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# If w/x = 2/3 and w/y = 8/15, then (x + y)/y =

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Math Expert
Joined: 02 Sep 2009
Posts: 44599
If w/x = 2/3 and w/y = 8/15, then (x + y)/y = [#permalink]

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27 Feb 2015, 05:54
5
KUDOS
Expert's post
1
This post was
BOOKMARKED
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Difficulty:

5% (low)

Question Stats:

86% (04:29) correct 14% (01:14) wrong based on 173 sessions

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If w/x = 2/3 and w/y = 8/15, then (x + y)/y =

A. 4/5
B. 6/5
C. 7/5
D. 8/5
E. 9/5

Kudos for a correct solution.
[Reveal] Spoiler: OA

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Joined: 26 May 2013
Posts: 96
Re: If w/x = 2/3 and w/y = 8/15, then (x + y)/y = [#permalink]

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Updated on: 27 Feb 2015, 19:25
1
KUDOS
Ratio 1:

3w = 2x
multiple of 5:
15w = 10x

Ratio 2:

15w = 8y

LCM of 8, 15, 10 = 120.

Ratio 1 : 15(8) = 10(12)
therefore x = 12

Ratio 2 : 15(8) = 8(15)
therefore y = 15

(15+12)/15 is reduced to 9/5.

Posted from my mobile device

Originally posted by ak1802 on 27 Feb 2015, 08:22.
Last edited by ak1802 on 27 Feb 2015, 19:25, edited 1 time in total.
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Re: If w/x = 2/3 and w/y = 8/15, then (x + y)/y = [#permalink]

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27 Feb 2015, 09:52
1
KUDOS
Expert's post
Bunuel wrote:
If w/x = 2/3 and w/y = 8/15, then (x + y)/y =

A. 4/5
B. 6/5
C. 7/5
D. 8/5
E. 9/5

Kudos for a correct solution.

We need (x+y)/y
= x/y + 1
Now, w/x = 2/3 => x = (3w)/2
Also, w/y = 8/15 => y = (15w)/8
We need x/y + 1
= (3w/2) / (15w/8) + 1
= (3w/2) * (8/15w) + 1
= 4/5 + 1
= 9/5
Hence option E.

--
Optimus Prep's GMAT On Demand course for only $299 covers all verbal and quant. concepts in detail. Visit the following link to get your 7 days free trial account: http://www.optimus-prep.com/gmat-on-demand-course EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 11500 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Re: If w/x = 2/3 and w/y = 8/15, then (x + y)/y = [#permalink] ### Show Tags 27 Feb 2015, 14:21 3 This post received KUDOS Expert's post 1 This post was BOOKMARKED Hi All, While many Test Takers would go about solving this problem with Algebra, TESTing VALUES provides an easy approach. We're told that W/X = 2/3 and W/Y = 8/15 Given these two ratios, we know that W is a multiple of 2 and a multiple of 8. The simplest value for W is 8.... W = 8 X = 12 Y = 15 Using these values, we can now answer the question: (X+Y)/Y = ..... (12 + 15)/15 = 27/15 = 9/5 Final Answer: [Reveal] Spoiler: E GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Manager
Joined: 26 May 2013
Posts: 96
Re: If w/x = 2/3 and w/y = 8/15, then (x + y)/y = [#permalink]

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27 Feb 2015, 19:26
EMPOWERgmatRichC wrote:
Hi All,

While many Test Takers would go about solving this problem with Algebra, TESTing VALUES provides an easy approach.

We're told that W/X = 2/3 and W/Y = 8/15

Given these two ratios, we know that W is a multiple of 2 and a multiple of 8. The simplest value for W is 8....

W = 8
X = 12
Y = 15

Using these values, we can now answer the question: (X+Y)/Y = .....

(12 + 15)/15 = 27/15 = 9/5

[Reveal] Spoiler:
E

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

I took the same approach, however by finding the LCM of all the numbers involved you aren't necessarily "testing" numbers. The integer you found WILL work.
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
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Re: If w/x = 2/3 and w/y = 8/15, then (x + y)/y = [#permalink]

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27 Feb 2015, 19:41
Hi ak1802,

I didn't have to use the LCM; I chose to TEST VALUES that were the easiest AND fit the 'restrictions' that we were given. In a 'TEST VALUES' prompt, there may or may not be 'restrictions.' If there are few/no restrictions, then you have more freedom to TEST values that strike you as easy to work with. The more restrictions there are, the more specific you have to be with the VALUES that you TEST.

