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

 It is currently 21 Sep 2018, 08:52

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

M30-19

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49300

Show Tags

16 Sep 2014, 01:46
1
13
00:00

Difficulty:

95% (hard)

Question Stats:

43% (01:54) correct 57% (02:12) wrong based on 91 sessions

HideShow timer Statistics

If $$m^2 < 225$$ and $$n - m = -10$$, what is the difference between the smallest possible integer value of $$3m + 2n$$ and the greatest possible integer value of $$3m + 2n$$?

A. -190
B. -188
C. -150
D. -148
E. -40

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 49300

Show Tags

16 Sep 2014, 01:46
2
4
Official Solution:

If $$m^2 < 225$$ and $$n - m = -10$$, what is the difference between the smallest possible integer value of $$3m + 2n$$ and the greatest possible integer value of $$3m + 2n$$?

A. -190
B. -188
C. -150
D. -148
E. -40

This question is about algebraic manipulations with inequalities.

From $$n - m = -10$$ it follows that $$n=m-10$$. Thus, $$3m + 2n=3m+2(m-10)=5m-20$$. So, we need to find the difference between the smallest possible integer value of $$5m-20$$ and the greatest possible integer value of $$5m-20$$.

Now, lets' work on $$m^2 < 225$$:

Take the square root from both sides: $$|m| < 15$$;

Get rid of the modulus sign: $$-15 < m < 15$$;

Multiply all three parts by 5: $$-75 < 5m < 75$$;

Subtract 20 from all three parts: $$-95 < 5m -20 < 55$$;

From $$-95 < 5m -20 < 55$$ it follows that the smallest possible integer value of $$5m-20$$ is -94 and the greatest possible integer value of $$5m-20$$ is 54.

Therefore, the difference is $$-94 - 54= -148$$.

_________________
Intern
Joined: 06 Jun 2014
Posts: 5

Show Tags

25 May 2015, 00:02
Hello,

For the below solution is it also possible to directly put the least possible value of m(-14) and the greatest possible value of m(14) in the equation( 5m-20)?

Regards,
Mahuya

If $$m^2 < 225$$ and $$n - m = -10$$, what is the difference between the smallest possible integer value of $$3m + 2n$$ and the greatest possible integer value of $$3m + 2n$$?

A. -190
B. -188
C. -150
D. -148
E. -40

This question is about algebraic manipulations with inequalities.

From $$n - m = -10$$ it follows that $$n=m-10$$. Thus, $$3m + 2n=3m+2(m-10)=5m-20$$. So, we need to find the difference between the smallest possible integer value of $$5m-20$$ and the greatest possible integer value of $$5m-20$$.

Now, lets' work on $$m^2 < 225$$:

Take the square root from both sides: $$|m| < 15$$;

Get rid of the modulus sign: $$-15 < m < 15$$;

Multiply all three parts by 5: $$-75 < 5m < 75$$;

Subtract 20 from all three parts: $$-95 < 5m -20 < 55$$;

From $$-95 < 5m -20 < 55$$ it follows that the smallest possible integer value of $$5m-20$$ is -94 and the greatest possible integer value of $$5m-20$$ is 54.

Therefore, the difference is $$-94 - 54= -148$$.

Math Expert
Joined: 02 Sep 2009
Posts: 49300

Show Tags

25 May 2015, 01:53
mahuya78 wrote:
Hello,

For the below solution is it also possible to directly put the least possible value of m(-14) and the greatest possible value of m(14) in the equation( 5m-20)?

Regards,
Mahuya

We are NOT told that m is an integer, hence from -15<m<15 saying that the minimum value of m is -14 and the maximum value of m is 14 is wrong.
_________________
Current Student
Joined: 28 Aug 2016
Posts: 90
Concentration: Strategy, General Management

Show Tags

28 Sep 2016, 08:52
Bunuel wrote:
mahuya78 wrote:
Hello,

For the below solution is it also possible to directly put the least possible value of m(-14) and the greatest possible value of m(14) in the equation( 5m-20)?

Regards,
Mahuya

We are NOT told that m is an integer, hence from -15<m<15 saying that the minimum value of m is -14 and the maximum value of m is 14 is wrong.

That is exactly where I got stuck and ended up guessing the answer to be the closest number I got with max = 14 min = -14. Gotta read the question more carefully!
Intern
Joined: 09 Nov 2014
Posts: 4

Show Tags

02 Oct 2016, 03:13
I think this is a high-quality question and I agree with explanation.
Intern
Status: Pursuit of Happiness
Joined: 10 Sep 2016
Posts: 30
Location: United States (IL)
Concentration: Finance, Economics
Schools: HBS '19, CBS '19
GMAT 1: 590 Q44 V27
GMAT 2: 690 Q50 V34
GPA: 3.94

Show Tags

16 Oct 2016, 19:15
Hi,

I am a little bit confused as for the meaning of "the difference between x and y". In this question, the wording has not effect on the solution since all the answers are negative. However, it may cause trouble in future problems.
That being said, does "the difference between x and y" get translated to "x-y" or to "y-x"?

