BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Inequalities-division

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 107
Joined: Tue Oct 07, 2014 3:50 am

Inequalities-division

by mallika hunsur » Wed Apr 01, 2015 4:22 am
Image

Hi All,

Could anyone please explain the information in the question stem.

As I understand if-

mn<np<0 as in the Q stem, I can divide the inequality by n and get m<p<0, in which case statement 1 by itself is enough.

Why is this wrong..?


Thanks,
Mallika
Top
Source: — Data Sufficiency |
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Wed Apr 01, 2015 5:23 am
If mn < np < 0, is n < 1?

1) n is an integer.
2) m < p.
From the question stem:
mn < np
mn - np < 0
n(m-p) < 0.
Implication:
n and m-p are DIFFERENT SIGNS.

Statement 1: n is an integer
It's possible that n=1 and that m and p are negative values such that m-p=-1.
In this case, is n<1?
NO.
It's possible that n=-1 and that m and p are positive values such that m-p=1.
In this case, is n<1?
YES.
INSUFFICIENT.

Statement 2: m < p
Thus, m-p < 0, implying that n>0.
It's possible that n=1 and that m and p are negative values such that m-p =-1.
In this case, is n<1?
NO.
It's possible that n=1/2 and that m and p are negative values such that m-p=-1.
In this case, is n<1?
YES.
INSUFFICIENT.

Statements combined:
Since m-p<0 -- implying that n>0 -- n must be a POSITIVE INTEGER.
Thus, it is not possible that n<1.
SUFFICIENT.

The correct answer is C.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Master | Next Rank: 500 Posts
Posts: 107
Joined: Tue Oct 07, 2014 3:50 am

by mallika hunsur » Wed Apr 01, 2015 6:25 am
GMATGuruNY wrote:
If mn < np < 0, is n < 1?

1) n is an integer.
2) m < p.
From the question stem:
mn < np
mn - np < 0
n(m-p) < 0.
Implication:
n and m-p are DIFFERENT SIGNS.

Statement 1: n is an integer
It's possible that n=1 and that m and p are negative values such that m-p=-1.
In this case, is n<1?
NO.
It's possible that n=-1 and that m and p are positive values such that m-p=1.
In this case, is n<1?
YES.
INSUFFICIENT.

Statement 2: m < p
Thus, m-p < 0, implying that n>0.
It's possible that n=1 and that m and p are negative values such that m-p =-1.
In this case, is n<1?
NO.
It's possible that n=1/2 and that m and p are negative values such that m-p=-1.
In this case, is n<1?
YES.
INSUFFICIENT.

Statements combined:
Since m-p<0 -- implying that n>0 -- n must be a POSITIVE INTEGER.
Thus, it is not possible that n<1.
SUFFICIENT.

The correct answer is C.
Hi Mitch,

The key is not to divide the inequality inthe Qstem unless we know the sign of n..?Is this correct..?

I think this is where I went wrong, I just divided mn<np<0 by n, to happily get m<p<0 and chose statement 1
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Wed Apr 01, 2015 7:49 am
mallika hunsur wrote:
Hi Mitch,

The key is not to divide the inequality inthe Qstem unless we know the sign of n..?Is this correct..?

I think this is where I went wrong, I just divided mn<np<0 by n, to happily get m<p<0 and chose statement 1
Constraint: mn < np < 0.

Since the sign of n is unknown, dividing by n requires that we consider two cases:
If n>0, then dividing by n yields m < p < 0.
If n<0 then we must FLIP the inequality symbols when we divide by n, with the result that m > p > 0.

Because many students will neglect to consider both cases, I generally discourage multiplying or dividing an inequality by a variable whose sign is known.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top

GMAT/MBA Expert

User avatar
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

by Brent@GMATPrepNow » Wed Apr 01, 2015 7:58 am
If mn < np < 0, is n < 1?

1) n is an integer.
2) m < p.
Target question: Is n < 1?

Given: mn < np < 0

Statement 1: n is an integer.
There are several values of m, n and p that satisfy this condition. Here are two:
Case a: m = 3, n = -1 and p = 2, in which case n IS less than 1
Case b: m = -2, n = 3 and p = -1, in which case n is NOT less than 1
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: m < p
IMPORTANT: Notice that if we take this inequality, m < p, and multiply both sides, we get the given inequality, mn < np . Notice that the direction of the inequality STAYS THE SAME. This tells us that n is POSITIVE

Aside: This is an often-tested concept on the GMAT. If we multiply both sides of an inequality by a POSITIVE number, the direction of the inequality STAYS THE SAME. If we multiply both sides of an inequality by a NEGATIVE number, the direction of the inequality IS REVERSED.

So, statement 2 tells us that n is a POSITIVE number. Is this enough information to determine whether n < 1? No.
Consider these two conflicting cases:
Case a: m = -4, n = 1/2 and p = -2, in which case n IS less than 1
Case b: m = -2, n = 3 and p = -1, in which case n is NOT less than 1
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 2 tells us that n is POSITIVE
Statement 1 tells us that n is an INTEGER
So, n = 1 or 2 or 3 or 4 or...
This means that n is definitely NOT less than 1
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Post new topic Post Reply
• Page 1 of 1