GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 28 Mar 2020, 21:41

### 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

# If john makes a contribution to a charity fund at school, th

Author Message
TAGS:

### Hide Tags

Intern
Joined: 15 Jan 2010
Posts: 6
If john makes a contribution to a charity fund at school, th  [#permalink]

### Show Tags

22 Jan 2010, 10:16
33
00:00

Difficulty:

55% (hard)

Question Stats:

67% (01:53) correct 33% (02:07) wrong based on 500 sessions

### HideShow timer Statistics

If john makes a contribution to a charity fund at school, the average contribution size will increase by 50% reaching $75 per person. If there were 5 other contributions made before john's, what is the size of his donation? A.$100
B. $150 C.$200
D. $250 E.$450
Math Expert
Joined: 02 Sep 2009
Posts: 62287
Re: 700-800 level problem Statistics  [#permalink]

### Show Tags

22 Jan 2010, 10:35
5
7
GMAT10 wrote:
If john makes a contribution to a charity fund at school, the average contribution size will increase by 50% reaching $75 per person.If there were 5 other contributions made before john's,what is the size of his donation? a)$100
b)$150 c)$200
d)$250 e)$450

Let $$a$$ be the average contribution size before John makes his contribution.
Let $$c$$ be the total contribution size before John makes his contribution.
Let $$x$$ be John's contribution.

$$1.5a=75$$ --> $$a=50$$

$$a=50=\frac{c}{5}$$ --> $$c=250$$

$$\frac{c+x}{6}=75$$ --> $$\frac{250+x}{6}=75$$ --> $$x=200$$

_________________
SVP
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2461
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Re: 700-800 level problem Statistics  [#permalink]

### Show Tags

22 Jan 2010, 10:33
11
2
yes 200 is the ans.

final avg = 75 = 1.5 of old

i.e old avg = 50 = total of five/5

total of five = 250

new avg = 75 = total of six/6

total of 6 = 450

so John's contribution = 450-250 =200
_________________
Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned

Jo Bole So Nihaal , Sat Shri Akaal

GMAT Club Premium Membership - big benefits and savings

Gmat test review :
http://gmatclub.com/forum/670-to-710-a-long-journey-without-destination-still-happy-141642.html
##### General Discussion
Intern
Joined: 21 Jan 2010
Posts: 45
Re: 700-800 level problem Statistics  [#permalink]

### Show Tags

22 Jan 2010, 10:20
4
1
Cavg = average contribution before John

Cavg*1.5 = 75, therefore the average cont is $50 before John. If he needs to increase the average contribution by$25, he must put in $25 for each of the 5 people. so$125.
But, he also has to put in the average for himself (the sixth person), so add $75. So$200 is your answer.
Intern
Joined: 06 Aug 2011
Posts: 49
Concentration: Entrepreneurship, Finance
GPA: 3.87
Re: Contribution to a charity Fund  [#permalink]

### Show Tags

17 Nov 2011, 16:25
If, after John's donation, the average was $75 per person then the total is$75(6) which comes to a total of 450 contributed dollars by all donees. If John's donation increases the total contributions by 50% then it is now 150% of what it was and John's contribution was 1/3 of that, which would be 1/3 of the $450. John contributed$150.

Manager
Status: D-Day is on February 10th. and I am not stressed
Affiliations: American Management association, American Association of financial accountants
Joined: 12 Apr 2011
Posts: 153
Location: Kuwait
Schools: Columbia university
Re: Contribution to a charity Fund  [#permalink]

### Show Tags

Updated on: 18 Nov 2011, 13:48
ok here is how I approached this question:

I, first, got the original average before the increase and without john's:

1.5x=75
x=50

then, I got the sum of the contributions of the 5 dominees without John:

5x/5=50
hence, 5x=250

after that, i set up the average equation with john's contribution:

250+x/6=75

250+x=75(6)

250+x=450
hence, x, which is John's amouts= 200
so the answer I got is C, hope this helps

