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If a, b and c are integers such that b > a, is b+c > a [#permalink]
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25 Sep 2007, 07:33
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If a, b and c are integers such that b > a, is b+c > a ?
(1) c > a
(2) abc > 0



Director
Joined: 11 Sep 2006
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From stem, all variables are integers, but no indication whether they are negative, nonnegative, etc. so negative, positive and zero must be tried. From statement 1  c>a. That's fine, but what if a = 2, c is 1, and b is 1? Then b+c not bigger than a. Could plug in numbers to make statement true as well  therefore insufficient.
From statement 2  abc>0. So all integers are positive. but no indication that they are different integers. If a = 1, b = 2, and c = 1, then answer is no. But would be easy to plug in other #'s to make it true. So statement 2 also insufficient.
Together  c >a, b>a, all numbers are positive...therefore b+c>a. Sufficient.
C it is.
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GMAT Instructor
Joined: 04 Jul 2006
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uphillclimb wrote: From stem, all variables are integers, but no indication whether they are negative, nonnegative, etc. so negative, positive and zero must be tried. From statement 1  c>a. That's fine, but what if a = 2, c is 1, and b is 1? Then b+c not bigger than a. Could plug in numbers to make statement true as well  therefore insufficient. From statement 2  abc>0. So all integers are positive. but no indication that they are different integers. If a = 1, b = 2, and c = 1, then answer is no. But would be easy to plug in other #'s to make it true. So statement 2 also insufficient. Together  c >a, b>a, all numbers are positive...therefore b+c>a. Sufficient. C it is.
Not necessarily true, but otherwise perfect!



Intern
Joined: 15 Mar 2007
Posts: 45

kevincan wrote: uphillclimb wrote: From stem, all variables are integers, but no indication whether they are negative, nonnegative, etc. so negative, positive and zero must be tried. From statement 1  c>a. That's fine, but what if a = 2, c is 1, and b is 1? Then b+c not bigger than a. Could plug in numbers to make statement true as well  therefore insufficient. From statement 2  abc>0. So all integers are positive. but no indication that they are different integers. If a = 1, b = 2, and c = 1, then answer is no. But would be easy to plug in other #'s to make it true. So statement 2 also insufficient. Together  c >a, b>a, all numbers are positive...therefore b+c>a. Sufficient. C it is. Not necessarily true, but otherwise perfect!
I wud say it is B.
Here's an example:
Given:
1. b > a ( From Question Stem)
2. abc > 0 ( From Statement II)
From 2: either all are positive or two of them are negative.
eg 1: a=3;b=2;c=1 ==> abc>0(holds); b>a(holds) b+c=(1) > a(3)(holds)
eg 2: a=3;b=2;c=1 ==> abc>0(holds); b>a(holds); b+c(1) > a(3) holds
eg: a=1;b=2;c=1 ==> abc>0(holds);b>a(holds); b+c(3) > a(1) (holds)
Statement II alone is sufficient.
Any sample of numbers for which this fails?



GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5043
Location: Singapore

St1:
c > a
If c = 1, a = 2, and b = 0, then b>a and b+c > a
If c = 2, a = 3, and b = 1, then b>a but b+c = a
Insufficient.
St2:
abc > 0
Could be all positive, or two negatives and one positive.
All positive:
b = 2, a = 1, c = 3, then b+c > a
b+c > a > for b positive, a and c negative
b+c > a > for c positive, a and b negative
(no need to test a positive and b & c negative as b > a and c > a)
Sufficient.
Ans C
Last edited by ywilfred on 25 Sep 2007, 19:06, edited 1 time in total.



Intern
Joined: 15 Mar 2007
Posts: 45

This sample set in your inputs fails to hold the condition b > a provided in the question stem.
b = 1, c = 2, a = 6, then b+c < a



GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5043
Location: Singapore

done_gre_now_gmat wrote: This sample set in your inputs fails to hold the condition b > a provided in the question stem.
b = 1, c = 2, a = 6, then b+c < a
well, take it out and the answer is still C =)



CEO
Joined: 29 Mar 2007
Posts: 2559

Re: DS Three variable inequality [#permalink]
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25 Sep 2007, 19:08
kevincan wrote: If a, b and c are integers such that b > a, is b+c > a ?
(1) c > a (2) abc > 0
C.
S1: b>a and c>a. u can think of many + values that will make this work. to make this not work try negs. a>b: 2>3 c>a: 2>3
4 not greater than 3. so S1 insuff.
S2: abc>0. could all be + or could be two negatives
Insuff.
1 and 2. b/c c>a and b>a. and abc>0. only positives work here.



VP
Joined: 09 Jul 2007
Posts: 1100
Location: London

Re: DS Three variable inequality [#permalink]
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25 Sep 2007, 19:11
1 and 2. b/c c>a and b>a. and abc>0. only positives work here.[/
should all necessarily be positive: c=3, b=1 and a=2 still holds true,




Re: DS Three variable inequality
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25 Sep 2007, 19:11






