gmat prep 2

[jainrahul1985]

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

OA E

How to calculate LCM of fractions . Please help . No idea how to approach this question .

[GMATGuruNY]

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.

[lunarpower]

received a pm.
mitch has already done a nice job of answering the question. however, one comment on the following --

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.

this method works, of course, but it is probably best left to numbers that are already expressed as prime factorizations. for instance, if you see (5^3)(7^6) and (5^4)(7^2), then the least common multiple of these 2 numbers is (5^4)(7^6).

if you are given actual integers, then, in most cases, it's much faster just to consider multiples of one number (usually the bigger one) until you find a multiple of the other one.
for instance:
given 210 and 60 ... let's look at multiples of 210.
is 210 a multiple of 60? no.
is 420 a multiple of 60? yes.
done; the LCM is 420.

[GMATGuruNY]

received a pm.
mitch has already done a nice job of answering the question. however, one comment on the following --

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.

this method works, of course, but it is probably best left to numbers that are already expressed as prime factorizations. for instance, if you see (5^3)(7^6) and (5^4)(7^2), then the least common multiple of these 2 numbers is (5^4)(7^6).

if you are given actual integers, then, in most cases, it's much faster just to consider multiples of one number (usually the bigger one) until you find a multiple of the other one.
for instance:
given 210 and 60 ... let's look at multiples of 210.
is 210 a multiple of 60? no.
is 420 a multiple of 60? yes.
done; the LCM is 420.

Agreed.

I would recommend prime-factoring when the integers are less familiar. To illustrate:

What is the LCM of 33 and 39?

Calculating multiples of 39:
2*39 = 78. Not a multiple of 33.
3*39 = 117. Not a multiple of 33.
4*39 = 156. Not a multiple of 33.
Since the LCM = 11*39, the process will take some time (even if we're wise enough to ignore the even multiples of 39, recognizing that the LCM of 33 and 39 cannot be even).

Prime-factoring would be quicker:
33 = 3...11
39 = 3.........13
The LCM = 3*11*13.

[lunarpower]

I would recommend prime-factoring when the integers are less familiar.

oh, ya, for sure. i think we're actually on the same page here.
however, knowing the gmat, students will probably see the following situations most often:
* "nice" integers given as actual integers (e.g., 60 and 210)
* "ugly" integers given as prime factorizations

this is overwhelmingly not a "grunt work" type of test, so i think that examples like the one above, while not totally absent from the test, will be comparatively rare.

but, as usual, the key idea is ... more approaches = better