Forum Home > GMAT > Quantitative > Problem Solving (PS)
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.
Jan 2110:00 AM PST
-11:59 PM PST
For a limited time, get 20% off our GMAT courses, including private tutoring! Work with an expert who will help you ace the GMAT and achieve your dreams. Use code 20NEW.
Jan 2410:00 AM EST
-12:00 PM EST
The Target Test Prep team is proud to introduce GMAT OnDemand, a video course created by Scott Woodbury-Stewart, founder and CEO, designed to provide you with everything you need to master the GMAT and achieve your score goals.
Jan 2511:00 AM IST
-01:00 PM IST
Attend this session to learn how to Deconstruct arguments, Pre-Think Author’s Assumptions, and apply Negation Test.- Jan 26
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.
16 Sep 2014, 01:25
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
71% (01:17) correct
29%
(01:38)
wrong
based on 319
sessions
History
Date
Time
Result
Not Attempted Yet
What is the smallest positive integer \(k\) such that \(126*\sqrt{k}\) is the square of a positive integer?
A. 14
B. 36
C. 144
D. 196
E. 441
A. 14
B. 36
C. 144
D. 196
E. 441
16 Sep 2014, 01:25
Kudos
Bookmarks
Official Solution:
What is the smallest positive integer \(k\) such that \(126*\sqrt{k}\) is the square of a positive integer?
A. 14
B. 36
C. 144
D. 196
E. 441
\(126=23^27\), so for \(126*\sqrt{k}\) to be the square of an integer, \(\sqrt{k}\) must complete the powers of 2 and 7 to an even number. Therefore, the smallest value of \(\sqrt{k}\) must be \(2*7=14\), which makes the smallest value of \(k\) equal to \(14^2=196\).
Answer: D
What is the smallest positive integer \(k\) such that \(126*\sqrt{k}\) is the square of a positive integer?
A. 14
B. 36
C. 144
D. 196
E. 441
\(126=23^27\), so for \(126*\sqrt{k}\) to be the square of an integer, \(\sqrt{k}\) must complete the powers of 2 and 7 to an even number. Therefore, the smallest value of \(\sqrt{k}\) must be \(2*7=14\), which makes the smallest value of \(k\) equal to \(14^2=196\).
Answer: D
General Discussion
15 Aug 2018, 20:56
Kudos
Bookmarks
Bunuel
What is the smallest positive integer \(k\) such that \(126*\sqrt{k}\) is the square of a positive integer?
A. 14
B. 36
C. 144
D. 196
E. 441
A. 14
B. 36
C. 144
D. 196
E. 441
This question can be easily solved by factorisation.
126*√k
=> 2*3*3*7*√k
=> 3^2*14*√k
i.e. we need another 14 to make it a square of positive number
i.e. √k=14
K= 14^2 = 196
D is the answer.