Originally posted by manalq8 on 18 Nov 2011, 01:43.
Last edited by manalq8 on 18 Nov 2011, 13:48, edited 1 time in total.
Intern
Joined: 06 Aug 2011
Posts: 49
Concentration: Entrepreneurship, Finance
GPA: 3.87
Re: Contribution to a charity Fund  [#permalink]

### Show Tags

18 Nov 2011, 07:52
1
Thought I'd write my reasoning out in a more quantitative form.

J = {6($75)}/3, or J = [{1($75) +5($75)}/150]*50. The key, I think, is to realize that John's contribution was 1/3 of all the current contributions. Since we know the total contribution is 6($75)=$450, then we know his contribution was 1/3 of that. 1/3*450=$150.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10219
Location: Pune, India
Re: Contribution to a charity Fund  [#permalink]

### Show Tags

20 Nov 2011, 00:07
1
1
enigma123 wrote:
If John makes a contribution to a charity fund at school, the average contribution size will increase by 50%, reaching $75 per person. If there were 5 other contributions made before John’s, what is the size of his donation? (A)$100
(B) $150 (C)$200
(D) $250 (E)$450

OA is not provided, but I have got C. Do you guys think C is the right answer?

Responding to a pm:

After John's contribution, the average size increases by 50% and reaches $75. What must have been the average size of contribution before John's donation? It must have been$50 since a 50% increase would lead us to $75.$50 was the average size for 5 donations. Total amount donated = $250$75 is the average size for 6 donations. Total amount donated = $450 John's contribution must have been 450 - 250 =$200

_________________
Karishma
Veritas Prep GMAT Instructor

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10219
Location: Pune, India
Re: Contribution to a charity Fund  [#permalink]

### Show Tags

20 Nov 2011, 08:04
1
Stoneface wrote:
If, after John's donation, the average was $75 per person then the total is$75(6) which comes to a total of 450 contributed dollars by all donees. If John's donation increases the total contributions by 50% then it is now 150% of what it was and John's contribution was 1/3 of that, which would be 1/3 of the $450. John contributed$150.

Responding to a pm:

We cannot say that John's contribution is a third. To increase the average by 50%, you need to invest more than a third of the total. The reason is that previous average is for 5 people. New average has another person so the total contribution needs to be higher.

The total contribution now = 75*6 = 450
Out of this, if 150 were contributed by John, the previous total contribution must have been 300. With 5 people, that would mean an average of 60. We need 6 people to make the average 50 but before John made the contribution, there were only 5 people. That's where you made a mistake. Since a person increases, the contribution needs to be even higher than a third.
_________________
Karishma
Veritas Prep GMAT Instructor

Intern
Joined: 06 Aug 2011
Posts: 49
Concentration: Entrepreneurship, Finance
GPA: 3.87
Re: Contribution to a charity Fund  [#permalink]

### Show Tags

21 Nov 2011, 06:02
I do not understand at all, but thanks for your time. I think I'll spend a little extra time in the ol' GMAT book today.
Intern
Joined: 27 Feb 2015
Posts: 40
Concentration: General Management, Economics
GMAT 1: 630 Q42 V34
WE: Engineering (Transportation)
Re: If john makes a contribution to a charity fund at school, th  [#permalink]

### Show Tags

18 Oct 2016, 04:00
VeritasPrepKarishma wrote:
enigma123 wrote:
If John makes a contribution to a charity fund at school, the average contribution size will increase by 50%, reaching $75 per person. If there were 5 other contributions made before John’s, what is the size of his donation? (A)$100
(B) $150 (C)$200
(D) $250 (E)$450

OA is not provided, but I have got C. Do you guys think C is the right answer?

Responding to a pm:

After John's contribution, the average size increases by 50% and reaches $75. What must have been the average size of contribution before John's donation? It must have been$50 since a 50% increase would lead us to $75.$50 was the average size for 5 donations. Total amount donated = $250$75 is the average size for 6 donations. Total amount donated = $450 John's contribution must have been 450 - 250 =$200

I got this wrong by attempting this problem logically (Fan of your logical approach ), please let me know what's wrong in my logic.

