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mun23
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If a and b are each greater than x and y, which of the 24 Feb 2013, 12:16
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65% (01:20) correct 35% (01:14) wrong based on 2162 sessions

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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
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A
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Bunuel
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If a and b are each greater than x and y, which of the 24 Feb 2013, 12:30
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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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If a and b are each greater than x and y, which of the 25 Feb 2013, 07:43
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Bunuel
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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If a and b are each greater than x and y, which of the 15 Jun 2013, 20:34
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Bunuel
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.


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.....
Show more

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.
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If a and b are each greater than x and y, which of the 01 Jul 2013, 09:13
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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)
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If a and b are each greater than x and y, which of the 05 Sep 2013, 07:23
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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
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If a and b are each greater than x and y, which of the 11 Feb 2016, 16:57
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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.
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If a and b are each greater than x and y, which of the 06 Jul 2018, 16:15
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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.

Posted from my mobile device
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If a and b are each greater than x and y, which of the 20 Jul 2022, 22:20
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mun23
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
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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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If a and b are each greater than x and y, which of the 20 Feb 2023, 21:56
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ScottTargetTestPrep
mun23
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

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?
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If a and b are each greater than x and y, which of the 11 Jan 2025, 15:55
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Hello! Is it possible to generalize that if a number a is greater than x and also greater than y, a will be always greater or equal to the sum of both numbers (x+y)?
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If a and b are each greater than x and y, which of the 11 Jan 2025, 16:01
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No, suppose a=11, x=10, and y=9; a < x+y

patronumbeagle
Hello! Is it possible to generalize that if a number a is greater than x and also greater than y, a will be always greater or equal to the sum of both numbers (x+y)?
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If a and b are each greater than x and y, which of the 21 Mar 2026, 07:01
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