Events & Promotions
|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Nov 2211:00 AM IST
-01:00 PM IST
Do RC/MSR passages scare you? e-GMAT is conducting a masterclass to help you learn – Learn effective reading strategies Tackle difficult RC & MSR with confidence Excel in timed test environment- Nov 23
11:00 AM IST
-01:00 PM IST
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease. 
Nov 2510:00 AM EST
-11:00 AM EST
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors.
Kaushik786
Joined: 20 May 2018
Last visit: 13 Dec 2023
Posts: 71
Given Kudos: 71
Location: India
Schools: Booth '22 Anderson '22 CBS '22 Johnson '22
GMAT 1: 740 Q50 V41
Updated on: 12 Mar 2021, 20:54
Originally posted by Kaushik786 on 11 Mar 2021, 23:24.
Last edited by chetan2u on 12 Mar 2021, 20:54, edited 1 time in total.
Last edited by chetan2u on 12 Mar 2021, 20:54, edited 1 time in total.
Corrected the question
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
31% (03:16) correct
69%
(02:36)
wrong
based on 59
sessions
History
Date
Time
Result
Not Attempted Yet
P, Q and R are positive single integers. Does the three digit number PQR lie between 100 and 300 ?
1. Q=P+S, R=Q+0.75S, where S is a positive single digit integer.
2. Q=P+T+2, R=Q+3T/2, where T is a positive single digit integer.
1. Q=P+S, R=Q+0.75S, where S is a positive single digit integer.
2. Q=P+T+2, R=Q+3T/2, where T is a positive single digit integer.
12 Mar 2021, 20:53
Kudos
Bookmarks
Kaushik786
Of course, the statement I is wrong the way it is written.
If R and Q are integers, R=Q+0.75 is not possible. R would not be an integer in this case.
Looking at statement II, I believe the statement I should be
1. Q=P+S, R=Q+0.75S, where S is a positive single digit integer.
Now we are concerned with only the digit in hundreds place, as tens and ones digit can take any values from 0 to 10, while hundreds digit, P, can take only 1 or 2 as values.
\(R=Q+\frac{3S}{4}\)
So S has to be a multiple of 4, that is 4 or 8.
(a) \(S=8.....R=Q+6=(P+S)+6=P+8+6\)
But R is a single digit. So S cannot be 8.
(b) \(S=4.....R=Q+3=(P+S)+3=P+4+3=P+7\)
So, R=P+7. But R is a single digit, so R can be 8 or 9. Thus P will be 1 or 2.
So PQR=1QR or 2QR
In both cases, the integer PQR will lie between 100 and 300
2. Q=P+T+2, R=Q+3/2T. T is a positive single digit integer.
\(R=Q+\frac{3T}{2}\)
So T has to be a multiple of 2, that is 2, 4, 6 or 8.
a) T=2.....R=Q+3=(P+T+2)+3=P+2+2+3=P+7
So, R=P+7. But R is a single digit, so R can be 8 or 9. Thus P will be 1 or 2.
So PQR=1QR or 2QR
In both cases, the integer PQR will lie between 100 and 300
b) T=4.....R=Q+6=(P+T+2)+6=P+4+2+6=P+12
R=P+12.
But R is a single digit. So S cannot be 8.
All other values will make R even bigger than the value in case b.
Thus only case (a) possible.
D
23 Jul 2022, 04:32
Kudos
Bookmarks
Here is one way to do it (although it took long!)
PQR --> all positive integers, single-digit. This means P,Q,R could be 1,2,3,4,5,6,7,8,9
Is PQR between 100 and 300? This simply translates to whether P is 1 or 2.
Why? Because Q and R are never zero, so when P = 1 or 2, PQR minimum = 111, PQR maximum = 299
Let's look at the statements now.
Statement #1
Q = P+S
R = Q + 0.75S
We want to know what values P will take. So, use these equations --
P = Q - S = R - 0.75S - S = R - 1.75S
For P to be an integer, R - 1.75S must be an integer. So, 1.75S must be an integer. 1.75S = 7S/4. This takes an integer values only when S = 4 or 8
At S = 4, P = R - 7 --> P can be 1 or 2 because R can be 8 or 9 for P to be > 0 and single-digit.
At S = 8, P = R - 14 --> here, R will have to be greater than 14 for P to be a positive integer. That is not possible!
P = 1 or 2. Statement is sufficient.
Statement #2
The approach is same as that for statement 1.
Q = P+T+2 --> P = Q-T-2 = (R-3T/2)-T-2 = R - 5T/2 - 2
Again, to get integer values for P, 5T/2 must be an integer. T = 2,4,6,8.
At T = 2, P = R - 7. Same situation as statement #1. P = 1 or 2.
For T = 4,6,8, R cannot be single-digit.
Sufficient.
Answer = D
---
Edit: Just saw that another similar solution is already posted. I hope this helps in any case!
PQR --> all positive integers, single-digit. This means P,Q,R could be 1,2,3,4,5,6,7,8,9
Is PQR between 100 and 300? This simply translates to whether P is 1 or 2.
Why? Because Q and R are never zero, so when P = 1 or 2, PQR minimum = 111, PQR maximum = 299
Let's look at the statements now.
Statement #1
Q = P+S
R = Q + 0.75S
We want to know what values P will take. So, use these equations --
P = Q - S = R - 0.75S - S = R - 1.75S
For P to be an integer, R - 1.75S must be an integer. So, 1.75S must be an integer. 1.75S = 7S/4. This takes an integer values only when S = 4 or 8
At S = 4, P = R - 7 --> P can be 1 or 2 because R can be 8 or 9 for P to be > 0 and single-digit.
At S = 8, P = R - 14 --> here, R will have to be greater than 14 for P to be a positive integer. That is not possible!
P = 1 or 2. Statement is sufficient.
Statement #2
The approach is same as that for statement 1.
Q = P+T+2 --> P = Q-T-2 = (R-3T/2)-T-2 = R - 5T/2 - 2
Again, to get integer values for P, 5T/2 must be an integer. T = 2,4,6,8.
At T = 2, P = R - 7. Same situation as statement #1. P = 1 or 2.
For T = 4,6,8, R cannot be single-digit.
Sufficient.
Answer = D
---
Edit: Just saw that another similar solution is already posted. I hope this helps in any case!
