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Retired Moderator
Joined: 07 Jun 2014
Posts: 4805
GRE 1: Q167 V156
WE:Business Development (Energy and Utilities)
The number of distinct prime factors of 100,000
[#permalink]
12 Aug 2018, 16:01
12 Aug 2018, 16:01
3
Expert Reply
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Question Stats:
71% (00:42) correct
28% (00:36) wrong based on 101 sessions
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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.
_________________
Sandy
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Re: The number of distinct prime factors of 100,000
[#permalink]
15 Aug 2018, 23:22
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.
Quantity B gives 4 distinct factors 2, 3, 5, 11.
Hence B is greater.
Option B is the answer.
Retired Moderator
Joined: 07 Jun 2014
Posts: 4805
GRE 1: Q167 V156
WE:Business Development (Energy and Utilities)
Re: The number of distinct prime factors of 100,000
[#permalink]
17 Aug 2018, 16:10
17 Aug 2018, 16:10
2
Expert Reply
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.
_________________
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.
_________________
Sandy
If you found this post useful, please let me know by pressing the Kudos Button
Try our free Online GRE Test
If you found this post useful, please let me know by pressing the Kudos Button
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Re: The number of distinct prime factors of 100,000
[#permalink]
14 Mar 2020, 11:05
14 Mar 2020, 11:05
More DISTINCT prime factors in B. Don't be like dumb me and find the total number of factors of each wasting precious time. Read the question.
Re: The number of distinct prime factors of 100,000
[#permalink]
23 Jun 2022, 08:13
23 Jun 2022, 08:13
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