Here's another example that doesn't use the LCM....

W/X = 2/3 and W/Y = 8/15

W = 16
X = 24
Y = 30

(X+Y)/Y = (24+30)/30 = 54/30 = 9/5

It still gets us the correct answer.

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

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

# Rich Cohen

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Manager
Joined: 26 May 2013
Posts: 96
Re: If w/x = 2/3 and w/y = 8/15, then (x + y)/y = [#permalink]

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27 Feb 2015, 19:49
EMPOWERgmatRichC wrote:
Hi ak1802,

I didn't have to use the LCM; I chose to TEST VALUES that were the easiest AND fit the 'restrictions' that we were given. In a 'TEST VALUES' prompt, there may or may not be 'restrictions.' If there are few/no restrictions, then you have more freedom to TEST values that strike you as easy to work with. The more restrictions there are, the more specific you have to be with the VALUES that you TEST.

Here's another example that doesn't use the LCM....

W/X = 2/3 and W/Y = 8/15

W = 16
X = 24
Y = 30

(X+Y)/Y = (24+30)/30 = 54/30 = 9/5

It still gets us the correct answer.

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

All I'm saying is that the value wasn't necessarily being "tested", given the restrictions on it. You found the LCM of X, Y, and Z. If this number was calculated properly, you aren't really "testing" an integer. This integer WILL fit the given rations.

I suppose it's just the semantics of "testing", which I associate some level of uncertainty with. Whereas in this case, there is no uncertainty, as the number both of us used was the LCM.

Don't get me wrong, I am a big supporter of using SMART numbers when "testing" for solutions. However I suppose I just felt that classifying this as testing sounds misleading.
Math Expert
Joined: 02 Sep 2009
Posts: 44599
Re: If w/x = 2/3 and w/y = 8/15, then (x + y)/y = [#permalink]

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02 Mar 2015, 05:50
Bunuel wrote:
If w/x = 2/3 and w/y = 8/15, then (x + y)/y =

A. 4/5
B. 6/5
C. 7/5
D. 8/5
E. 9/5

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:
Attachment:

wxandy_text.PNG [ 13.86 KiB | Viewed 2508 times ]

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Re: If w/x = 2/3 and w/y = 8/15, then (x + y)/y = [#permalink]

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14 Nov 2017, 06:54
Bunuel wrote:
Bunuel wrote:
If w/x = 2/3 and w/y = 8/15, then (x + y)/y =

A. 4/5
B. 6/5
C. 7/5
D. 8/5
E. 9/5

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:
Attachment:
wxandy_text.PNG

(x+y)/y = (x/y) +1
so, if we need to get the value of x/y

by dividing w/x by w/y we get the following:

w/x ÷ w/y = w/x *y/w=y/x = 2/3*15/8= 5/4

Therefore x/y=4/5
(x+y)/y= (x/y)+1= 4/5+5/5=9/5 ==> E
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Re: If w/x = 2/3 and w/y = 8/15, then (x + y)/y = [#permalink]

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14 Nov 2017, 09:34
Bunuel wrote:
If w/x = 2/3 and w/y = 8/15, then (x + y)/y =

A. 4/5
B. 6/5
C. 7/5
D. 8/5
E. 9/5

Kudos for a correct solution.

$$\frac{w}{x} = \frac{2}{3}$$ Or, $$\frac{w}{x} = \frac{8}{12}$$

And, $$\frac{w}{y} = \frac{8}{15}$$

So, $$w = 8$$ , $$x = 12$$ & $$y = 15$$

Thus, \frac{(x + y)}{y} = \frac{12 + 15}{15}

= $$\frac{27}{15}$$

= $$\frac{9}{5}$$, answer will be (E)
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Re: If w/x = 2/3 and w/y = 8/15, then (x + y)/y =   [#permalink] 14 Nov 2017, 09:34
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