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x=120 and y=150

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x=120 and y=150 [#permalink] New post 12 Aug 2017, 10:17
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x=120 and x=150

Quantity A
Quantity B
The number of positive divisors of x
The number of positive divisors of y
[Reveal] Spoiler: OA

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Joined: 10 Apr 2015
Posts: 638
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Kudos [?]: 450 [0], given: 3

Re: x=120 and y=150 [#permalink] New post 22 Aug 2017, 14:25
Expert's post
Carcass wrote:
x=120 and x=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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Kudos [?]: 450 [1] , given: 3

Re: x=120 and y=150 [#permalink] New post 22 Aug 2017, 14:32
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Expert's post
Carcass wrote:
x=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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Re: x=120 and y=150   [#permalink] 22 Aug 2017, 14:32
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