Author 
Message 
TAGS:

Hide Tags

Director
Joined: 29 Aug 2005
Posts: 808

Mary persuaded n friends to donate $500 each to her election
[#permalink]
Show Tags
07 Apr 2009, 15:51
Question Stats:
62% (01:31) correct 38% (01:33) wrong based on 2000 sessions
HideShow timer Statistics
Mary persuaded n friends to donate $500 each to her election campaign, and then each of these n friends persuaded n more people to donate $500 each to Mary’s campaign. If no one donated more than once and if there were no other donations, what was the value of n? (1) The first n people donated 1/16 of the total amount donated. (2) The total amount donated was $120,000.
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 47981

Re: Need Solution for some DS problems from SET1
[#permalink]
Show Tags
23 Jun 2010, 15:04
Mary persuaded n friends to donate $500 each to her election campaign, and then each of these n friends persuaded n more people to donate $500 each to Mary's campaign. If no one donated more than once and if there were no other donations, what was the value of n?# of people donated at the firs stage  \(n\), amount  \(500n\); # of people donated at the second  \(n^2\), amount  \(500n^2\); Total amount donated  \(500n+500n^2\) Little assumption here: \(n>0\). (1) The first n people donated 1/16 of the total amount donated > \(16(500n)=500n+500n^2\) > \(n=15\). Sufficient. (2) The total amount donated was $120,000 > \(500n+500n^2=120,000\) > \(n=15\). Sufficient. Answer: D.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




Manager
Status: Preparing Apps
Joined: 04 Mar 2009
Posts: 91
Concentration: Marketing, Strategy
GMAT 1: 650 Q48 V31 GMAT 2: 710 Q49 V38
WE: Information Technology (Consulting)

Re: Mary persuaded n friends
[#permalink]
Show Tags
14 Nov 2010, 12:59
I have understood the approach GT took to solve the problem its very similar to mine... but i cannot make out how can the first stmt give a solution for n as 0 or a ve value.
Could someone explain this?



Math Expert
Joined: 02 Sep 2009
Posts: 47981

Mary persuaded n friends to donate $500 each to her election
[#permalink]
Show Tags
14 Nov 2010, 13:21
aalriy wrote: I have understood the approach GT took to solve the problem its very similar to mine... but i cannot make out how can the first stmt give a solution for n as 0 or a ve value.
Could someone explain this? It cannot give negative solution for \(n\), though it can give \(n=0\) as a solution. See below: Mary persuaded n friends to donate $500 each to her election campaign, and then each of these n friends persuaded n more people to donate $500 each to Mary's campaign. If no one donated more than once and if there were no other donations, what was the value of n?# of people donated at the firs stage  \(n\), amount donated  \(500n\); # of people donated at the second  \(n^2\), amount donated  \(500n^2\); Total amount donated  \(500n+500n^2\) Little assumption here: \(n>0\). (1) The first n people donated 1/16 of the total amount donated > \(500n=\frac{1}{16}(500n+500n^2)\) > \(n=15\) (we can rule out \(n=0\), which is also a solution of this equation). Sufficient. (2) The total amount donated was $120,000 > \(500n+500n^2=120,000\) > \(n=15\). Sufficient. Answer: D. Hope it's clear.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Director
Joined: 01 Feb 2011
Posts: 671

Re: Mary persuaded n friends
[#permalink]
Show Tags
12 Mar 2011, 18:50
My answer is D.
1. sufficient
500n = x/16 = (500n+500n^2)/16 sufficient enough to find n.
2. 500n+500n^2 = 120,000
sufficient enough to find n.
Answer D.



