GRE Prep 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.
x=120 and y=150
[#permalink]
12 Aug 2017, 10:17
12 Aug 2017, 10:17
3
Expert Reply
3
Bookmarks
00:00
Question Stats:
81% (01:07) correct
18% (01:06) wrong based on 331 sessions
Hide Show timer Statistics
x=120 and y=150
Quantity A |
Quantity B |
The number of positive divisors of x |
The number of positive divisors of y |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: x=120 and y=150
[#permalink]
22 Aug 2017, 14:32
22 Aug 2017, 14:32
9
1
1
Bookmarks
Carcass wrote:
y=120 and x=150
Quantity A |
Quantity B |
The number of positive divisors of x |
The number of positive divisors of y |
-------ASIDE-----------------------------------
Useful rule:
If the prime factorization of N = (p^a)(q^b)(r^c) . . . (where p, q, r, etc are different prime numbers), then N has a total of (a+1)(b+1)(c+1)(etc) positive divisors.
Example: 14000 = (2^4)(5^3)(7^1)
So, the number of positive divisors of 14000 = (4+1)(3+1)(1+1) =(5)(4)(2) = 40
------NOW ONTO THE QUESTION--------------------
120 = (2)(2)(2)(3)(5)
= (2^3)(3^1)(5^1)
So, the number of positive divisors of 120 = (3+1)(1+1)(1+1)
= (4)(2)(2)
= 16
150 = (2)(3)(5)(5)
= (2^1)(3^1)(5^2)
So, the number of positive divisors of 150 = (1+1)(1+1)(2+1)
= (2)(2)(3)
= 12
We get:
Quantity A: 16
Quantity B: 12
Answer: A
RELATED VIDEO FROM OUR COURSE
General Discussion
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: x=120 and y=150
[#permalink]
22 Aug 2017, 14:25
22 Aug 2017, 14:25
2
1
Bookmarks
Carcass wrote:
x=120 and y=150
Quantity A |
Quantity B |
The number of positive divisors of x |
The number of positive divisors of y |
Let's list the positive divisors of 120 and 150
120: {1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120} (16 values)
150: {1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150} (12 values)
So, we get:
Quantity A: 16
Quantity B: 12
Answer: A
RELATED VIDEO FROM OUR COURSE
