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Data Sufficiency question from Manhattan GMAT CAT

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by tomada » Tue Feb 11, 2014 2:30 pm
I purchased 6 CATs through the Manhattan GMAT website. This Data Sufficiency question comes from one such test.
My answer conflicts with the answer provided by Manhattan GMAT and, after reviewing my logic multiple times, I'm still not able to see why my answer is incorrect. I won't post the answer given by Manhattan GMAT until a few people comment.


Is the product st negative?

(1) s2 - s < 0
(2) (s-4)/(t-3) = 1
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Tue Feb 11, 2014 2:47 pm
tomada wrote: Is the product st negative?

(1) s² - s < 0
(2) (s-4)/(t-3) = 1
Target question: Is the product st negative?

Statement 1: s² - s < 0
No information about t, so there's no way to determine whether or not st is negative.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: (s-4)/(t-3) = 1
This means that s - 4 = t - 3
Rearrange to get: t = s - 1
There are several values of s and t that satisfy this condition. Here are two:
Case a: s = 4 and t = 3, in which case st is positive
Case b: s = 0.5 and t = -0.5, in which case st is negative
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that s² - s < 0
Factor to get: s(s - 1) < 0

From statement 2, we determined that t = s - 1

So, let's take s(s - 1) < 0 and replace (s - 1) with t to get: s < t
So, st must be negative
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

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by Bill@VeritasPrep » Tue Feb 11, 2014 2:48 pm
For s*t to be negative, either s or t must be negative.

From statement 1:

s^2 - s < 0

s^2 < s

If squaring s gives you a smaller value, then s must be a positive fraction less than 1. Since we don't know anything about t, we don't know if the product is negative. Insufficient

From statement 2:

(s-4)/(t-3) = 1

s - 4 = t - 3

s = t + 1

We can get a positive product (if t=3 and s=4, for example) or a negative product ( t= -1/2 and s = 1/2) here, so it is also insufficient.

Together:

If 0 < s < 1, and s = t + 1, then 0 < t+1 < 1, or -1 < t < 0. Thus, s is a positive fraction, t is a negative fraction, and s*t is negative. Sufficient.
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by Bill@VeritasPrep » Tue Feb 11, 2014 2:50 pm
Brent@GMATPrepNow wrote:
Statement 2: (s-4)/(t-3) = 1
This means that s - 4 = t - 3
Rearrange to get: t = s - 1
There are several values of s and t that satisfy this condition. Here are two:
Case a: s = 4 and t = 3, in which case st is positive
Case b: s = 0.5 and t = -0.5, in which case st is negative
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Ha, those are the exact values I tested. Great minds and all that :D
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by Brent@GMATPrepNow » Tue Feb 11, 2014 3:08 pm
Bill@VeritasPrep wrote: Ha, those are the exact values I tested. Great minds and all that :D
Perhaps we were separated at birth?

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by tomada » Tue Feb 11, 2014 3:20 pm
I thank both of you for responding and for highlighting the mistake I made. I proceeded from a baseless assumption that 'S' and 'T' were integers. When I saw the values "-1/2" and "1/2" to show how the product could be negative, I emitted a silently potent "ohhhhhh".
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by Bill@VeritasPrep » Tue Feb 11, 2014 3:24 pm
tomada wrote:I thank both of you for responding and for highlighting the mistake I made. I proceeded from a baseless assumption that 'S' and 'T' were integers. When I saw the values "-1/2" and "1/2" to show how the product could be negative, I emitted a silently potent "ohhhhhh".
Trust me, I know that feeling :D Once you get burned a few times, you start to catch those little twists in the wording. DS questions are very deliberate and consistent with the terminology used.
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