New avg - 75 per person
old avg- 50 per person
so 25 per person was extra added by john , that mean John had Extra $Extra John carried was = 25*(5+1) i.e. for 5 others and John Extra = 150, this is the extra amount. ..oh no! I think while writing this I got my mistake (silly one!) . I'll still continue so that people who find this interesting will adopt this and not make silly error as me So john contributed 150$ extra plus he also had the old avg amt. i.e. 50 $so total john contributed is 150+50 =$200

You must have figured what mistake I did. I picked B.150$. But that's just the extra amount John has apart from 50$.
Thanks.
Current Student
Joined: 12 Aug 2015
Posts: 2537
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Re: If john makes a contribution to a charity fund at school, th  [#permalink]

### Show Tags

11 Dec 2016, 08:00
Here is my take on this one -->
Mean 1=>50
Mean 2=>75
Sum(1)=50*5=250
Sum(2)=75*6=450.
Hence,John's contribution => 450-250=200.

Alternatively =>
John donated => 50+25*6=> 50+150=200.

Great explanation by VeritasPrepKarishma

Regards
Stone Cold

_________________
GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4542
GMAT 1: 770 Q49 V46
Re: If john makes a contribution to a charity fund at school, th  [#permalink]

### Show Tags

23 Jul 2018, 06:49
Top Contributor
GMAT10 wrote:
If john makes a contribution to a charity fund at school, the average contribution size will increase by 50% reaching $75 per person. If there were 5 other contributions made before john's, what is the size of his donation? A.$100
B. $150 C.$200
D. $250 E.$450

Let J = the John's donation
Let a, b, c, d and e = the donations of the other 5 donors.

John makes a contribution to a charity fund at school, the average contribution size will increase by 50% reaching $75 per person. If the average contribution for all 6 donors =$75, we can write: (a + b + c + d + e + J)/6 = $75 Multiply both sides by 6 to get: a + b + c + d + e + J =$450

John makes a contribution to a charity fund at school, the average contribution size will increase by 50% reaching $75 per person. If we let x = the OLD (before John) average donation, then we can write 1.5x =$75
Solve for x to get x = $50 So,$50 is the OLD (before John) average donation for donors a, b, c, d and e
We can write: (a + b + c + d + e)/5 = $50 Multiply both sides by 5 to get: a + b + c + d + e =$250

We now have two equations:
a + b + c + d + e + J = $450 a + b + c + d + e =$250

Subtract the bottom equation from the top equation to get: J = $200 Answer: C RELATED VIDEO FROM OUR COURSE _________________ Test confidently with gmatprepnow.com Target Test Prep Representative Status: Head GMAT Instructor Affiliations: Target Test Prep Joined: 04 Mar 2011 Posts: 2801 Re: If john makes a contribution to a charity fund at school, th [#permalink] ### Show Tags 25 Jul 2018, 16:35 GMAT10 wrote: If john makes a contribution to a charity fund at school, the average contribution size will increase by 50% reaching$75 per person. If there were 5 other contributions made before john's, what is the size of his donation?

A. $100 B.$150
C. $200 D.$250
E. \$450

We can let the old average = a and create the equation:

1.5a = 75

a = 50

Thus, the original sum was 250.

So we can create another equation, where j = the size of John’s contribution:

75 = (j + 250)/6

450 = j + 250

200 = j

_________________

# Jeffrey Miller

Jeff@TargetTestPrep.com
197 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Non-Human User
Joined: 09 Sep 2013
Posts: 14454
Re: If john makes a contribution to a charity fund at school, th  [#permalink]

### Show Tags

11 Aug 2019, 21:22
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.
_________________
Re: If john makes a contribution to a charity fund at school, th   [#permalink] 11 Aug 2019, 21:22
Display posts from previous: Sort by