Ratio problem?

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pm; Thanked: 11 times; Followed by:8 members

Ratio problem?

by gmattesttaker2 » Tue May 28, 2013 10:13 pm

Hello,

Can you please assist with this:

Some computers at a certain company are Brand X and the rest are Brand Y. If the ratio of the number of Brand Y computers to the number of Brand X computers at the company is 5 to 6, how many of the computers are Brand Y?

(1) There are 80 more brand X computers than Brand Y computers at the company

(2) There is a total of 880 computers at the company

OA: D

I was not clear with the approach explained in the OG.

Thanks for your help.

Best Regards,
Sri

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Source: Beat The GMAT — Data Sufficiency | Tue May 28, 2013 10:13 pm

srcc25anu: Master | Next Rank: 500 Posts; Posts: 423; Joined: Fri Jun 11, 2010 7:59 am; Location: Seattle, WA; Thanked: 86 times; Followed by:2 members

by srcc25anu » Tue May 28, 2013 11:36 pm

Lets Brand X computers be 6x
Lets Brand Y computers be 5x
Total compueters = 11x

St1: 6x - 5x = 80 or x = 80
# of Brand Y computers = 80 * 5 = 400
Sufficient

St2: 11x = 880 or x = 80
# of Brand Y computers = 80 * 5 = 400
Sufficient

Hence D

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Wed May 29, 2013 3:41 am

gmattesttaker2 wrote:Hello,

Can you please assist with this:

Some computers at a certain company are Brand X and the rest are Brand Y. If the ratio of the number of Brand Y computers to the number of Brand X computers at the company is 5 to 6, how many of the computers are Brand Y?

(1) There are 80 more brand X computers than Brand Y computers at the company

(2) There are a total of 880 computers at the company

OA: D

Question stem:
y/x = 5/6
5x = 6y.

Statement 1: There are 80 more brand X computers than Brand Y computers at the company.
x = y + 80.
Since we have two variables and two distinct linear equations (5x=6y and x=y+80), we can solve for each variable.
SUFFICIENT.

Statement 2: There are a total of 880 computers at the company.
x+y = 880.
Since we have two variables and two distinct linear equations (5x=6y and x+y=880), we can solve for each variable.
SUFFICIENT.

The correct answer is D.

A quick way to solve for x and y that requires little algebra:
y/x = 5/6.
If x=6 and y=5, then x-y = 1.
Statement 1 indicates that x-y = 80.
To yield a difference 80 TIMES AS GREAT as x-y=1, x and y must each be multiplied by a FACTOR OF 80:
x = 6*80 = 480.
y = 5*80 = 400.
These values satisfy both statements:
x-y = 80.
x+y = 880.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8083; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

Re: Ratio problem?

by Scott@TargetTestPrep » Wed Jun 16, 2021 4:54 am

gmattesttaker2 wrote: ↑
Tue May 28, 2013 10:13 pm

Some computers at a certain company are Brand X and the rest are Brand Y. If the ratio of the number of Brand Y computers to the number of Brand X computers at the company is 5 to 6, how many of the computers are Brand Y?

(1) There are 80 more brand X computers than Brand Y computers at the company

(2) There is a total of 880 computers at the company

OA: D

Solution:

Question Stem Analysis:

We need to determine the number of Brand Y computers at a certain company, given that the ratio of the number of brand Y computers to the number of Brand X computers at the company is 5 to 6. That is, if let the number of Brand Y computers be y, then the number of Brand X computers is 6y / 5 (notice that y / (6y/5) = 5/6). We need to determine the value of y.

Statement One Alone:

We can create the equation:

y + 80 = 6y/5

80 = y/5

400 = y

Statement one alone is sufficient.

Statement Two Alone:

We can create the equation:

y + 6y/5 = 880

11y/5 = 880

y/5 = 80

y = 400

Statement two alone is sufficient

Answer: D

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