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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] New post 24 Feb 2013, 11:16
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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
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Re: If a and b are each greater than x and y, which of the [#permalink] New post 24 Feb 2013, 11:30
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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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Re: If a and b are each greater than x and y, which of the [#permalink] 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.....
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Re: If a and b are each greater than x and y, which of the [#permalink] New post 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|.

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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Re: If a and b are each greater than x and y, which of the [#permalink] New post 01 Jul 2013, 08:13
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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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Re: If a and b are each greater than x and y, which of the [#permalink] 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
Re: If a and b are each greater than x and y, which of the   [#permalink] 05 Sep 2013, 06:23
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