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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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58% (00:48) correct 42% (00:47) wrong based on 1020 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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24 Feb 2013, 12:30




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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.
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]
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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.
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]
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01 Jul 2013, 09:13
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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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



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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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Re: If a and b are each greater than x and y, which of the [#permalink]
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06 Jul 2018, 16:15
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
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