|
|
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.
25 Apr 2023, 10:30
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
80% (00:54) correct
20%
(00:59)
wrong
based on 55
sessions
History
Date
Time
Result
Not Attempted Yet
If x, y are positive integers, is \(xy=1\)?
(1) \(x^2y^2=xy\)
(2) \(\frac{1}{y}=x\)
(1) \(x^2y^2=xy\)
(2) \(\frac{1}{y}=x\)
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
15 May 2023, 21:31
Kudos
Bookmarks
Bunuel
Solution:
Pre Analysis:
- x, y are positive integers
- We are asked if \(xy=1\) or not
Statement 1: \(x^2y^2=xy\)
- 3 ways to do this:
- Inference:
- We have \((xy)^2=xy\) which means its square of positive integer is equal to the same positive integer
- This is true only when the positive integer is 1
- Thus, \(xy=1\)
- Algebra 1:
- We have \(x^2y^2=xy\)
- Since x and y are positive integers, we can cancel them from opposite sides of equal to sign and say \(xy=1\)
- Algebra 2:
- We have \(x^2y^2=xy\)
\(⇒x^2y^2-xy=0\)
\(⇒xy(xy-1)=0\) - Either \(xy=0\) which is not possible because x and y are positive integers
- Or \(xy=1\)
- We have \(x^2y^2=xy\)
- Thus, statement 1 alone is sufficient and we can eliminate options B, C and E
Statement 2: \(\frac{1}{y}=x\)
- We can multiply positive integer y to both the sides and get \(xy=1\)
- Thus, statement 2 alone is also sufficient
Hence the right answer is Option D
Moderator:
