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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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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 [ 4.16 KiB | Viewed 14551 times ]

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Sentence Correction-Collection of Ron Purewal's "elliptical construction/analogies" for SC Challenges

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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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.
##### General Discussion
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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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Updated on: 17 Jun 2017, 12:35
3
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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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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28 Jun 2017, 07:05
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Top Contributor
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

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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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28 Jun 2017, 08:25
1
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, $$r = 3$$

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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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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.

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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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22 Sep 2018, 02:35
why cannot we multiply the right side simply by 3 but 1/3?
Sorry, cannot understand this moment...
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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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10 Oct 2018, 10:37
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

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

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

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

$$1=\frac{r}{3}$$

$$r=3$$

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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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07 Jul 2019, 10:58
GMATPrepNow wrote:
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

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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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15 Jul 2019, 00:17
take 1/3 common from the equation after =
cross multiply.
R=3

This has to be the fastest way
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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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13 Sep 2019, 23:30
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

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

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

r = 3

IMO C
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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] 13 Sep 2019, 23:30
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