--
Need Kudos
_________________

If you find this post hepful, please press +1 Kudos

Intern
Joined: 02 Aug 2016
Posts: 7

Show Tags

02 Nov 2016, 00:04
is there any other way to do this
Math Expert
Joined: 02 Sep 2009
Posts: 49300

Show Tags

02 Nov 2016, 02:15
phanikrishna wrote:
is there any other way to do this

Check here: if-m-2-225-and-n-m-10-what-is-the-sum-f-the-smallest-173113.html
_________________
Manager
Joined: 11 Feb 2015
Posts: 78
Location: United States
Concentration: Strategy, General Management
Schools: Duke '20 (A)
GMAT 1: 760 Q50 V42
GPA: 3.7
WE: Engineering (Energy and Utilities)

Show Tags

05 Nov 2016, 19:05
I think this is a high-quality question and I agree with explanation.
Intern
Joined: 23 May 2016
Posts: 7
Location: India
GPA: 3.04
WE: Analyst (Retail)

Show Tags

16 Apr 2017, 00:34
Hi Experts,

I have a question on this. The mentioned answer will work only when m =+-15, which is not possible as m2 has to be lass that 225. Also this question does mention that 3m+2n should be greatest and minimum INTEGER. Should it make any difference in the answer?
Math Expert
Joined: 02 Sep 2009
Posts: 49300

Show Tags

16 Apr 2017, 01:32
vnitnagpur wrote:
Hi Experts,

I have a question on this. The mentioned answer will work only when m =+-15, which is not possible as m2 has to be lass that 225. Also this question does mention that 3m+2n should be greatest and minimum INTEGER. Should it make any difference in the answer?

How did you got this?

5m - 20 = -94 --> m = -14.8

5m - 20 = 54 --> m = 14.8
_________________
Intern
Joined: 07 Feb 2016
Posts: 21
GMAT 1: 650 Q47 V34
GMAT 2: 710 Q48 V39

Show Tags

02 May 2017, 12:18
phanikrishna wrote:
is there any other way to do this

I solved the equation for $$m=15$$ and $$m=-15$$ and just used the next smaller/larger integer.

$$m=15 > 5m-20=55 --> value=54$$
$$m=-15 > 5m-20=-95 --> value=-94$$

$$difference=148$$
Intern
Joined: 30 May 2013
Posts: 29
GMAT 1: 600 Q50 V21
GMAT 2: 640 Q49 V29

Show Tags

16 Jun 2017, 21:47
I solved it like this:

Given information :
Square(m) < 225 => -15<m<15 --- (1) & n-m=10 ---(2)

Manipulation starts :
We will fit n in the inequality using (1) & (2) as that is the demand of the question.
Replace m in (1) with n-10 from (2),
new equation will be -25<n<5 --- (3)

Now, simply make (1) & (3) in the form of equation as asked in the question i.e. 3m+2n
-45<3m<45 (Multiplying (1) by 3)
-50<2n<10 (Multiplying (3) by 2)

Add above two equations , we will get
-95<3m+2n<55

Remember integer criteria is applicable on 3m+2n & not on m & n separately.

From above equation, Min integer = -94 & Max integer is 54
Difference = -94-54 = -148
Intern
Joined: 13 Apr 2017
Posts: 2

Show Tags

05 Sep 2017, 04:29
What if we take m = -14 , n = -24 and m = 14 , n = 4 and try to find the answer?
Math Expert
Joined: 02 Sep 2009
Posts: 49300

Show Tags

05 Sep 2017, 04:36
amritmohanty wrote:
What if we take m = -14 , n = -24 and m = 14 , n = 4 and try to find the answer?

Have you tried that? Did you get the correct answer?

We are NOT told that m is an integer, hence from -15<m<15 saying that the minimum value of m is -14 and the maximum value of m is 14 is wrong.
_________________
Intern
Joined: 31 Jul 2013
Posts: 15
Location: Viet Nam
Concentration: General Management, Entrepreneurship
GMAT 1: 650 Q49 V28
GPA: 3.46
WE: Sales (Computer Software)

Show Tags

30 Oct 2017, 23:59
I think this is a high-quality question and I agree with explanation.
Intern
Joined: 18 Jun 2017
Posts: 13

Show Tags

13 Feb 2018, 07:07
I agree with the solution. But, what's wrong with the following:

-15<m<15
-45<3m<45
2n-45<3m+2n<2n+45

the least number will be 2n-44 and the greatest number will be 2n+44. When you subtract greatest from the least, you will get -88. What is the role of n in this? Am I missing something?
Intern
Joined: 22 Jan 2018
Posts: 27

Show Tags

13 Feb 2018, 07:09
Thanks for explaining so nicely
Re: M30-19 &nbs [#permalink] 13 Feb 2018, 07:09
Display posts from previous: Sort by

M30-19

Moderators: chetan2u, Bunuel

Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.