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13 Oct 2022, 01:31
Kudos
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D
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Difficulty:
75%
(hard)
Question Stats:
60% (02:46) correct
40%
(03:00)
wrong
based on 214
sessions
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The last four digits of a positive integer n are 1680. If you erase these four digits you get positive integer k. How many different values of n are there such that n/k is an integer ? (Assume that n has more than four digits)
A. 8
B. 16
C. 39
D. 40
E. 41
A. 8
B. 16
C. 39
D. 40
E. 41
Attachment:
Wonka.jpg
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13 Oct 2022, 03:01
Kudos
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Bunuel
Thus, the number is k1680, where k is a positive INTEGER, could be 1-,2-,3-digit and so on.
Now \(\frac{n}{k}=\frac{k1680}{k}=\frac{k*10000+1680}{k}=10000+\frac{1680}{k}\)
This means k should be a factor of 1680.
1680=2^4*3*5*7
Number of positive factors = (4+1)(1+1)(1+1)(1+1)=5*2*2*2=40
D
General Discussion
24 Apr 2026, 05:39
Kudos
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