OG Sum of fractions

AbeNeedsAnswers wrote:If (1/3 + 1/4 + 1/5 + 1/6) = r(1/9 + 1/12 + 1/15 + 1/18), then r =

A) 1/3
B) 4/3
C) 3
D) 4
E) 12

C

One of the time-taking approaches is taking the LCM and get r--not recommended!

Let us try to find out any pattern among the fractions. We see that 1/3 is 3 times of 1/9; 1/4 is 3 times of 1/12; 1/5 is 3 times of 1/15; and 1/6 is 3 times of 1/18.

Thus, (1/3 + 1/4 + 1/5 + 1/6) = (3/9 + 3/12 + 3/15 + 3/18) = 3*(1/9 + 1/12 + 1/15 + 1/18)

=> 3(1/9 + 1/12 + 1/15 + 1/18) = r(1/9 + 1/12 + 1/15 + 1/18)

=> [spoiler]r = 3[/spoiler]

The correct answer: C

Hope this helps!

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AbeNeedsAnswers wrote:If (1/3 + 1/4 + 1/5 + 1/6) = r(1/9 + 1/12 + 1/15 + 1/18), then r =

A) 1/3
B) 4/3
C) 3
D) 4
E) 12

C

Another approach is to eliminate the fractions by multiplying both sides by the least common multiple (LCM) of all 8 denominators.

The LCM is 180
So take: (1/3 + 1/4 + 1/5 + 1/6) = r(1/9 + 1/12 + 1/15 + 1/18)
Multiply both sides by 180 to get: 180 (1/3 + 1/4 + 1/5 + 1/6) = r(180 )(1/9 + 1/12 + 1/15 + 1/18)
Expand: 60 + 45 + 36 + 30 = r(20 + 15 + 12 + 10)

At this point, it's easy so see that r = 3

Answer: C

Cheers,
Brent

Hi AbeNeedsAnswers,

Here, we're given one big equation to deal with and we're asked to find the value of R. Since there's just one variable - and the answer choices are numbers - we can TEST THE ANSWERS.

It's important to remember that nothing about a GMAT question is ever 'random' - every prompt is carefully designed to test you on specific concepts, every word and every number is carefully chosen (and even the wrong answer choices are specifically chosen). As such, you can use the typical design elements 'against' the prompt.

In this question, notice how both sides of the equation include the sum of 4 fractions. That's interesting.... maybe multiplying each fraction on the right side by R will get you one of the fractions on the left side.... Let's compare the first fraction of each 1/3 vs. 1/9. Could you multiply 1/9 by any of the answer choices and get 1/3? YES... (3)(1/9) = 1/3. Does that relationship exist among the other three pairs of fractions?

3(1/12) = 1/4
3(1/15) = 1/5
3(1/18) = 1/6

Thus, 3 is clearly the value of R.

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

AbeNeedsAnswers wrote:If (1/3 + 1/4 + 1/5 + 1/6) = r(1/9 + 1/12 + 1/15 + 1/18), then r =

A) 1/3
B) 4/3
C) 3
D) 4
E) 12

C

We can simplify the given expression by multiplying by 180, and we have:

60 + 45 + 36 + 30 = 20r + 15r + 12r + 10r

171 = 57r

r = 3

Alternate Solution:

We should note that each fraction on the left-hand side is 3 times the corresponding fraction on the right.

For example, 1/3 is 3 times 1/9, 1/4 is 3 times 1/12, etc.

Thus, r MUST be 3.

Answer: C