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If a, b, and c are positive numbers, is a < b < c

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by Shalabh's Quants » Fri Apr 13, 2012 9:50 pm
vinodhinir wrote:If a, b, and c are positive numbers, is a < b < c

(1) ab = bc
(2) ac = bc

OA:D Explain.
Stat. 1....

Since ab = bc, by cancelling b, we get a = c => It means a is not less than c.Ans is No.

Sufficient condn.

Stat. 2....

Since ac = bc, by cancelling c, we get a = b => It means a is not less than b.Ans is No.

Sufficient condn.
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by GMATGuruNY » Fri Apr 13, 2012 10:00 pm
vinodhinir wrote:If a, b, and c are positive numbers, is a < b < c

(1) ab = bc
(2) ac = bc

OA:D Explain.
Statement 1: ab = bc
Since b>0, we can divide by b.
The result: a=c.
Thus, it is not true that a<c.
SUFFICIENT.

Statement 2: ac = bc
Since c>0, we can divide by c.
The result: a=b.
Thus, it is not true that a<b.
SUFFICIENT.

The correct answer is D.
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by vinodhinir » Sun Apr 15, 2012 8:06 pm
it is not true that a<c.
but how can we conclude that a is not less than b

lets say if b is 3 and a is 2 then a<b ...
if it s the other way round then a > b

how can this be a sufficient condn ?

I know am missing something very trivial here,but cannot think of what could it be ...
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by GMATGuruNY » Mon Apr 16, 2012 3:20 am
vinodhinir wrote:it is not true that a<c.
but how can we conclude that a is not less than b

lets say if b is 3 and a is 2 then a<b ...
if it s the other way round then a > b

how can this be a sufficient condn ?

I know am missing something very trivial here,but cannot think of what could it be ...
The information in statement 1 (a=c) renders the value of b irrelevant.
Since a=c, it is not possible that a<b<c.
SUFFICIENT.

There are only 3 possible scenarios:
If a=c and a<b, then c<b. Thus, a<b<c is not true.
If a=c and a=b, then a=b=c. Thus, a<b<c is not true.
If a=c and a>b, then c>b. Thus, a<b<c is not true.
In each case, it is not true that a<b<c.
SUFFICIENT.

Similar reasoning can be applied to statement 2.
Last edited by GMATGuruNY on Mon Apr 16, 2012 5:55 am, edited 1 time in total.
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by Birottam Dutta » Mon Apr 16, 2012 5:53 am
You have to understand that if you can prove any of a<b, a<c or b<c false, then it is sufficient to answer the question.

Remember in DS, the answer need not always be a correct one, even if the statements can prove the question to be incorrect, even that is considered as a sufficient statement.
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