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

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Manager
Status: struggling with GMAT
Joined: 06 Dec 2012
Posts: 213
Concentration: Accounting
GMAT Date: 04-06-2013
GPA: 3.65
If a and b are each greater than x and y, which of the [#permalink]

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24 Feb 2013, 12:16
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Question Stats:

55% (01:47) correct 45% (00:50) wrong based on 861 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
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 39593
Re: If a and b are each greater than x and y, which of the [#permalink]

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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|.

Hope its clear.
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Intern
Joined: 24 Jan 2013
Posts: 9
Re: If a and b are each greater than x and y, which of the [#permalink]

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25 Feb 2013, 07:43
Bunuel wrote:
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|.

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.....
Intern
Joined: 22 May 2013
Posts: 49
Concentration: General Management, Technology
GPA: 3.9
WE: Information Technology (Computer Software)
Re: If a and b are each greater than x and y, which of the [#permalink]

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15 Jun 2013, 20:34
jubinder wrote:
Bunuel wrote:
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|.

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.....

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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Joined: 13 May 2013
Posts: 469
Re: If a and b are each greater than x and y, which of the [#permalink]

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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)
Current Student
Joined: 26 Jul 2012
Posts: 63
Re: If a and b are each greater than x and y, which of the [#permalink]

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05 Sep 2013, 07:23
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
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15918
Re: If a and b are each greater than x and y, which of the [#permalink]

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07 Nov 2014, 10:38
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Joined: 09 Sep 2013
Posts: 15918
Re: If a and b are each greater than x and y, which of the [#permalink]

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13 Jan 2016, 03:53
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Joined: 03 Feb 2016
Posts: 10
Re: If a and b are each greater than x and y, which of the [#permalink]

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11 Feb 2016, 16:57
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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Joined: 09 Sep 2013
Posts: 15918
Re: If a and b are each greater than x and y, which of the [#permalink]

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08 Apr 2017, 10:34
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If a and b are each greater than x and y, which of the   [#permalink] 08 Apr 2017, 10:34
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