 1, then xy IS greater than 3.

Answer: E

[BTGmoderatorDC]

Is xy > 3 ?

(1) x + y > 3
(2) x - y > 3

We need to determine whether xy > 3.

Statement One Alone:

x + y > 3

Statement one alone is not sufficient to answer the question. For instance, if x = 1/2 and y = 3, then xy = 3/2 IS NOT greater than 3. However, if x = 2 and y = 3, then xy = 6 IS greater than 3.

Statement Two Alone:

x - y > 3

Statement two alone is not sufficient to answer the question. For instance, if x = 4 and y =1/2, then xy = 2 IS NOT greater than 3. However, if x = 5 and y = 1, then xy = 5 IS greater than 3.

Statements One and Two Together:

If we add the two inequalities from statements one and two, we will have:

(x + y > 3)

+ (x - y > 3)

2x > 6

x > 3

However, this still is not enough information to answer the question.

For instance, if if x = 4 and y =1/2, then xy IS NOT greater than 3. However, if x = 5 and y = 1, then xy IS greater than 3.

Answer: E

Thanks a lot!