If a and b are each greater than x and y, which of the

If a and b are each greater than x and y, which of the following must be true?

I. a + b > x + y
II. ab > xy
III. |a| + |b| > |x| + |y|

(A) I only
(B) II only
(C) I and II
(D) I and III
(E) I, II and III

I. a + b > x + y. Since a and b are each greater than x and y, then the sum of a and b will also be greater than the sum of x and y.

II. ab > xy. Not necessarily true, consider a = b = 0 and x = y = -1 --> ab = 0 < 1 = xy.

III. |a| + |b| > |x| + |y|. Not necessarily true, consider a = b = 0 and x = y = -1 --> |a| + |b| = 0 < 2 = |x| + |y|.

Answer: A.

Hope its clear.
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Is this the only way - i mean hit and trial and then negate the options one by one. Aren't there chances of missing some exceptional combination and the method may turn out to be time consuming.....
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Note that the question asks for which of the solutions must be true, so in that case, as long as you can find atleast one solution for which it does not hold true, then it should be enough to discard that option.
And hence, you need not think about all the possible cobinations at all.
Which is pretty easy over here.

If a and b are each greater than x and y, which of the following must be true?

I. a + b > x + y
II. ab > xy
III. |a| + |b| > |x| + |y|

(A) I only
(B) II only
(C) I and II
(D) I and III
(E) I, II and III

If a and b are greater than x and y:

I. a + b > x + y

(-1) + (-2) > (-3) + (-4) = -3 > -7 VALID

(1) + (-1) > (-2) + (-4) = 0 > -6 VALID

(1) + (2) > (0) + (-1) = 3 > -1 VALID

II. ab > xy

(4)*(3) > (1)*(2) = 12 > 2 VALID

(4)*(3) > (-4)*(-5) = 12 > 20 INVALID

III. |a| + |b| > |x| + |y|

|3| + |4| > |1| + |2| = 7 > 3 VALID

|3| + |4| > |-5| + |-6| = 7 > 11 INVALID

(A)

I was stumped by the language on this one - I thought "If a and b are each greater than x and y, which of the following must be true? " Meant a >x , a > y and b > x and b> y

I think the main reason to get this question wrong, like I did, is not to read it properly. If a and b are each greater than x and y. I missed that "each", so I ended up with a>x and b>y, instead of a>x and a>y, and b>x and b>y, hence I got confused and picked the wrong answer.

Bunuel, my problem with testing cases is that it takes me at least 5mins to get these cases right, are these questions frequent on the GMAT because I'm having a hard time managing time on these questions.

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Let's evaluate the given statements.

Statement I: a + b > x + y

Since a and b are each greater than x and y, a > x and b > y. Adding these two inequalities together, we obtain a + b > x + y. Statement I must be true.

Statement II: ab > xy

If a = b = -1 and x = y = -2, then the condition "a and b are each greater than x and y" is satisfied. However, ab = 1 is not greater than xy = 4. Statement II is not necessarily true.

Statement III: |a| + |b| > |x| + |y|

We can use the same numbers that we used in the previous statement. If a = b = -1 and x = y = -2, then |a| + |b| = 1 + 1 = 2, but |x| + |y| = 2 + 2 = 4. This shows that |a| + |b| is not necessarily greater than |x| + |y|. Statement III is not necessarily true.

Answer: A
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Hi ScottTargetTestPrep

a and b are each greater than x and y-doesn't it mean that a>x, b>x & a>y, b>y?

Or else the question must mentioned the word "respectively" . How can someone decode this type of confusing wording?