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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 =  [#permalink]

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New post Updated on: 12 Jul 2017, 10:59
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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

Attachment:
2018.OG.05.072.q.png
2018.OG.05.072.q.png [ 4.16 KiB | Viewed 6308 times ]

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Originally posted by AbdurRakib on 17 Jun 2017, 09:10.
Last edited by Bunuel on 12 Jul 2017, 10:59, edited 2 times in total.
Renamed the topic and edited the question.
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Re: If (1/3 + 1/4 + 1/5 + 1/6) = r(1/9 + 1/12 + 1/15 + 1/18), then r =  [#permalink]

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New post Updated on: 17 Jun 2017, 12:30
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AbdurRakib wrote:
Attachment:
2018.OG.05.072.q.png
A. \(\frac{1}{3}\)
B. \(\frac{4}{3}\)
C. 3
D. 4
E. 12


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

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

\(r*\frac{1}{3} =1\)

\(r = 3.\) Answer (C)..


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Originally posted by sashiim20 on 17 Jun 2017, 09:16.
Last edited by sashiim20 on 17 Jun 2017, 12:30, edited 1 time in total.
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Re: If (1/3 + 1/4 + 1/5 + 1/6) = r(1/9 + 1/12 + 1/15 + 1/18), then r =  [#permalink]

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New post Updated on: 17 Jun 2017, 12:35
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sashiim20 wrote:
AbdurRakib wrote:
Attachment:
2018.OG.05.072.q.png
A. \(\frac{1}{3}\)
B. \(\frac{4}{3}\)
C. 3
D. 4
E. 12


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

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

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

\(r = 3.\) Answer (C)..


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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

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

\(r = 0\)
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Originally posted by generis on 17 Jun 2017, 12:26.
Last edited by generis on 17 Jun 2017, 12:35, edited 1 time in total.
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Re: If (1/3 + 1/4 + 1/5 + 1/6) = r(1/9 + 1/12 + 1/15 + 1/18), then r =  [#permalink]

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New post 17 Jun 2017, 12:33
Silly typo mistake. Thank you ... Updated the post. :)
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Re: If (1/3 + 1/4 + 1/5 + 1/6) = r(1/9 + 1/12 + 1/15 + 1/18), then r =  [#permalink]

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New post 28 Jun 2017, 07:05
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AbdurRakib wrote:
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


Attachment:
2018.OG.05.072.q.png


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:

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Re: If (1/3 + 1/4 + 1/5 + 1/6) = r(1/9 + 1/12 + 1/15 + 1/18), then r =  [#permalink]

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New post 28 Jun 2017, 08:25
AbdurRakib wrote:
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
Attachment:
2018.OG.05.072.q.png


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

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)

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Re: If (1/3 + 1/4 + 1/5 + 1/6) = r(1/9 + 1/12 + 1/15 + 1/18), then r =  [#permalink]

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New post 30 Jun 2017, 09:25
AbdurRakib wrote:
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


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
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Re: If (1/3 + 1/4 + 1/5 + 1/6) = r(1/9 + 1/12 + 1/15 + 1/18), then r =  [#permalink]

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Re: If (1/3 + 1/4 + 1/5 + 1/6) = r(1/9 + 1/12 + 1/15 + 1/18), then r = &nbs [#permalink] 13 Jul 2018, 03:23
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