We have one unknown.. "n". If we can come up with 1 equation with "n" and numbers, we should be able to solve.
(1) really complicated situation with a value. Pretty sure I can come up with an equation out of that! Might end up with n^2, so would usually worry about 2 solutions... but in this case, negative solutions can be ignored - seems sufficient!
(2) ditto to (1) - should be able to create an equation with "n"s and numbers - sufficient!
Choose (d).
BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course
Redeem
Featured Course
Target Test Prep GMAT OnDemand
Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.
- 715+ score guarantee — highest in the industry (99th percentile)
- 52 chapters · 1,500+ lessons · 4,000+ practice questions
- 400 hours of video · 1,500+ instructor-led HD smartboard lessons
- 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
- 24/7 live support + weekly Zoom office hours with GMAT instructors
- TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
- 1,200+ flashcards + AI-powered study assistant & daily calendar
- OnDemand, LiveTeach & GMAT Bootcamp formats available
- Also: GRE, SAT Math & Executive Assessment courses
- MBA Admissions Consulting now available
- 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
- 200,000+ students served
- 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★
5.0
(559 reviews)
130-pt guarantee
$0 to start
then $127/mo
Mary persuaded n friends to donate $500 each to her election
Source: Beat The GMAT — Data Sufficiency |
-
Stuart@KaplanGMAT
- GMAT Instructor
- Posts: 3225
- Location: Toronto
- Thanked: 1710 times
- GMAT Score:800
Stuart Kovinsky | Kaplan GMAT Faculty | Toronto
Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course
Can you please post the equation for 1? didnt get that part. thanks.Stuart Kovinsky wrote:We have one unknown.. "n". If we can come up with 1 equation with "n" and numbers, we should be able to solve.
(1) really complicated situation with a value. Pretty sure I can come up with an equation out of that! Might end up with n^2, so would usually worry about 2 solutions... but in this case, negative solutions can be ignored - seems sufficient!
(2) ditto to (1) - should be able to create an equation with "n"s and numbers - sufficient!
Choose (d).
ON MY WAY TO HBS......
-
simplyjat
- Master | Next Rank: 500 Posts
- Posts: 423
- Location: Hyderabad, India
- Thanked: 36 times
- GMAT Score:770
Here is the equation.
Let n be the initial number of contributors, and x be the total amount donated.
For the first level of donation, we have n contribution. For second level of donation we have n more donation per person. You can simplify/remove the second level by saying that every person in first level contributed n+1 times. So we have.
n*(n+1) = x/500.
Now do not simplify the equation on left to square powers. See the expression on the left as product of two consecutive numbers.
The first expression tells us that n/n(n+1) = 1/16. or 1/(n+1) =16, or n = 15.
The second expression tells us that n*(n+1) = 120000/500 = 240 = 15*16, or n = 15
Let n be the initial number of contributors, and x be the total amount donated.
For the first level of donation, we have n contribution. For second level of donation we have n more donation per person. You can simplify/remove the second level by saying that every person in first level contributed n+1 times. So we have.
n*(n+1) = x/500.
Now do not simplify the equation on left to square powers. See the expression on the left as product of two consecutive numbers.
The first expression tells us that n/n(n+1) = 1/16. or 1/(n+1) =16, or n = 15.
The second expression tells us that n*(n+1) = 120000/500 = 240 = 15*16, or n = 15
simplyjat
-
Stuart@KaplanGMAT
- GMAT Instructor
- Posts: 3225
- Location: Toronto
- Thanked: 1710 times
- GMAT Score:800
I didn't post the equation because the beauty of data sufficiency is that you only need to know if an equation exists (and which variables are involved) - you don't actually need to translate or solve the equation.HarvardDreamin wrote:Can you please post the equation for 1? didnt get that part. thanks.Stuart Kovinsky wrote:We have one unknown.. "n". If we can come up with 1 equation with "n" and numbers, we should be able to solve.
