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

 It is currently 21 Oct 2018, 01:09

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

In how many ways can two integers m and n, with m > n, be selected fro

Author Message
TAGS:

Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6390
GMAT 1: 760 Q51 V42
GPA: 3.82
In how many ways can two integers m and n, with m > n, be selected fro  [#permalink]

Show Tags

19 Mar 2018, 02:15
1
8
00:00

Difficulty:

25% (medium)

Question Stats:

76% (01:52) correct 24% (01:40) wrong based on 93 sessions

HideShow timer Statistics

[GMAT math practice question]

In how many ways can two integers $$m$$ and $$n$$, with $$m > n$$, be selected from the whole numbers from $$12$$ to $$32$$, inclusive?

$$A. 150$$
$$B. 180$$
$$C. 190$$
$$D. 210$$
$$E. 240$$

_________________

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 $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Senior PS Moderator Joined: 26 Feb 2016 Posts: 3188 Location: India GPA: 3.12 In how many ways can two integers m and n, with m > n, be selected fro [#permalink] Show Tags 19 Mar 2018, 02:25 1 1 MathRevolution wrote: [GMAT math practice question] In how many ways can two integers $$m$$ and $$n$$, with $$m > n$$, be selected from the whole numbers from $$12$$ to $$32$$, inclusive? $$A. 150$$ $$B. 180$$ $$C. 190$$ $$D. 210$$ $$E. 240$$ There are $$21(32 - 12 + 1)$$ integers between 12 and 32. Since the integers m and n are selected from the 21 available numbers, there are 21*20 ways of choosing these integers. Of these integers, half the possibilities satisfy the condition m > n. Therefore, there are $$\frac{21*20}{2} = 210$$ ways of selecting these integers (Option D) _________________ You've got what it takes, but it will take everything you've got CEO Joined: 12 Sep 2015 Posts: 3021 Location: Canada Re: In how many ways can two integers m and n, with m > n, be selected fro [#permalink] Show Tags 19 Mar 2018, 08:15 1 Top Contributor MathRevolution wrote: [GMAT math practice question] In how many ways can two integers $$m$$ and $$n$$, with $$m > n$$, be selected from the whole numbers from $$12$$ to $$32$$, inclusive? $$A. 150$$ $$B. 180$$ $$C. 190$$ $$D. 210$$ $$E. 240$$ A nice rule says: the number of integers from x to y inclusive equals y - x + 1 32 - 12 + 1 = 21 So, there are 21 numbers from which to choose NOTE: the order in which we select the numbers does not matter because, once we have selected the 2 numbers, we'll let m equal the larger value (to maintain the condition that m > n) Since order does not matter, we can use combinations. We can select 2 numbers from 21 numbers in 21C2 ways 21C2 = (21)(20)/(2)(1) = 210 Answer: D RELATED VIDEO - calculating combinations (like 21C2) in your head _________________ Brent Hanneson – GMATPrepNow.com Sign up for our free Question of the Day emails Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6390 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: In how many ways can two integers m and n, with m > n, be selected fro [#permalink] Show Tags 21 Mar 2018, 02:51 => Since the order of $$m$$ and $$n$$ is fixed, we only need to count the number of ways to choose $$2$$ numbers from $$12, 13, …, 32.$$ We have $$21$$ numbers to choose from since $$32 – 12 + 1 = 21.$$ The number of selections is $$21C2 = \frac{(21*20)}{(1*2)} = 210.$$ Therefore, D is the answer. Answer: D _________________ 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$99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Intern
Joined: 08 Aug 2018
Posts: 27
WE: Engineering (Energy and Utilities)
Re: In how many ways can two integers m and n, with m > n, be selected fro  [#permalink]

Show Tags

22 Aug 2018, 00:10
Why not answer 190? there will be 20 combinations where m=n example {12,12}, {13,13}. We need to take out those 20 combinations from 210.
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3188
Location: India
GPA: 3.12
Re: In how many ways can two integers m and n, with m > n, be selected fro  [#permalink]

Show Tags

24 Aug 2018, 06:09
1
PLUTO wrote:
Why not answer 190? there will be 20 combinations where m=n example {12,12}, {13,13}. We need to take out those 20 combinations from 210.

Hey PLUTO

Welcome to GMATClub!

We only choose different integers, as the number of ways of choosing the integers is $$\frac{21*20}{2} = 210$$.

If what you said was possible, the number of ways of choosing the integers are 21*21 = 441
and we will eliminate 21 options - (12,12),(13,13).......(31,31),(32,32). This will bring down
the number of options to 441 - 21 = 420. Now, since (12,21) is the same as selecting (21,12)
we will have to eliminate those options(which are exactly half of the options). Therefore, the
total number of ways of choosing the integers are $$\frac{420}{2} = 210$$

_________________

You've got what it takes, but it will take everything you've got

Re: In how many ways can two integers m and n, with m > n, be selected fro &nbs [#permalink] 24 Aug 2018, 06:09
Display posts from previous: Sort by