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The number of distinct prime factors of 100,000

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GMAT Club Legend
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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 prime factors of 100,000 [#permalink] New post 12 Aug 2018, 16:01
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Question Stats:

100% (00:33) correct 0% (00:00) wrong based on 11 sessions
Quantity A
Quantity B
The number of distinct prime factors of 100,000
The number of distinct prime factors of 99,000


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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Re: The number of distinct prime factors of 100,000 [#permalink] New post 15 Aug 2018, 23:22
Quantity A gives 2 distinct factors 2 and 5.
Quantity B gives 4 distinct factors 2, 3, 5, 11.
Hence B is greater.
Option B is the answer.
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4749
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1653 [0], given: 396

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Re: The number of distinct prime factors of 100,000 [#permalink] New post 17 Aug 2018, 16:10
Expert's post
Explanation

Since only the number of distinct prime factors matter, not what they are or how many times they are present, it is possible to tell on sight that Quantity A has only 2 distinct prime factors, because 100,000 is a power of 10. (Any prime tree for 10, 100, or 1,000, etc. will contain only the prime factors 2 and 5, occurring in pairs.)

In Quantity B, 99,000 breaks down as 99 × 1,000. Since 1,000 also contains 2’s and 5’s, and 99 contains even more factors (specifically 3, 3, and 11), Quantity B is greater. It is not necessary to make prime factor trees for each number.
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Re: The number of distinct prime factors of 100,000   [#permalink] 17 Aug 2018, 16:10
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The number of distinct prime factors of 100,000

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