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

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

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New post 24 Feb 2013, 11:16
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A
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Difficulty:

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Question Stats:

57% (01:16) correct 43% (01:12) wrong based on 1095 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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Re: If a and b are each greater than x and y, which of the  [#permalink]

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New post 24 Feb 2013, 11:30
11
1
7
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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Joined: 24 Jan 2013
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Re: If a and b are each greater than x and y, which of the  [#permalink]

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New post 25 Feb 2013, 06:43
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|.

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.....
Intern
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Joined: 22 May 2013
Posts: 46
Concentration: General Management, Technology
GPA: 3.9
WE: Information Technology (Computer Software)
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Re: If a and b are each greater than x and y, which of the  [#permalink]

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New post 15 Jun 2013, 19:34
1
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|.

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.....


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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PS: Like my approach? Please Help me with some Kudos. :-)

Senior Manager
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Posts: 425
Re: If a and b are each greater than x and y, which of the  [#permalink]

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New post 01 Jul 2013, 08:13
1
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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Re: If a and b are each greater than x and y, which of the  [#permalink]

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New post 05 Sep 2013, 06:23
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
Intern
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Posts: 10
Re: If a and b are each greater than x and y, which of the  [#permalink]

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New post 11 Feb 2016, 15:57
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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Posts: 73
Re: If a and b are each greater than x and y, which of the  [#permalink]

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New post 06 Jul 2018, 15:15
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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Re: If a and b are each greater than x and y, which of the &nbs [#permalink] 06 Jul 2018, 15:15
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If a and b are each greater than x and y, which of the

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