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a, b, c, d are positive integers such that exactly one of

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a, b, c, d are positive integers such that exactly one of [#permalink] New post 15 Nov 2009, 17:15
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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.
[Reveal] Spoiler: OA

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Re: False inequality [#permalink] New post 15 Nov 2009, 17:27
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.


I'm going to guess B

A). a < b to prove this false let's say a = 4 and b = 3 this would make C) false as well and only one can be false

we are left with B, D, E

c<d

let's say c = 4 and d = 3 to prove this false

and let's say a = 1 and b = 5

d) 1 + 4 < 5 + 3 is still true
e)1 < 5 + 3 + 4 still true

so my guess is B if i'm reading the question correctly
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Re: False inequality [#permalink] New post 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.
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Re: False inequality [#permalink] New post 16 Nov 2009, 11:38
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Re: False inequality [#permalink] New post 16 Nov 2009, 20:10
Definitely an interesting question... I have to work on my inequalities
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Re: False inequality [#permalink] New post 16 Nov 2009, 20:13
do you have a set of ds geometry?

thanks for the inequality set
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Re: a, b, c, d are positive integers such that exactly one of [#permalink] New post 17 Jun 2013, 04:51
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Re: a, b, c, d are positive integers such that exactly one of [#permalink] New post 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=7 7>-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
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Re: a, b, c, d are positive integers such that exactly one of [#permalink] New post 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
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Re: a, b, c, d are positive integers such that exactly one of [#permalink] New post 10 Sep 2013, 00:24
I substituted a,b,c,d as 2,1,3,4 and 1,2,4,3 (as only A or B is true ).. plugged in the options.. got the right anser in 2 mins..
Re: a, b, c, d are positive integers such that exactly one of   [#permalink] 10 Sep 2013, 00:24
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