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
Target Test Prep is 20% off right now!
Use code FLASH20
Available with Beat the GMAT members only code
MORE DETAILS
Data Sufficiency question from Manhattan GMAT CAT
This topic has expert replies
GMAT/MBA Expert
-
Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Target question: Is the product st negative?tomada wrote: Is the product st negative?
(1) s² - s < 0
(2) (s-4)/(t-3) = 1
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
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
-
Bill@VeritasPrep
- GMAT Instructor
- Posts: 1248
- Joined: Thu Mar 29, 2012 2:57 pm
- Location: Everywhere
- Thanked: 503 times
- Followed by:192 members
- GMAT Score:780
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.
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.
Join Veritas Prep's 2010 Instructor of the Year, Matt Douglas for GMATT Mondays
Visit the Veritas Prep Blog
Try the FREE Veritas Prep Practice Test
Visit the Veritas Prep Blog
Try the FREE Veritas Prep Practice Test
-
Bill@VeritasPrep
- GMAT Instructor
- Posts: 1248
- Joined: Thu Mar 29, 2012 2:57 pm
- Location: Everywhere
- Thanked: 503 times
- Followed by:192 members
- GMAT Score:780
Ha, those are the exact values I tested. Great minds and all thatBrent@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
Join Veritas Prep's 2010 Instructor of the Year, Matt Douglas for GMATT Mondays
Visit the Veritas Prep Blog
Try the FREE Veritas Prep Practice Test
Visit the Veritas Prep Blog
Try the FREE Veritas Prep Practice Test
GMAT/MBA Expert
-
Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Perhaps we were separated at birth?Bill@VeritasPrep wrote: Ha, those are the exact values I tested. Great minds and all that
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
-
tomada
- Master | Next Rank: 500 Posts
- Posts: 406
- Joined: Mon Jan 25, 2010 11:36 am
- Location: Syracuse, NY
- Thanked: 23 times
- Followed by:4 members
- GMAT Score:740
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".
I'm really old, but I'll never be too old to become more educated.
-
Bill@VeritasPrep
- GMAT Instructor
- Posts: 1248
- Joined: Thu Mar 29, 2012 2:57 pm
- Location: Everywhere
- Thanked: 503 times
- Followed by:192 members
- GMAT Score:780
Trust me, I know that feelingtomada 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".
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.Join Veritas Prep's 2010 Instructor of the Year, Matt Douglas for GMATT Mondays
Visit the Veritas Prep Blog
Try the FREE Veritas Prep Practice Test
Visit the Veritas Prep Blog
Try the FREE Veritas Prep Practice Test
