Divisor of a

[hk]

If a and b are positive integers such that a/b = 2.86, which of the following must be a divisor of a?

A. 10
B. 13
C. 18
D. 26
E. 50

[gmatplayer]

Answer: E

Question is what is b?

Since a is an integer only one of the five values given for B gives 'a' an integer value, & other four values will not be integer.

Try multiplying 2.86 by all five value choices

2.86*50 = 143 (integer)

[Ian Stewart]

If a and b are positive integers such that a/b = 2.86, which of the following must be a divisor of a?

A. 10
B. 13
C. 18
D. 26
E. 50

a/b = 2.86
a/b = 286/100
a/b = 143/50

So,

50a = 143b

Now 143 is a divisor of the right side of this equation, so it must be a divisor of the left side of the equation - that is, 50a is divisible by 143 - and since 50 can't be divided by 143, a must be divisible by 143 = 11*13. So a must be divisible by 11 and 13; B.

[gmatplayer]

I apologize for incomplete answer, you are right
I think I have solved too many problems today

[chintanjadwani]

i used a pretty stupid technique(tho the answers came out right)
if u can pls explain..!

i jus divided 2.86 by 26 , so got 22.... now 26 and 22 further 2 as a common factor, so we get 13 and 11...!! (got the same numbers as Ian .!!

so ..somehow i got the answer...but wat method is this..!!!

[dumb.doofus]

i used a pretty stupid technique(tho the answers came out right)
if u can pls explain..!

i jus divided 2.86 by 26 , so got 22.... now 26 and 22 further 2 as a common factor, so we get 13 and 11...!! (got the same numbers as Ian .!!

so ..somehow i got the answer...but wat method is this..!!!

It's called sixth sense