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Retired Moderator Joined: 07 Jun 2014
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GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
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The number of distinct factors of 32 [#permalink]
Expert's post 00:00

Question Stats: 59% (00:43) correct 40% (00:24) wrong based on 61 sessions
 Quantity A Quantity B The number of distinct positive factors of 32 The number of distinct positive factors of 20

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Sandy
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Active Member Joined: 29 May 2018
Posts: 126
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Kudos [?]: 112 , given: 4

Re: The number of distinct factors of 32 [#permalink]
sandy wrote:
 Quantity A Quantity B The number of distinct positive factors of 32 The number of distinct positive factors of 20

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

Rule : First make prime factorization of an integer N = a^p * b ^q * c^r , where a, b , and c and are prime factors of and p , q , and r are their powers.
The number of factors of will be expressed by the formula (p+1) (q+1) (r+1). NOTE: this will include 1 and n itself.

Now factorise Col A : we get 2^5 and
Col B : 2^2 * 5^1.

As per above formula Col A : (5+1) = 6
Col B : (2+1)(1+1) = 6.

Both same .

C. GRE Instructor Joined: 10 Apr 2015
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Re: The number of distinct factors of 32 [#permalink]
2
KUDOS
Expert's post
sandy wrote:
 Quantity A Quantity B The number of distinct positive factors of 32 The number of distinct positive factors of 20

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

Alternatively, we can just list and count the positive factors of 32 and 20

QUANTITY A: Factors of 32: 1, 2, 4, 8, 16, 32 (6 factors)
QUANTITY B: Factors of 20: 1, 2, 4, 5, 10, 20 (6 factors)

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com  Intern  Joined: 07 May 2020
Posts: 20
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Kudos [?]: 12  , given: 72

Re: The number of distinct factors of 32 [#permalink]
1
KUDOS
A
1*32
2*16
4*8
Seems we have 6 factors

B
1*20
2*10
4*5
Again, we have 6 factors here as well Re: The number of distinct factors of 32   [#permalink] 21 Jun 2020, 07:13
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