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 1912:30 PM EST
-01:30 PM EST
Learn how Keshav, a Chartered Accountant, scored an impressive 705 on GMAT in just 30 days with GMATWhiz's expert guidance. In this video, he shares preparation tips and strategies that worked for him, including the mock, time management, and more
Nov 2001:30 PM EST
-02:30 PM IST
Learn how Kamakshi achieved a GMAT 675 with an impressive 96th %ile in Data Insights. Discover the unique methods and exam strategies that helped her excel in DI along with other sections for a balanced and high score.
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 2407:00 PM PST
-08:00 PM PST
Full-length FE mock with insightful analytics, weakness diagnosis, and video explanations!
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.
23 Dec 2022, 07:00
Kudos
Bookmarks
A
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:
32% (02:00) correct
68%
(01:55)
wrong
based on 112
sessions
History
Date
Time
Result
Not Attempted Yet
12 Days of Christmas GMAT Competition with Lots of Fun
If x and y are non-zero integers, is \(\frac{x}{30} + \frac{y}{50} = 10\)?
(1) \(x + y = 500\)
(2) \(y – x = 20\)
If x and y are non-zero integers, is \(\frac{x}{30} + \frac{y}{50} = 10\)?
(1) \(x + y = 500\)
(2) \(y – x = 20\)
|
24 Dec 2022, 04:02
Kudos
Bookmarks
Bunuel
GMATWhiz Official Explanation:
Step 1: Analyse Question Stem
- x and y are non-zero integers
- We are given x/30+y/50=10
- ⇒ (5x+3y)/150=10
⇒ 5x+3y=1500
⇒ 3y=1500-5x
⇒ y=(1500-5x)/3
⇒ y=500-5x/3 - Since y is an integer, therefore 5x/3 has to be an integer for which we can assume x=3k where k is non-zero integer
- Plugging x = 3k, we get y=500-(5×3k)/3 ⇒ y=500-5k
- So, for x/30+y/50=10 to exist, the value of x and y has to be of the form 3k and 500 – 5k respectively
Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE
Statement 1: x + y = 500
- If x=3k and y=500-5k is true:
- o We know x + y = 3k + 500 – 5k = 500 – 2k
o 500 – 2k is never equal to 500 because k is non-zero - So, x=3k and y=500-5k is not true
- Thus statement 1 alone is sufficient and we can eliminate options B, C and E
Statement 2: y – x = 20
- If x=3k and y=500-5k is true:
- o We know y – x = 500 – 5k – 3k = 500 – 8k
- 500 – 8k = 20 when k = 60
- And 500 – 8k ≠ 20 for other values of k.
- 500 – 8k = 20 when k = 60
Hence the right answer is Option A.
General Discussion
UtkarshAnand
Joined: 08 May 2021
Last visit: 17 Nov 2025
Posts: 85
Given Kudos: 1,156
Location: India
Schools: Booth '24 Harvard '24 LBS '24 Stanford '24 Wharton '24
23 Dec 2022, 08:29
Kudos
Bookmarks
Bunuel
Solution:
Given, x and y are non-zero integers
\(\frac{x}{30} + \frac{y}{50} = 10\)?
or 5x + 3y = 1500?
Statement (1) \(x + y = 500\)
Multiplying the equation by 3 we have, 3x + 3y = 1500. This when compared to 5x + 3y = 1500 has a difference of 2x unaccounted for.
As x and y are non-zero integers, clearly 2x will have some value and hence, either 5x + 3y>1500 or 5x + 3y<1500. But 5x + 3y cannot equal 1500 (as x cannot be equal to 0).
Sufficient.
Statement (2) \(y – x = 20\)
As the difference is given, we cannot manipulate the statement to arrive at something similar to question statement, 5x + 3y = 1500. Clearly, insufficient.
ANSWER A.
