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

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Manager
Joined: 29 Nov 2011
Posts: 76
If a, b, and c are positive numbers, is a < b < c?  [#permalink]

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13 Apr 2012, 22:21
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If a, b, and c are positive numbers, is a < b < c?

(1) ab = bc
(2) ac = bc
Senior Manager
Joined: 13 Mar 2012
Posts: 254
Concentration: Operations, Strategy

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14 Apr 2012, 00:14
Smita04 wrote:
If a, b, and c are positive numbers, is a < b < c?

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

statement 1:

b(a-c)=0
i.e. either b=0 or a=c

given b>0
hence a=c

=> a IS NOT LESS THAN c.
sufficient

statement 2:

similarly by above reasoning a=b
so NO
hence SUfficient

hence D

HOPE THIS HELPS...!!
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14 Apr 2012, 01:45
If a, b, and c are positive numbers, is a < b < c?

(1) ab = bc --> since b>0 we can reduce given equation by b and we'll get a = c, so a < b < c is not true. Sufficient.
(2) ac = bc --> since c>0 we can reduce given equation by c and we'll get a = b, so a < b < c is not true. Sufficient.

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Re: If a, b, and c are positive numbers, is a < b < c?  [#permalink]

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26 Nov 2017, 11:25
Smita04 wrote:
If a, b, and c are positive numbers, is a < b < c?

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

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 3 variables and 0 equation, we need to consider both conditions together first.

Condition 1) & 2)
Since b is positive, ab = bc ⇔ a = c.
Since c is positive, ac = bc ⇔ a = b.
Thus the answer to a < b < c is no.
They are sufficient by CMT (Common Mistake Type) 1, since the answer is no.

In addition, since this is an inequality question (one of the key question areas), we should also consider choices A and B by CMT 4(A).

Condition 1)
Since b is positive, ab = bc ⇔ a = c.
Thus the answer to a < b < c is no.
This is sufficient by CMT1.

Condition 2)
Since c is positive, ac = bc ⇔ a = b.
This is sufficient by CMT1.

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.
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Re: If a, b, and c are positive numbers, is a < b < c? &nbs [#permalink] 26 Nov 2017, 11:25
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