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27 Oct 2006, 01:31
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N
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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.
(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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27 Oct 2006, 07:21
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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
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
27 Oct 2006, 07:28
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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
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
