Fraction of parts inspected?

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

by gmattesttaker2 » Thu Feb 13, 2014 10:12 pm

Hello,

Can you please tell my if my solution is correct here:

At a quality control facility, Harry and Sylvia rejected 0.5% and 0.8%, respectively,
of the parts of a shipment they inspected. If Sylvia and Harry were the only quality
controllers at the facility and together rejected 0.75% of the total number of parts
in the shipment, what fraction of the parts in the shipment were inspected by Sylvia?

H---------H+S-------------S
0.5------0.75------------0.8

H/S = (0.80 - 0.75)/(0.75 - 0.50) = 0.05/0.25 = 5/25 = 1/5

Hence,

H--------H+S------------S
----5----- ------1------

So, fraction of the parts in the shipment were inspected by Sylvia = 5/6

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Source: Beat The GMAT — Problem Solving | Thu Feb 13, 2014 10:12 pm

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Fri Feb 14, 2014 12:32 am

Hi gmattesttaker2,

Yes, your solution is correct. In these types of weighted average questions, there are a number of ways to "do the math", so it's best to approach using whatever method:

1) Gets you the correct answer
2) Is fastest

If you're comfortable with this approach and can use it quickly, then it's a good way to go about solving this problem.

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

Contact Rich at [email protected]

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Fri Feb 14, 2014 9:24 am

gmattesttaker2 wrote:
At a quality control facility, Harry and Sylvia rejected 0.5% and 0.8%, respectively,
of the parts of a shipment they inspected. If Sylvia and Harry were the only quality
controllers at the facility and together rejected 0.75% of the total number of parts
in the shipment, what fraction of the parts in the shipment were inspected by Sylvia?

Another approach is to use the formula for weighted averages:

Weighted average of total population = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...

So, we get: 0.75% = (proportion inspected by Sylvia)(0.8%) + (proportion inspected by Harry)(0.5%)

If we want to convert the percents to decimals, we can write: 0.0075 = (proportion inspected by Sylvia)(0.008) + (proportion inspected by Harry)(0.005)

Let's let F = the FRACTION of the parts inspected by Sylvia
This means that 1-F = the FRACTION of the parts inspected by Harry [since Harry inspected the rest]

When we plug in F and 1-F, we get: 0.0075 = (F)(0.008) + (1 - F)(0.005)
To get rid of the decimals, let's multiply both sides by 10,000 to get: 75 = (F)(80) + (1 - F)(50)
Expand to get: 75 = 80F + 50 - 50F
Simplify: 75 = 30F + 50
Rearrange: 25 = 30F
Solve for F to get: F = 25/30 = [spoiler]5/6[/spoiler]

So, Sylivia inspected [spoiler]5/6[/spoiler] of the parts.

For more information on weighted averages, you can watch this free GMAT Prep Now video: https://www.gmatprepnow.com/module/gmat- ... ics?id=805

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Bill@VeritasPrep: GMAT Instructor; Posts: 1248; Joined: Thu Mar 29, 2012 2:57 pmFollowed by: 192 members; Location: Everywhere; Thanked: 503 times; GMAT Score:780

by Bill@VeritasPrep » Fri Feb 14, 2014 11:13 am

gmattesttaker2 wrote:Hello,

Can you please tell my if my solution is correct here:

At a quality control facility, Harry and Sylvia rejected 0.5% and 0.8%, respectively,
of the parts of a shipment they inspected. If Sylvia and Harry were the only quality
controllers at the facility and together rejected 0.75% of the total number of parts
in the shipment, what fraction of the parts in the shipment were inspected by Sylvia?

H---------H+S-------------S
0.5------0.75------------0.8

H/S = (0.80 - 0.75)/(0.75 - 0.50) = 0.05/0.25 = 5/25 = 1/5

Hence,

H--------H+S------------S
----5----- ------1------

So, fraction of the parts in the shipment were inspected by Sylvia = 5/6

That's exactly how I would solve it.

Join Veritas Prep's 2010 Instructor of the Year, Matt Douglas for GMATT Mondays

Visit the Veritas Prep Blog

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Abhishek009: Master | Next Rank: 500 Posts; Posts: 359; Joined: Wed Mar 11, 2009 4:37 amFollowed by: 2 members; Location: Kolkata, India; Thanked: 50 times

by Abhishek009 » Fri Feb 14, 2014 11:23 am

gmattesttaker2 wrote:Hello,

Can you please tell my if my solution is correct here:

At a quality control facility, Harry and Sylvia rejected 0.5% and 0.8%, respectively,
of the parts of a shipment they inspected. If Sylvia and Harry were the only quality
controllers at the facility and together rejected 0.75% of the total number of parts
in the shipment, what fraction of the parts in the shipment were inspected by Sylvia?

H---------H+S-------------S
0.5------0.75------------0.8

H/S = (0.80 - 0.75)/(0.75 - 0.50) = 0.05/0.25 = 5/25 = 1/5

Hence,

H--------H+S------------S
----5----- ------1------

So, fraction of the parts in the shipment were inspected by Sylvia = 5/6

Use the method of alligation

The ratio of Inspection done by Harry to Sylvia is 1 : 5

So , Ratio of Inspection done by Sylvia to the total Inspection work conducted is - 5/6

Attachments

Abhishek

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