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# If a three digit number ‘xyz’ has 3 factors, how many factors does the

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CR Forum Moderator
Status: The best is yet to come.....
Joined: 10 Mar 2013
Posts: 529
If a three digit number ‘xyz’ has 3 factors, how many factors does the [#permalink]

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20 Oct 2017, 07:44
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65% (hard)

Question Stats:

36% (01:03) correct 64% (00:58) wrong based on 28 sessions

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If a three digit number ‘xyz’ has 3 factors, how many factors does the 6-digit number ‘xyzxyz’ have?

A. 16 factors
B. 20 factors
C. 24 factors
D. 16 or 20 factors
E. 16 or 24 factors
[Reveal] Spoiler: OA

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Hasan Mahmud

Math Expert
Joined: 02 Aug 2009
Posts: 5660
If a three digit number ‘xyz’ has 3 factors, how many factors does the [#permalink]

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20 Oct 2017, 07:56
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Mahmud6 wrote:
If a three digit number ‘xyz’ has 3 factors, how many factors does the 6-digit number ‘xyzxyz’ have?

A. 16 factors
B. 20 factors
C. 24 factors
D. 16 or 20 factors
E. 16 or 24 factors

$$xyzxyz=xyz*1001=xyz*7*11*13$$
and $$xyz = a^2$$ as it has ONLY 3 factors so it is SQUARE of prime number..
so $$xyzxyz=a^2*7*11*13$$..
two possibilities now:-
1) if a is a different PRIME, number of factors = 3*2*2*2=24..
2) If a is one of 7,11 or 13 # = 11^3*7*13 = 4*2*2=16

so 16 or 24

E
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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If a three digit number ‘xyz’ has 3 factors, how many factors does the   [#permalink] 20 Oct 2017, 07:56
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