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x=120 and y=150

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


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GreenlightTestPrep
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Re: x=120 and y=150 [#permalink] New post   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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Re: x=120 and y=150 [#permalink] New post   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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Re: x=120 and y=150 [#permalink] New post   09 Dec 2019, 03:05
Carcass wrote:

This question is part of GREPrepClub - The Questions Vault Project



x=120 and x=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.


which one is 'X', and which one is 'Y' ?
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Re: x=120 and y=150 [#permalink] New post   09 Dec 2019, 03:08
GreenlightTestPrep wrote:
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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IF it did not tell us indicating about positive divisor then, do we need to count the negative values also?
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Re: x=120 and y=150 [#permalink] New post   09 Dec 2019, 11:09
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huda wrote:
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


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.


which one is 'X', and which one is 'Y' ?


Good catch! I've edited the original post
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Re: x=120 and y=150 [#permalink] New post   09 Dec 2019, 11:10
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huda wrote:
IF it did not tell us indicating about positive divisor then, do we need to count the negative values also?


That is correct. For example, -12 is also considered a divisor of 120.
However, when it comes to Integer Properties questions, you will find that the GRE always limits are the values to positive integers.

Cheers,
Brent
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Re: x=120 and y=150 [#permalink] New post   28 Feb 2024, 22:34
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Prime Factors of x=120 are 2, 2, 3, 5, 2

Prime Factors of y=150 are 5, 5, 3, 2

Well, 120 has more prime factors than 150, so it will have more factors than 150
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Re: x=120 and y=150 [#permalink] New post   05 Mar 2025, 08:02
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