(1) really complicated situation with a value. Pretty sure I can come up with an equation out of that! Might end up with n^2, so would usually worry about 2 solutions... but in this case, negative solutions can be ignored - seems sufficient!
(2) ditto to (1) - should be able to create an equation with "n"s and numbers - sufficient!
Choose (d).
On test day, you need to be in "fast and furious" mode and don't have time to translate/solve every DS question. Being able to quickly recognize how many equations you have is an invaluable skill.
Also, without a doubt, the "number of equations/number of unknowns" rule is THE most important rule to know for DS.
Stuart Kovinsky | Kaplan GMAT Faculty | Toronto
Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course
Thanks for that - unsurprisingly you'll realize that DS is the weakest part of the test for me.Stuart Kovinsky wrote:I didn't post the equation because the beauty of data sufficiency is that you only need to know if an equation exists (and which variables are involved) - you don't actually need to translate or solve the equation.HarvardDreamin wrote:Can you please post the equation for 1? didnt get that part. thanks.Stuart Kovinsky wrote:We have one unknown.. "n". If we can come up with 1 equation with "n" and numbers, we should be able to solve.
(1) really complicated situation with a value. Pretty sure I can come up with an equation out of that! Might end up with n^2, so would usually worry about 2 solutions... but in this case, negative solutions can be ignored - seems sufficient!
(2) ditto to (1) - should be able to create an equation with "n"s and numbers - sufficient!
Choose (d).
On test day, you need to be in "fast and furious" mode and don't have time to translate/solve every DS question. Being able to quickly recognize how many equations you have is an invaluable skill.
Also, without a doubt, the "number of equations/number of unknowns" rule is THE most important rule to know for DS.
ON MY WAY TO HBS......
Absolutely agree with Stuart on this point : "without a doubt, the "number of equations/number of unknowns" rule is THE most important rule to know for DS".
This has made a big improvement on my DS skills.
This has made a big improvement on my DS skills.
-
codesnooker
- Legendary Member
- Posts: 543
- Thanked: 43 times
- GMAT Score:580
Answer is (D).
Solution:
According to question, we try to derive the number of people then we come to know that there are n * (n+1) people are there.
HOW? for example there are 3 friends of Mary, so now each of the friend would ask help to their respective 3 friends.
Mary's friends = 3
Friends's friends = 3 X 3
Therefore total friends = 12 i.e 3 X 4
So, I guess, now you know how I have derived the formula.
So now with statement 1: 1/16 of total money is donated by Mary's n friends.
On the first look, its really hard to formulate any formula by just looking at the statement 1. so lets better try with statement 2.
On looking at statement 2,
we comet to know that n * (n + 1) * 500 = 120,000. So n = 15
So, statement (B) is alone sufficient.
Now, again looks at statement 1 which states that 1/16 of total money is mary's friend. That is 15/16 of total money is deposited by mary's friends' friends. Now, it looks very clear that there are 15 friends of mary who has deposited 1/16 of money.
Still didn't get???
Okay let me try to explain it in more details (how ever it still very confusing).
1/16 of total money means 1/16 of totals person who donated the money. 1/16 persons means 1/16 of n * (n + 1). So, now as persons are divided into 16 groups (because value is 1/16) so n + 1 = 16. (Remember n can't be equal to 16, as there are only 16 groups).
So n = 15.
So both statements are alone able to satisfy the answer.
Let me know the real answer.
Solution:
According to question, we try to derive the number of people then we come to know that there are n * (n+1) people are there.
HOW? for example there are 3 friends of Mary, so now each of the friend would ask help to their respective 3 friends.
Mary's friends = 3
Friends's friends = 3 X 3
Therefore total friends = 12 i.e 3 X 4
So, I guess, now you know how I have derived the formula.
So now with statement 1: 1/16 of total money is donated by Mary's n friends.
On the first look, its really hard to formulate any formula by just looking at the statement 1. so lets better try with statement 2.
