 It is currently 20 Mar 2019, 20:16 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # np < 0  Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
Moderator  Joined: 18 Apr 2015
Posts: 5835
Followers: 93

Kudos [?]: 1143 , given: 5441

np < 0 [#permalink]
Expert's post 00:00

Question Stats: 87% (00:22) correct 12% (00:32) wrong based on 70 sessions

np < 0

 Quantity A Quantity B | p + n | |p| + |n|

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

_________________ GRE Prep Club Legend  Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 105

Kudos [?]: 1776  , given: 397

Re: np < 0 [#permalink]
3
KUDOS
Expert's post
Explanation

This is a very popular theorem of mathematics known as the Triangle inequality

Triangle Inequality: $$|a + b| \leq |a| + |b|$$

Now the Left hand side and right hand side are equal if and only if both a and b are either positive of negative at the same time.

Now looking at our problem: np < 0. This means either n is negative p is positive or p is negative n is positive.

By triangle equality we know that $$|n + p| < |n| + |p|$$. In this case equality is not an option as n and p can not be positive or negative at the same time.

Hence clearly quantity B is greater.
_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

Intern Joined: 09 Feb 2018
Posts: 1
Followers: 0

Kudos [?]: 0 , given: 1

Re: np < 0 [#permalink]
I understand the triangle inequality theorem, but have never seen it written this way with the absolute values like this. Can you please clarify? Manager  Joined: 15 Jan 2018
Posts: 147
GMAT 1: Q V
Followers: 3

Kudos [?]: 182  , given: 0

Re: np < 0 [#permalink]
4
KUDOS
How about we look at the problem from a totally different perspective? We've been told that np < 0. Thus, one must be negative and one positive. In quantity A, the two of them are being added. This means the negative will actually be subtracted from the positive, so whatever results will be smaller than whichever had the larger absolute value. Trying numbers will illustrate. Imagine p = -4 and n = 10. Thus, quantity A would be |-4 + 10|, which is 6. If we pick p = 12 and n = -3, quantity A would be |12 - 3|, which is 9. Either way, the answer is smaller than the bigger one.

For quantity B, however, we're going to get something bigger than the one with absolute value, since we're actually adding the absolute value of the smaller one to the absolute value of the larger one. If we use the same numbers we did before, -4 and 10, we get 14, which is larger than quantity A's value, which would be 6. If we use our second set of numbers, 12, and -3, we get 15, which is also larger than quantity A's value of 9. No matter what numbers we pick, quantity B will always be bigger, so the answer is B. Hope that helped.
_________________

-
-
-
-
-

Need help with GRE math? Check out our ground-breaking books and app. Intern Joined: 11 Jan 2018
Posts: 44
Followers: 0

Kudos [?]: 33  , given: 7

Re: np < 0 [#permalink]
2
KUDOS
As the product of n and p is negative. This implies that one of the two numbers is negative and the other is positive.

So the mode of summation of negative and one positive is always less than the individual mode of the two numbers.

Thus, Quantity B is greater than Quantity A.

Choice B is correct.
_________________

Persistence >>>>>>> Success

Don't say thanks, just give KUDOS.
1 kudos = 1000 Thanks Re: np < 0   [#permalink] 17 Feb 2018, 01:05
Display posts from previous: Sort by

# np < 0  Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.