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If k is a two digit positive integer, what is the value of

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If k is a two digit positive integer, what is the value of [#permalink] New post 27 Oct 2006, 00:31
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If k is a two digit positive integer, what is the value of k?

(1) There is exactly 1 three digit integer that is a multiple of both 140 and 21k.
(2) Each prime factor of k is a factor of 140.
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 [#permalink] New post 27 Oct 2006, 06:21
C

Stem: k has to be 2 digit

Stat1: One 3 digit number multiple of both 140 and 21k

For 140: You can multiply 140 from 1 to 7 and still have 3 digit number
factors of 140 are 2,2,5,7


For 21k: factors are 3,7,k

It means: 140's multiple has to have 3 as a factor...that gives two choices multiply by 3 or 6....420 or 840....both of them have k=20 or 40....Insuff

Stat2:Each prime factor of k is a factor of 140
means k=10,14,20,28,35,70......Insuff

Combining...

k=20...Suff
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 [#permalink] New post 27 Oct 2006, 06:28
State 1)
The 3 digit number, let say Y, can be:
140 - 280 - 420 - 560 - 700 - 840 - 980
We can write 21k like 3*7*k. That means that the 3 digit number Y, must be divided at least by 3 and 7
From the group, there are only two possibilities : 420 and 840
Dividing 420 and 840 by 21 (3*7), we can obtain the value of k
K can be 20 or 40
INSUFF

State 2)
The prime factors of 140 are 2,5 and 7
The 2 digits possibilities with those factors are : 4,10,14,20,28,35,70
K can be anyone from this group
INSUFF

State 1+2)
From 1) : K can be 20 or 40
From 2) Only 20 is one of the alternatives
SUFFICIENT

Answer is C
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Re: DS: Value of k [#permalink] New post 27 Oct 2006, 07:06
kevincan wrote:
If k is a two digit positive integer, what is the value of k?

(1) There is exactly 1 three digit integer that is a multiple of both 140 and 21k.



I like A.

Strategy-wise, this is a tough question, therefore, answers C and E are doubtful.

If 140 and 21k has exactly one 3 digit common multiple, then K is solvable.

Find all 3 digit multiples of 140

140, 280, 420, 560, 700, 840, 980

The only ones divisible by 21 are 420 and 840.

If k=20, then there are TWO 3 digit multiples of 140 and 21k (420 and 840).
If k=40, then there is only ONE 3 digit multiple of 140 and 21k (840)

Therefore K=40.

SUFF

------------------------

kevincan wrote:
(2) Each prime factor of k is a factor of 140.


The prime factors of 140 = 2, 2, 5, 7

Therefore, the prime factors of K=any combination of above prime factors.

K=10, 20, 28, 35, 70 etc etc. Too many options,
INSUFF
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 [#permalink] New post 27 Oct 2006, 12:39
I beleive (A).

Stat (1) - SUFF
420 and 840 are the only three digit numbers which can be a multiple of 140 and 21*k.
Again for k=8 we get only "1 three digit integer" as 840

Stat(2) - INSUFF
Because k=2 or k=7 etc..
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Re: DS: Value of k [#permalink] New post 30 Oct 2006, 08:09
is the stem sayin 21*K or 21k; where k is a 2 digit number..in the later case...its not possible..

kevincan wrote:
If k is a two digit positive integer, what is the value of k?

(1) There is exactly 1 three digit integer that is a multiple of both 140 and 21k.
(2) Each prime factor of k is a factor of 140.
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Re: DS: Value of k [#permalink] New post 30 Oct 2006, 17:29
kevincan wrote:
If k is a two digit positive integer, what is the value of k?

(1) There is exactly 1 three digit integer that is a multiple of both 140 and 21k.
(2) Each prime factor of k is a factor of 140.


It should be E

From 1) k can be 20 or 40

From (2) each prime factor of k is a factor of 140 NOT SUFF

Combining both both 20 and 40 prime factors are also factor od 140

So INSUFF
Re: DS: Value of k   [#permalink] 30 Oct 2006, 17:29
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