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Re: False inequality [#permalink]
15 Nov 2009, 20:00

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Essentially, we need to find the statement that could be false if all the other statements are true.

The first thing that jumps out to me is statements A and C:

(A) a < b (C) a+c < b+c

Regardless of the value of c, these statement are either both false or both true. Since only statement CAN be false, we can eliminate these two.

(E) a < b+c+d

Since c and d are both positive integers, and we have determined that statement A is true, statement E must be true as well. This leaves us with:

(B) c < d (D) a+c < b+d

Since we know statement A (a < b) to be true, if statement B is true, statement D MUST be true. However, if statement D is true, as long as c-d < b-a, statement B does NOT have to be true.

Therefore, the answer is B: c < d . Good question, +1.

Re: a, b, c, d are positive integers such that exactly one of [#permalink]
17 Jun 2013, 09:48

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Bunuel wrote:

a, b, c, d are positive integers such that exactly one of the following inequalities is false. Which inequality is false?

(A) a<b

(B) c<d

(C) a+c<b+c

(D) a+c<b+d

(E) a<b+c+d

I'm not sure whether we can see such problem on GMAT, but I found this one quite interesting so posting for discussion.

An algebrical approach:

first of all (A) a<b and (C) a+c<b+c are the same: both tell us that a<b. Since exactly one inequality is false, both A and C must be true. With a<b enstablished we can focus on

(B) c<d

(D) a+c<b+d

(E) a<b+c+d

E must be true since a<b also a<b+(+veNumber)+(+veNumber) is true as well.

(B) 0<d-c (D) a-b<d-c but since a-b is negative => -ve<d-c

(B) d-c>0(>-ve) number (D) d-c>-ve number

if B is true, also D is true for sure (d-c=77>-ve and 7>0) this goes against the text of the question if D is true, B could be false (d-c=-1-1>-ve(-2)(for example) and -1>0 FALSE) Hence B must be the false inequality

Simpler approach: given a<b if B is true c<d also D is true a+c<b+d, once more this is against the question _________________

It is beyond a doubt that all our knowledge that begins with experience.

Re: a, b, c, d are positive integers such that exactly one of [#permalink]
09 Sep 2013, 05:32

C, D & E depend on the true/false of the equation A (a < b) C ( a+c<b+c ) will be true for any a < b D ( a+c<b+d ) can be true for any a < b . It can be true when c > d, if c-d < b-a E is true always if a < b. Since C D E depend on A for the major part, the one inequality that can be wrong is B