Retired Moderator
Joined: 20 Dec 2010
Posts: 1877

Re: Mary persuaded n friends
[#permalink]
Show Tags
13 Mar 2011, 05:52
seofah wrote: Mary persuaded n friends to donate $500 each to her election campaign, and then each of these n friends persuaded n more people to donate $500 each to Mary’s campaign. If no one donated more than once and if there were no other donations, what was the value of n? (1) The first n people donated 1/16 of the total amount donated. (2) The total amount donated was $120,000. *********************************************************** Minor detour: Please see; applesandappleswordproblem85741.htmlSusie can buy apples from two stores: a supermarket that sells apples only in bundles of 4, and a convenience store that sells single, unbundled apples. If Susie wants to ensure that the total number of apples she buys is a multiple of 5, what is the minimum number of apples she must buy from the convenience store? A. 0 B. 1 C. 2 D. 3 E. 4 ******************************** If Susie can buy '0' apples, why can't Mary persuade '0' friends? Absurd!!!
_________________
~fluke
GMAT Club Premium Membership  big benefits and savings



Director
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 549

Re: Mary persuaded n friends
[#permalink]
Show Tags
13 Mar 2011, 08:38



Manager
Joined: 22 Feb 2012
Posts: 88
GMAT 1: 740 Q49 V42 GMAT 2: 670 Q42 V40
GPA: 3.47
WE: Corporate Finance (Aerospace and Defense)

Re: Mary persuaded n friends to donate $500 each to her election
[#permalink]
Show Tags
03 Mar 2012, 22:54
Man this question makes me mad that i got it wrong initially and it took me a while to figure it out.. OK so (1) n/(n + n^2) = 1/16 16n = n^2 + n n^2 15n = 0 n(n15) = 0 But n cant really be zero Sufficient (2) (n + n ^2)* 500 = 120,000 n + n^2 = 240 n^2 + n 240=0 (n +16) (n15) = 0 But n cant really be 16 Sufficient Answer is D I couldnt figure out the way to factor n^2 +n 240 = 0 for a long time I guess my real issue was trying to solve it.. once i constructed the quadratic i shouldve just moved on with life!!!



Intern
Joined: 14 Mar 2012
Posts: 10

Re: Mary persuaded n friends
[#permalink]
Show Tags
08 Apr 2012, 05:49
fluke wrote: seofah wrote: Mary persuaded n friends to donate $500 each to her election campaign, and then each of these n friends persuaded n more people to donate $500 each to Mary’s campaign. If no one donated more than once and if there were no other donations, what was the value of n? (1) The first n people donated 1/16 of the total amount donated. (2) The total amount donated was $120,000. *********************************************************** Susie can buy apples from two stores: a supermarket that sells apples only in bundles of 4, and a convenience store that sells single, unbundled apples. If Susie wants to ensure that the total number of apples she buys is a multiple of 5, what is the minimum number of apples she must buy from the convenience store? A. 0 B. 1 C. 2 D. 3 E. 4 ******************************** If Susie can buy '0' apples, why can't Mary persuade '0' friends? Absurd!!! Can someone please answer the above mentioned fluke's query ? I have the same confusion "If Susie can buy '0' apples, why can't Mary persuade '0' friends?" In that case, Condition I will not be sufficient.



Intern
Joined: 04 Jan 2012
Posts: 17

Re: Mary persuaded n friends
[#permalink]
Show Tags
13 Apr 2012, 23:13
Bunuel wrote: aalriy wrote: I have understood the approach GT took to solve the problem its very similar to mine... but i cannot make out how can the first stmt give a solution for n as 0 or a ve value.
Could someone explain this? It can not give negative solution for \(n\), though it can give \(n=0\) as a solution. See below: Mary persuaded n friends to donate $500 each to her election campaign, and then each of these n friends persuaded n more people to donate $500 each to Mary's campaign. If no one donated more than once and if there were no other donations, what was the value of n?# of people donated at the firs stage  \(n\), amount donated  \(500n\); # of people donated at the second  \(n^2\), amount donated  \(500n^2\); Total amount donated  \(500n+500n^2\) Little assumption here: \(n>0\). (1) The first n people donated 1/16 of the total amount donated > \(500n=\frac{1}{16}(500n+500n^2)\) > \(n=15\) (we can rule out \(n=0\), which is also a solution of this equation). Sufficient. (2) The total amount donated was $120,000 > \(500n+500n^2=120,000\) > \(n=15\). Sufficient. Answer: D. Hope it's clear. How to solve equation like 500n^2 + 500n = 120,000 This translates to quadratic equation n^2 + n = 240 Should one use formula of \sqrt{b^2  4ac}



