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If a three-digit number 'ABC' has 2 factors, where A, B, and C are

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General GMAT Forum Moderator
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If a three-digit number 'ABC' has 2 factors, where A, B, and C are  [#permalink]

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New post 06 Jan 2020, 22:44
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A
B
C
D
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Difficulty:

  65% (hard)

Question Stats:

47% (01:59) correct 53% (02:07) wrong based on 30 sessions

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If a three-digit number 'ABC' has two factors, where A, B, and C are digits, then how many factors does the six-digit number 'ABCABC' have?

A. 16
B. 18
C. 20
D. 24
E. 30

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Re: If a three-digit number 'ABC' has 2 factors, where A, B, and C are  [#permalink]

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New post 06 Jan 2020, 22:50
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1
If 'ABC' has only 2 factors, ABC must be a prime number.

'ABCABC'= ABC* 1001= ABC*7*11*13

Number of factors of 'ABCABC'= 2*2*2*2= 16


DisciplinedPrep wrote:
If a three-digit number 'ABC' has two factors, where A, B, and C are digits, then how many factors does the six-digit number 'ABCABC' have?

A. 16
B. 18
C. 20
D. 24
E. 30
General Discussion
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Re: If a three-digit number 'ABC' has 2 factors, where A, B, and C are  [#permalink]

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New post 26 Jan 2020, 20:44
1
nick1816 thanks for the debrief. I managed to obtain the answer but it took me a longer process of assuming a 3 digit prime (i.e 103) and finding its factors.

May i know if the 1001 from below is based on a known properties or an assumption?
Quote:
'ABCABC'= ABC* 1001= ABC*7*11*13
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Re: If a three-digit number 'ABC' has 2 factors, where A, B, and C are  [#permalink]

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New post 27 Jan 2020, 14:36
1
aaronlcr93

abc * 1001
= abc* (1000+1)
= abc*1000 + abc*1
= abc000+ abc
=abcabc

aaronlcr93 wrote:
nick1816 thanks for the debrief. I managed to obtain the answer but it took me a longer process of assuming a 3 digit prime (i.e 103) and finding its factors.

May i know if the 1001 from below is based on a known properties or an assumption?
Quote:
'ABCABC'= ABC* 1001= ABC*7*11*13
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Re: If a three-digit number 'ABC' has 2 factors, where A, B, and C are  [#permalink]

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New post 28 Jan 2020, 03:53
nick1816 wrote:

Number of factors of 'ABCABC'= 2*2*2*2= 16


DisciplinedPrep wrote:
If a three-digit number 'ABC' has two factors, where A, B, and C are digits, then how many factors does the six-digit number 'ABCABC' have?

A. 16
B. 18
C. 20
D. 24
E. 30


Don't understand this. Take 127 for example

ABC = 127
ABCABC = 127127

Factors:

127127, 127, 1001, 143, 13, 11, 7, 1

??
GMAT Club Bot
Re: If a three-digit number 'ABC' has 2 factors, where A, B, and C are   [#permalink] 28 Jan 2020, 03:53
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