Last visit was: 24 Apr 2026, 05:32 It is currently 24 Apr 2026, 05:32
Home
Messages
Tests
Schools
Events
Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
lalania1
User avatar
Joined: 17 Nov 2013
Last visit: 04 May 2017
Posts: 63
Own Kudos:
297
 [24]
Given Kudos: 19
Posts: 63
Kudos: 297
 [24]
Judith and Quincy started with the same amount of money to invest at t 01 Nov 2016, 05:26
2
Kudos
Add Kudos
22
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

75% (hard)

Question Stats:

61% (02:43) correct 39% (02:52) wrong based on 417 sessions

History

Date
Time
Result
Not Attempted Yet
Judith and Quincy started with the same amount of money to invest at the beginning of 2012. Judith's investments increased by P percent in the year 2012 and then increased by Q percent in the year 2013. From the start of 2012 to the end of 2013, Quincy's investment increased by R percent. Which one of them had more money by the end of 2013?

(1) P + Q < R

(2) R - P - Q < (PQ/100)
ShowHide Answer
Official Answer
B
Most Helpful Reply
User avatar
GMATGuruNY
User avatar
Joined: 04 Aug 2010
Last visit: 02 Apr 2026
Posts: 1,347
Own Kudos:
3,905
 [9]
Given Kudos: 9
Schools:Dartmouth College
Expert
Expert reply
Posts: 1,347
Kudos: 3,905
 [9]
Judith and Quincy started with the same amount of money to invest at t 30 Jun 2018, 03:39
9
Kudos
Add Kudos
Bookmarks
Bookmark this Post
lalania1
Judith and Quincy started with the same amount of money to invest at the beginning of 2012. Judith's investments increased by P percent in the year 2012 and then increased by Q percent in the year 2013. From the start of 2012 to the end of 2013, Quincy's investment increased by R percent. Which one of them had more money by the end of 2013?

(1) P + Q < R

(2) R - P - Q < (PQ/100)
Show more

Let the original investment in each case = 100.

JUDITH:
In 2012, Judith's P% increase = \(\frac{P}{100}(100) = P\).
Thus, Judith's amount at the end of 2012 = \(100+P\).
In 2013, Judith's Q% increase = \(\frac{Q}{100}(100+P) = Q+\frac{PQ}{100}\).
Thus, Judith's total increase = \(P+Q+\frac{PQ}{100}\).


QUINCY:
Quincy's R% increase = \(\frac{R}{100}(100) = R\).


Judith's final amount will be greater than Quincy's final amount if her total increase is greater than his increase:
Question stem, rephrased:
Is \(P+Q+\frac{PQ}{100} > R\)?


Statement 1: \(P+Q < R\)
Case 1: P=10, Q=10 and R=21
In this case, \(P+Q+\frac{PQ}{100} = 10+10+\frac{(10*10)}{100} = 21\) and \(R=21\), so the answer to the rephrased question stem is NO.
Case 2: P=40, Q=50 and R=100
In this case, \(P+Q+\frac{PQ}{100} = 40+50+\frac{(40*50)}{100} = 110\) and \(R=100\), so the answer to the rephrased question stem is YES.
Since the answer is NO in Case 1 but YES in Case 2, INSUFFICIENT.


Statement 2: \(R - P - Q < \frac{PQ}{100}\)
\(R < P+Q+\frac{PQ}{100}\)
\(P+Q+\frac{PQ}{100} > R\)
Thus, the answer to the rephrased question stem is YES.
SUFFICIENT.

Show Spoiler
B
General Discussion
User avatar
lalania1
User avatar
Joined: 17 Nov 2013
Last visit: 04 May 2017
Posts: 63
Own Kudos:
297
Given Kudos: 19
Posts: 63
Kudos: 297
Judith and Quincy started with the same amount of money to invest at t 01 Nov 2016, 05:31
Kudos
Add Kudos
Bookmarks
Bookmark this Post
the first statement is a trap.

the second statement is more complex. At first we dont know if it can be resolved.
reading the stem you can use formulas such as ((1+P)/100)((1+Q)/100) for Judy and ((1+R)/100) for Quincy.
in order to prove whether the 2nd stmt is correct, i need to solve the above equation. Once you solve it. you will find that it matches stmt 2, not only that, stmt2 gives you the > sign to answer the question from the stem.
User avatar
broall
User avatar
Retired Moderator
Joined: 10 Oct 2016
Last visit: 07 Apr 2021
Posts: 1,133
Own Kudos:
7,376
 [3]
Given Kudos: 65
Status:Long way to go!
Location: Viet Nam
Posts: 1,133
Kudos: 7,376
 [3]
Judith and Quincy started with the same amount of money to invest at t 23 Nov 2016, 00:53
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
lalania1
Judith and Quincy started with the same amount of money to invest at the beginning of 2012. Judith's investments increased by P percent in the year 2012 and then increased by Q percent in the year 2013. From the start of 2012 to the end of 2013, Quincy's investment increased by R percent. Which one of them had more money by the end of 2013?