Math Expert
Joined: 02 Sep 2009
Posts: 47981

Re: Mary persuaded n friends
[#permalink]
Show Tags
14 Apr 2012, 03:01
ps25 wrote: Bunuel wrote: aalriy wrote: I have understood the approach GT took to solve the problem its very similar to mine... but i cannot make out how can the first stmt give a solution for n as 0 or a ve value.
Could someone explain this? It can not give negative solution for \(n\), though it can give \(n=0\) as a solution. See below: Mary persuaded n friends to donate $500 each to her election campaign, and then each of these n friends persuaded n more people to donate $500 each to Mary's campaign. If no one donated more than once and if there were no other donations, what was the value of n?# of people donated at the firs stage  \(n\), amount donated  \(500n\); # of people donated at the second  \(n^2\), amount donated  \(500n^2\); Total amount donated  \(500n+500n^2\) Little assumption here: \(n>0\). (1) The first n people donated 1/16 of the total amount donated > \(500n=\frac{1}{16}(500n+500n^2)\) > \(n=15\) (we can rule out \(n=0\), which is also a solution of this equation). Sufficient. (2) The total amount donated was $120,000 > \(500n+500n^2=120,000\) > \(n=15\). Sufficient. Answer: D. Hope it's clear. How to solve equation like 500n^2 + 500n = 120,000 This translates to quadratic equation n^2 + n = 240 Should one use formula of \sqrt{b^2  4ac} You can solve it using the formula for quadratics, though it's better to use another approach: \(500n+500n^2=120,000\) > \(n+n^2=240\) > \(n(n+1)=240\). Since \(n\) is an integer then we have that the product of two consecutive integers is 240, now it's easy to find that \(n=15\). Hope it's clear.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 26 Jul 2012
Posts: 63

Re: Mary persuaded n friends to donate $500 each to her election
[#permalink]
Show Tags
24 Aug 2013, 18:49
I am just wondering if there is another way to solve this problem without the quadratics solution. Fundraising run 1 = 500n Fundraising run 2 = 500n^2
500n + 500n^2 = total amount donated.
Goal of our DS question, find n, and to find "n", we need to know: 1) Total amount donated OR 2) The RATIO of the two fundraising runs. If we have the ratio, we can set them against each other and get rid of "n"s.
Each given statement meets the criteria above, thus D.



Manager
Joined: 12 Jan 2013
Posts: 185

Re: Mary persuaded n friends to donate $500 each to her election
[#permalink]
Show Tags
10 Jan 2014, 09:08
seofah wrote: Mary persuaded n friends to donate $500 each to her election campaign, and then each of these n friends persuaded n more people to donate $500 each to Mary’s campaign. If no one donated more than once and if there were no other donations, what was the value of n?
(1) The first n people donated 1/16 of the total amount donated. (2) The total amount donated was $120,000. My problem with this question was that I foolishly assumed that there were two different n's, n1 and n2, and thus we had two variables (n1,n2) plus the total amount donated. 1 gave us the relation between n1,n2 and 2 gives us total donated so we can solve for the unknowns, that's why I picked C. It just simply couldnt comprehend how we could get n^2, hopefully I will not make the same mistake on the actual test in a couple of days.



Manager
Joined: 21 Oct 2013
Posts: 189
Location: Germany
GPA: 3.51

Re: Mary persuaded n friends to donate $500 each to her election
[#permalink]
Show Tags
13 Mar 2014, 07:42
Hey all,
I think I don't get the wording: If EACH of the n friends persuaded n people, wouldn't it be n^n??
Wouldn't really change the outcome, but I'd like to know it exactly....
Thanks!



Math Expert
Joined: 02 Sep 2009
Posts: 47981

Re: Mary persuaded n friends to donate $500 each to her election
[#permalink]
Show Tags
13 Mar 2014, 08:57



Intern
Joined: 12 Feb 2014
Posts: 4
GMAT Date: 06082014
WE: Information Technology (Computer Software)

Re: Mary persuaded n friends to donate $500 each to her election
[#permalink]
Show Tags
19 Apr 2014, 06:58
I still am confused with the phrase... "then each of these n friends persuaded n more people" How could this be \(n*n\) why not \(n+n\) If 3 people persuade 3 more people then the total would become 3+3=6 right.?? Pls clarify Bunuel wrote: unceldolan wrote: Hey all,
I think I don't get the wording: If EACH of the n friends persuaded n people, wouldn't it be n^n??
Wouldn't really change the outcome, but I'd like to know it exactly....
Thanks! No. Say n=3, then at the second stage the number of people who donated would be 3*3=9, not 3^3=27: Attachment: Untitled.png Hope it's clear.



