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.
Apr 2808:00 AM PDT
-11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
Apr 2912:30 AM EDT
-01:30 AM EDT
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.
Apr 3001:30 AM EDT
-02:30 AM EDT
At one point, she believed GMAT wasn’t for her. After scoring 595, self-doubt crept in and she questioned her potential. But instead of quitting, she made the right strategic changes. The result? A remarkable comeback to 695. Check out how Saakshi did it.
May 0111:00 AM PDT
-12:00 PM PDT
Free- full-length test + 15 concept videos + 150+ short videos + study plan!
May 0306:30 AM PDT
-08:30 AM PDT
Verbal trouble on GMAT? Fix it NOW! Join Sunita Singhvi for a focused webinar on actionable strategies to boost your Verbal score and take your performance to the next level.
24 Sep 2018, 06:03
Kudos
Bookmarks
C
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:
73% (01:37) correct
27%
(01:36)
wrong
based on 113
sessions
History
Date
Time
Result
Not Attempted Yet
If x, y, p and q are positive integers, is x^p a factor of y^q?
(1) x is a factor of y.
(2) p < q + 1
(1) x is a factor of y.
(2) p < q + 1
24 Sep 2018, 11:18
Kudos
Bookmarks
If x, y, p and q are positive integers, is x^p a factor of y^q?
(1) x is a factor of y.
There are 4 variables but we know relationship of just two, so not possible to have a definite answer.
If x is 2, y is 4..
A) p is 100 and q is 2..... x^p is NOT a factor of y^q
B) but if p is 2 and q is 100, YES
Insufficient
(2) p < q + 1
Nothing about x and y
Insufficient
Combined..
x is a factor of y and p is not greater than a..
x^p will be atleast equal to y^q or a factor of it..
Sufficient
C
(1) x is a factor of y.
There are 4 variables but we know relationship of just two, so not possible to have a definite answer.
If x is 2, y is 4..
A) p is 100 and q is 2..... x^p is NOT a factor of y^q
B) but if p is 2 and q is 100, YES
Insufficient
(2) p < q + 1
Nothing about x and y
Insufficient
Combined..
x is a factor of y and p is not greater than a..
x^p will be atleast equal to y^q or a factor of it..
Sufficient
C
alldaytestprep
Expert
Tutor
Joined: 08 May 2018
Last visit: 24 Apr 2023
Posts: 98
Own Kudos:
Given Kudos: 1
Affiliations: All Day Test Prep
Location: United States (IL)
Schools: Booth '20 (A)
GMAT 1: 770 Q51 V49
GRE 1: Q167 V167
GPA: 3.58
Expert reply
24 Sep 2018, 11:43
Kudos
Bookmarks
Bunuel
For x^p to be a factor of y^q, (y^q)/(x^p) must be an integer. This means if we were to break y and x into their prime factors, y must be a multiple of x and q must be greater than or equal to p.
This should make logical sense if you understand your basic divisibility rules and how to cancel out numbers when dividing. Some examples to illustrate:
Example 1: (3^5)/(3^2) = 3^3 = 27(an integer).
Example 2: (9^2)/(3^5) = (3^4)/(3^5) = 1/3(not an integer).
In the second case, note that how even though x is a multiple of y, q is less than p and therefore we don't get an integer.
Statement 1) Using our examples from above we see that in each case x is a factor of y. However in example 1 we get an integer and in example we do not get an integer.
INSUFFICIENT
Statement 2) Since p & q must be integers, this tells us q is greater than or equal to p. This is part of what we're looking for, however we still need to know if y is a multiple of x.
INSUFFICIENT
Statements 1 & 2) Now we know that y is a multiple of x and q is greater than or equal to p. Exactly what we're looking for.
SUFFICIENT
Answer: C
