GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 23 Oct 2019, 11:36

Close

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
Your Progress

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.

Close

Request Expert Reply

Confirm Cancel

Is kr<0?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 8033
GMAT 1: 760 Q51 V42
GPA: 3.82
Is kr<0?  [#permalink]

Show Tags

New post 17 May 2017, 01:31
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

63% (01:17) correct 37% (01:20) wrong based on 178 sessions

HideShow timer Statistics

Is kr<0?

1) \(k^2r^3<0\)
2) \(|k+r|<|k|+|r|\)

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Intern
Intern
avatar
B
Joined: 29 Jul 2013
Posts: 8
Location: India
Concentration: Human Resources, Strategy
Schools: MBS '21 (A)
WE: Information Technology (Computer Software)
GMAT ToolKit User
Re: Is kr<0?  [#permalink]

Show Tags

New post 17 May 2017, 09:49
1
condition 1 : k^2r^3<0, basically is the same as telling r<0, ignoring squares as it's always positive. We still dont know if k is positive or not, therefore Not Sufficient

Condition 2 : |k+r|<|k|+|r|

there are 4 scenarios we need to consider of which only 2 conditions are there where this rule will work
k is pos and r is pos (rule doesnt work)
k is pos and r is neg (rule works)
k is neg and r is pos (rule works)
k is neg and r is neg (rule doesnt work)

since for the conditions that work, since either k or r is negative, the product will be negative, hence this condition is Sufficient.
Retired Moderator
avatar
P
Joined: 22 Aug 2013
Posts: 1428
Location: India
Re: Is kr<0?  [#permalink]

Show Tags

New post 17 May 2017, 11:31
1
We need to know two things for this question.

First, product of two numbers is < 0 (negative) only if one of them is positive and the other is negative.

Secondly, lets compare |a+b| with |a| + |b|
|a| means absolute value of a, or the distance of a from zero on the number line.


If both a & b are positive, then |a+b| = |a| + |b| (you can check by substituting positive values for a & b)

If both a & b are negative, then also |a+b| = |a| + |b| (you can check by substituting negative values for a & b)

If both a & b are zero, then also |a+b| = |a| + |b|

If ONE of a & b is zero (other can be positive or negative), still |a+b| = |a| + |b|

But if one of a & b is positive and the other is negative, then |a+b| < |a| + |b|. Eg, if a=3 and b=-2, then |a+b| = |3-2| = 1,
but |a|+|b| = |3| + |-2| = 3+2 = 5

Now lets look at the statements.

Statement 1. k^2 r^3 <0
k^2 cannot be negative, which means r^3 < 0 or r < 0.
But we don't know anything about k, so we cannot say whether product of k & r will be negative or positive. Insufficient.

Statement 2. |k+r| < |k| + |r|
This can only happen when one of k and r is positive and other is negative (as discussed above).
So product kr < 0. Sufficient.

Hence answer is B
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 8033
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Is kr<0?  [#permalink]

Show Tags

New post 19 May 2017, 01:50
==> For con 1), you ignore the square, so t<0, and for con 2), you get kr<0, hence yes, it is sufficient. The reason is that from \((|k+r|)^2<(|k|+|r|)^2\), you get \(k^2+r^2+2kr<k^2+r^2+2|kr|\), and if you get rid of \(k^2+r^2\) from both sides, you get 2kr<2|kr|, then kr<|kr|, which becomes kr<0.

The answer is B.
Answer: B
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13420
Re: Is kr<0?  [#permalink]

Show Tags

New post 09 Aug 2018, 10:26
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Bot
Re: Is kr<0?   [#permalink] 09 Aug 2018, 10:26
Display posts from previous: Sort by

Is kr<0?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne