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x=120 and y=150
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12 Aug 2017, 10:17
12 Aug 2017, 10:17
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82% (01:09) correct
17% (01:06) wrong based on 346 sessions
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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
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22 Aug 2017, 14:32
22 Aug 2017, 14:32
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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
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General Discussion
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: x=120 and y=150
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22 Aug 2017, 14:25
22 Aug 2017, 14:25
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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
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