In the fraction a/b, where a and b are positive integers, what is the

Question

In the fraction a/b, where a and b are positive integers, what is the value of b?

(1) The lowest common denominator of a/b and 1/5 is 10.
(2) a = 3

DesiGmat · Answer

Here we go -

a and b are positive integers (given)

St1: The lowest common denominator of a/b and 1/5 is 10.

a = 1
b = 2
St1 satisfied

a = 6
b = 12
St1 satisfied

we have two different values for b
St1 is not sufficient

St2 : a = 3

Clearly insufficient

Combining

a = 3
b = 2

Both statements satisfied

a = 3
b = 6
again both statements satisfied.

we are getting two different values of b

option E is the correct answer.

anupamadw · Answer

Hi 
I know about LCM and GCD, wht is lowest common denominator?
3/6 and 1/5 --> has lowest common denominator 30 rt?
Please clarify me.
Thnx

manpreetsingh86 · Answer

hi,
 Least/lower common denominator :  the lowest common multiple of the denominators of several set of fractions.

3/6 = 1/2
so, least common denominator of 3/6=1/2 and 1/5 = 10.

similarly, LCD of 3/5 and 1/6 is 30

i hope it helps.

DesiGmat · Answer

+1 ManpreetSingh86

Perfectly explained

sagar2911 · Answer

St. 1: a/b & 1/5 to have a common denominator of 10, a/b can be 1/2, 2/4, 3/6 etc. We get diff values of b - Not satisfied

St. 2: a = 3; this does not tell anything about b - Not satisfied

Combining: Set a = 3, to get common denominator of 10, a/b can be 3/2 and 3/6. We get 2 diff values of b - Not satisfied

Correct ans: Option E

Thanks

Bunuel · Answer

OFFICIAL SOLUTION:

This problem seems simple, but if you try to solve it too quickly, you may miss something. So consider all possibilities.

Statement (1) is the potentially tricky one. You may quickly jump to the conclusion that if the lowest common denominator (LCD) of the two fractions is 10, then b
a must have a denominator of 10, which would mean that b = 10. However, b could also equal 2 and the two fractions would still have an LCD of 10. Because b has two possible values, statement (1) is insufficient. The answer is either B, C, or E.

Statement (2) is easier to evaluate. The value of the numerator has no bearing on the value of the denominator, so the fact that a = 3 is irrelevant to the value of b. Statement (2) is also insufficient, which means the answer is either C or E.

Knowing that a = 3 tells you nothing about whether the LCD is 10 or 2, so the two statements together are still insufficient to answer the question. Correct answer: E.

Bunuel · Answer

Similar question to practice: in-the-fraction-x-y-where-x-and-y-are-positive-integers-wh-168099.html

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In the fraction a/b, where a and b are positive integers, what is the

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