(1) P + Q < R

(2) R - P - Q < (PQ/100)
Show more

Judith's investments by the end of 2013: \(N(1+\frac{P}{100})(1+\frac{Q}{100})\)
Quincy's investments by the end of 2013: \(N(1+\frac{R}{100})\)

Comparing between Judith's investments and Quincy's investments is the same as comparing between \((1+\frac{P}{100})(1+\frac{Q}{100})\) and \((1+\frac{R}{100})\)
We have
\((1+\frac{P}{100})(1+\frac{Q}{100})-(1+\frac{R}{100})\)
\(=(\frac{100+P}{100})(\frac{100+Q}{100})-(\frac{100+R}{100})\)
\(=\frac{10^4+100P+100Q+PQ}{10^4}-\frac{100(100+R)}{10^4}\)
\(=\frac{100(P+Q-R)+PQ}{10^4}\)(*)

(1) \(P+Q<R\) so \(P+Q-R<0\). However, from (*) we cannot deduce anything. Insufficient.

(2) \(R - P - Q < \frac{PQ}{100} \iff 100(R-P-Q)<PQ \iff 100(P+Q-R)+PQ>0\).

Hence, from (*) we have \((1+\frac{P}{100})(1+\frac{Q}{100})>(1+\frac{R}{100})\) or Judith's investments is higher. Sufficient.

The answer is B
User avatar
Aadhitthyaa
User avatar
Joined: 24 Feb 2018
Last visit: 10 May 2021
Posts: 27
Own Kudos:
16
Given Kudos: 38
Posts: 27
Kudos: 16
Judith and Quincy started with the same amount of money to invest at t 30 Jun 2018, 06:13
Kudos
Add Kudos
Bookmarks
Bookmark this Post
How do you assume that its compound interest ?
User avatar
GMATGuruNY
User avatar
Joined: 04 Aug 2010
Last visit: 02 Apr 2026
Posts: 1,347
Own Kudos:
3,905
 [1]
Given Kudos: 9
Schools:Dartmouth College
Expert
Expert reply
Posts: 1,347
Kudos: 3,905
 [1]
Judith and Quincy started with the same amount of money to invest at t 30 Jun 2018, 06:42
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Aadhitthyaa
How do you assume that its compound interest ?
Show more

Judith's investments increased by P percent in the year 2012 and THEN increased by Q percent in the year 2013.
The usage of then implies that the interest in 2013 is accrued on the value of the investment at the end of 2012.
That said, the GMAT would use wording to make this intent crystal clear.
User avatar
Adit_
User avatar
Joined: 04 Jun 2024
Last visit: 24 Apr 2026
Posts: 700
Own Kudos:
230
Given Kudos: 117
Posts: 700
Kudos: 230
Judith and Quincy started with the same amount of money to invest at t 23 Feb 2026, 23:18
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Use successive percentage formula:
Judith basically increases like:

Am(1+P+Q+PQ/100) (Successive percentage formula applied)

Quincy increases like:

Am(1+R/100)

Now we can dirctly say statement 2 alone is SUFFICIENT as it is essentially R<P+Q+PQ/100

Statement 1 only says about P+Q, there could be a case where PQ/100 added to P+Q results in the value being greater than R.
NOT SUFFICIENT.

Option B
lalania1
Judith and Quincy started with the same amount of money to invest at the beginning of 2012. Judith's investments increased by P percent in the year 2012 and then increased by Q percent in the year 2013. From the start of 2012 to the end of 2013, Quincy's investment increased by R percent. Which one of them had more money by the end of 2013?

(1) P + Q < R

(2) R - P - Q < (PQ/100)
Show more
Moderators:
Bunuel
Math Expert
109811 posts
kingbucky
498 posts
Gmat860sanskar
212 posts