On looking at statement 2,
we comet to know that n * (n + 1) * 500 = 120,000. So n = 15
So, statement (B) is alone sufficient.
Now, again looks at statement 1 which states that 1/16 of total money is mary's friend. That is 15/16 of total money is deposited by mary's friends' friends. Now, it looks very clear that there are 15 friends of mary who has deposited 1/16 of money.
Still didn't get???
Okay let me try to explain it in more details (how ever it still very confusing).
1/16 of total money means 1/16 of totals person who donated the money. 1/16 persons means 1/16 of n * (n + 1). So, now as persons are divided into 16 groups (because value is 1/16) so n + 1 = 16. (Remember n can't be equal to 16, as there are only 16 groups).
So n = 15.
So both statements are alone able to satisfy the answer.
Let me know the real answer.
[quote="Stuart Kovinsky
Also, without a doubt, the "number of equations/number of unknowns" rule is THE most important rule to know for DS.[/quote]
Dear Stuart,
I'm wondering if it is true that if we have n equations with n or less unknowns, we can find n unknowns. If we have n equations with more than n unknowns, we can not find all n unknowns? I think that only with that fact can we solve the DS without solving the equations.
Thank you.
Also, without a doubt, the "number of equations/number of unknowns" rule is THE most important rule to know for DS.[/quote]
Dear Stuart,
I'm wondering if it is true that if we have n equations with n or less unknowns, we can find n unknowns. If we have n equations with more than n unknowns, we can not find all n unknowns? I think that only with that fact can we solve the DS without solving the equations.
Thank you.
Regarding the question in this thread, if we do not solve the equations in statement 1 and 2, we will not know that there is only one value for n in either statement 1 or 2. If I do not solve the equations, I will assume that the quadratic equation has 2 values for its variable.
Thank you Stuart if you can explain to me.
Thank you Stuart if you can explain to me.
I am 1000% certain that Stuart (800) can also provide the quadratic equation, but just in case Harvarddreaming is still needs it, here it is...
First group comprises of n people with each person contributing $500. So....... 500n
Second group comprises of n *n with each person paying $500. So....... 500n^2
Stmt 1: 500n = 1/16( 500n + 500n^2) , which will precipitate to n^2 - 15n = 0.
So n (n-15) = 0 , making either n = 0 ( this is what Stuart asked us to ignore) or n = 15
I hope that helps.
First group comprises of n people with each person contributing $500. So....... 500n
Second group comprises of n *n with each person paying $500. So....... 500n^2
Stmt 1: 500n = 1/16( 500n + 500n^2) , which will precipitate to n^2 - 15n = 0.
So n (n-15) = 0 , making either n = 0 ( this is what Stuart asked us to ignore) or n = 15
I hope that helps.
This quadratic equation led us to only 1 positive root. But to be completely sure of the choice you can go and check atleast the b^2 - 4ac test to find the properties of the solution. And if it has two real positive roots then the choice changesStuart Kovinsky wrote:I didn't post the equation because the beauty of data sufficiency is that you only need to know if an equation exists (and which variables are involved) - you don't actually need to translate or solve the equation.HarvardDreamin wrote:Can you please post the equation for 1? didnt get that part. thanks.Stuart Kovinsky wrote:We have one unknown.. "n". If we can come up with 1 equation with "n" and numbers, we should be able to solve.
(1) really complicated situation with a value. Pretty sure I can come up with an equation out of that! Might end up with n^2, so would usually worry about 2 solutions... but in this case, negative solutions can be ignored - seems sufficient!
(2) ditto to (1) - should be able to create an equation with "n"s and numbers - sufficient!
Choose (d).
On test day, you need to be in "fast and furious" mode and don't have time to translate/solve every DS question. Being able to quickly recognize how many equations you have is an invaluable skill.
Also, without a doubt, the "number of equations/number of unknowns" rule is THE most important rule to know for DS.
