In the fraction x/y , where x and y are positive integers, what is the value of y ?
(1) The least common denominator of x/y and 1/3 is 6.
(2) x = 1
The LCD of two fractions is the smallest positive integer that is a multiple of both denominators when each fraction is in its most reduced form.
Thus, the following combinations satisfy both statements:
x=1 and y=2, so that the two fractions are 1/2 and 1/3.
The LCD=6, because the smallest positive multiple of 2 and 3 is 6.
x=1 and y=6, so that the two fractions are 1/6 and 1/3.
The LCD=6, because the smallest positive multiple of 6 and 3 is 6.
Since it's possible that y=2 or that y=6, insufficient.
The correct answer is
E
Here's one way to calculate the LCM (least common multiple) of positive integers x and y:
1. List the prime factors of x and y in two rows.
2. Put any factors common both to x and y in a single column.
3. Include every column in the LCM.
Given x = 60 and y = 210:
x = 2...2...3...5
y = .....2...3...5...7
Including an entry for every column shown above, we get:
LCM = 2*2*3*5*7 = 420.
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