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

Question

If (\frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6}) = r(\frac{1}{9} + \frac{1}{12} + \frac{1}{15} + \frac{1}{18}) , then r = A. \frac{1}{3} B. \frac{4}{3} C. 3 D. 4 E. 12 2018.OG.05.072.q.png

sashiim20 · Accepted Answer

\frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6} = r(\frac{1}{9}+\frac{1}{12}+\frac{1}{15}+\frac{1}{18}) \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6} = r*\frac{1}{3}(\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}) r*\frac{1}{3} =1 r = 3. Answer (C).. _________________ Please Press "+1 Kudos" to appreciate. :-D

BrentGMATPrepNow · Answer

To solve this question, we need to recognize that there's a 1/3 + 1/4 + 1/5 + 1/6 "hiding" in 1/9 + 1/12 + 1/15 + 1/18
We can reveal this "secret" by factoring 1/3 out of 1/9 + 1/12 + 1/15 + 1/18
We get: 1/9 + 1/12 + 1/15 + 1/18 = (1/3)(1/3 + 1/4 + 1/5 + 1/6)

So.....
Given: 1/3 + 1/4 + 1/5 + 1/6 = r (1/9 + 1/12 + 1/15 + 1/18) 
Factor right side to get: 1/3 + 1/4 + 1/5 + 1/6 = (r) (1/3)(1/3 + 1/4 + 1/5 + 1/6) 
Divide (1/3 + 1/4 + 1/5 + 1/6) from both sides to get: 1 = (r)(1/3)
Multiply both sides by 3 to get: 3 = r
Answer: C

avigutman · Answer

Video solution from Quant Reasoning:
 https://www.youtube.com/watch?v=h6bf5TbxVqs

generis · Answer

sashiim20  - Nice! But I think you have a typo.

\frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6} = r*\frac{1}{3}(\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6})  - if you divide LHS by  last factor  on RHS, I think you get 1.

So in highlighted part,   r*\frac{1}{3} =0  , I think RHS should be 1, not 0. Otherwise you'll get

r*\frac{1}{3} * 3 =0 * 3

r = 0

sashiim20 · Answer

Silly typo mistake. Thank you ... Updated the post.

Abhishek009 · Answer

(\frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6}) = r(\frac{1}{9} + \frac{1}{12} + \frac{1}{15} + \frac{1}{18})

Or,  \frac{20+15+12+10}{60} = \frac{r(20+15+12+10)}{180}

Or,  20+15+12+10 = \frac{r(20+15+12+10)}{3}

Or,  57*3 = r*57

So,  r = 3 
  
Thus, answer will be (C)

ScottTargetTestPrep · Answer

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 instance 1/3 is 3 times 1/9, 1/4 is 3 times 1/12, etc.
 
Thus, r MUST be 3.
 
Answer: C

Ross7it · Answer

why cannot we multiply the right side simply by 3 but 1/3? 
Sorry, cannot understand this moment...

aa008 · Answer

(\frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6}) = r(\frac{1}{9} + \frac{1}{12} + \frac{1}{15} + \frac{1}{18})

(\frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6}) = r(\frac{1}{3*3} + \frac{1}{3*4} + \frac{1}{3*5} + \frac{1}{3*6})

(\frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6}) = \frac{r}{3}(\frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6})

1=\frac{r}{3}

r=3

C is the Correct answer

TheNightKing · Answer

I kept looking what is that I cannot see. I could not spot it. I solved it manually in 2 minutes and got the right answer and then I was able to see. Hahaha!

Prasannathawait · Answer

take 1/3 common from the equation after =
cross multiply. 
R=3

This has to be the fastest way

Kinshook · Answer

Given:  (\frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6}) = r(\frac{1}{9} + \frac{1}{12} + \frac{1}{15} + \frac{1}{18})

Asked: r = ?

(\frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6}) = 3(\frac{1}{9} + \frac{1}{12} + \frac{1}{15} + \frac{1}{18})

r = 3

IMO C

Target4bschool · Answer

Let (1/3 + 1/4 + 1/5 + 1/6) = A
Take 1/3 common from the right hand side. 
Then, we have:

A = r*1/3* A
so, r = 3

Ans. C

One may also commit a silly mistake and choose A. - write this in error log. Don't ignore

MHIKER · Answer

(\frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6}) = r(\frac{1}{9} + \frac{1}{12} + \frac{1}{15} + \frac{1}{18})

(\frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6}) = r\frac{1}{3}(\frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6})

1=\frac{1}{3}r

r=3

The answer is  C

CrackverbalGMAT · Answer

Solution:

1/3+1/4+1/5+1/6=r(1/9+1/12+1/15+1/18)

=>1/3+1/4+1/5+1/6=r∗1/3(1/3+1/4+1/5+1/6) (Taking the 1/3 common)

=>r∗1/3=1

=>r=3.r=3  (option c)

Devmitra Sen (GMAT Quant Expert)

GMATinsight · Answer

Answer: Option C

Video solution by  GMATinsight

https://www.youtube.com/watch?v=4gdubm51xFY

Paras96 · Answer

Given, (1/3+1/4+1/5+1/6)=r(1/9+1/12+1/15+1/18)

=> (1/3+1/4+1/5+1/6)=r(1/9+1/12+1/15+1/18)
=> (1/3+1/4+1/5+1/6)=r/3(1/3+1/4+1/5+1/6)
=> 1=r/3
=> r =3

Hence C

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

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

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