If a and b are each greater than x and y, which of the : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 23 Jan 2017, 07:37

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Manager
Status: struggling with GMAT
Joined: 06 Dec 2012
Posts: 225
Concentration: Accounting
GMAT Date: 04-06-2013
GPA: 3.65
Followers: 14

Kudos [?]: 346 [1] , given: 46

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

### Show Tags

24 Feb 2013, 11:16
1
KUDOS
7
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

54% (01:47) correct 46% (00:50) wrong based on 732 sessions

### HideShow timer Statistics

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: 36609
Followers: 7099

Kudos [?]: 93528 [5] , given: 10568

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

### Show Tags

24 Feb 2013, 11:30
5
KUDOS
Expert's post
4
This post was
BOOKMARKED
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.
_________________
Intern
Joined: 24 Jan 2013
Posts: 9
Followers: 0

Kudos [?]: 9 [0], given: 5

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

### Show Tags

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|.

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)
Followers: 0

Kudos [?]: 16 [0], given: 10

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

### Show Tags

15 Jun 2013, 19:34
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.
_________________

Senior Manager
Joined: 13 May 2013
Posts: 472
Followers: 3

Kudos [?]: 160 [1] , given: 134

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

### Show Tags

01 Jul 2013, 08:13
1
KUDOS
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
Followers: 0

Kudos [?]: 10 [0], given: 8

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

### Show Tags

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
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13514
Followers: 577

Kudos [?]: 163 [0], given: 0

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

### Show Tags

07 Nov 2014, 09:38
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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13514
Followers: 577

Kudos [?]: 163 [0], given: 0

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

### Show Tags

13 Jan 2016, 02:53
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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Intern
Joined: 03 Feb 2016
Posts: 10
Followers: 0

Kudos [?]: 1 [0], given: 77

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

### Show Tags

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.
Re: If a and b are each greater than x and y, which of the   [#permalink] 11 Feb 2016, 15:57
Similar topics Replies Last post
Similar
Topics:
2 If x and y are different prime numbers, each greater than 2, which of 2 17 Feb 2016, 03:38
For each value of y greater than 1 27 Feb 2013, 10:14
12 If x and y are distinct prime numbers, each greater than 2, 9 13 Nov 2010, 10:09
24 If y ≠ 3 and 3x/y is a prime integer greater than 2, which 21 01 Apr 2009, 01:27
19 If y 3 and 3x/y is a prime integer greater than 2, which of 9 30 Mar 2009, 04:02
Display posts from previous: Sort by