Math Expert
Joined: 02 Sep 2009
Posts: 47981

Re: Mary persuaded n friends to donate $500 each to her election
[#permalink]
Show Tags
19 Apr 2014, 09:41
hhakud wrote: I still am confused with the phrase... "then each of these n friends persuaded n more people" How could this be \(n*n\) why not \(n+n\) If 3 people persuade 3 more people then the total would become 3+3=6 right.?? Pls clarify Bunuel wrote: unceldolan wrote: Hey all,
I think I don't get the wording: If EACH of the n friends persuaded n people, wouldn't it be n^n??
Wouldn't really change the outcome, but I'd like to know it exactly....
Thanks! No. Say n=3, then at the second stage the number of people who donated would be 3*3=9, not 3^3=27: Attachment: Untitled.png Hope it's clear. Each of these n friends persuaded n more people, not that n people together persuaded n more people. Hope it's clear.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Senior Manager
Joined: 15 Aug 2013
Posts: 268

Mary persuaded n friends to donate $500 each to her election
[#permalink]
Show Tags
13 Aug 2014, 18:49
Bunuel wrote: unceldolan wrote: Hey all,
I think I don't get the wording: If EACH of the n friends persuaded n people, wouldn't it be n^n??
Wouldn't really change the outcome, but I'd like to know it exactly....
Thanks! No. Say n=3, then at the second stage the number of people who donated would be 3*3=9, not 3^3=27: Attachment: Untitled.png Hope it's clear. Not the OP but I was stuck at the same point  I didn't know how to go a level after N. I started plugging in numbers but that turned out to be a huge mess. Couple of questions: 1) I couldn't really understand (while first reading the question) as to when n would stop factoring. Meaning, if n was 3, would it go own 2 levels or 3 levels? meaning, would the total be 500(n + n^2 + n3) 2) a little confused as to why it's not 3n^2? sorry, having a hard time visualizing the total number of people. 3) would the third level be cubed like i wrote above or would it be n^4(squared of n^2?) Thanks!



Intern
Joined: 03 Oct 2014
Posts: 6
Location: United Kingdom
WE: Engineering (Energy and Utilities)

Re: Mary persuaded n friends to donate $500 each to her election
[#permalink]
Show Tags
09 Nov 2014, 08:34
Can someone please explain the logic in putting the equation in part (1) = 500n? In my own working i came up with the RHS, but in my mind that should be put equal to the total amount donated. I am not sure how this is equal to 500n (which in turn is equal to the total number of 1st tier friends who donated). I am sure its simple and I am just missing a logical step. The rest of Brunels/ OG's solution is crystal clear.



Math Expert
Joined: 02 Sep 2009
Posts: 47981

Re: Mary persuaded n friends to donate $500 each to her election
[#permalink]
Show Tags
10 Nov 2014, 02:35
Madrigal wrote: Can someone please explain the logic in putting the equation in part (1) = 500n? In my own working i came up with the RHS, but in my mind that should be put equal to the total amount donated. I am not sure how this is equal to 500n (which in turn is equal to the total number of 1st tier friends who donated). I am sure its simple and I am just missing a logical step. The rest of Brunels/ OG's solution is crystal clear. Amount donated by the first n people = \(500n\); Total amount donated = \(500n+500n^2\). (1) says that the first n people donated 1/16 of the total amount donated, thus \(500n=\frac{1}{16}(500n+500n^2)\) > \(16(500n)=500n+500n^2\). Hope it's clear.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




Re: Mary persuaded n friends to donate $500 each to her election &nbs
[#permalink]
10 Nov 2014, 02:35



Go to page
1 2
Next
[ 28 posts ]



