Gmat prep ratio defective chips

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cat er ina: Junior | Next Rank: 30 Posts; Posts: 23; Joined: Sat Feb 13, 2010 1:36 pm

by cat er ina » Sat Feb 13, 2010 1:58 pm

Shipment: S1, S2, S3, S4.
Number of defective chips in the shipment :2, 5, 6, 4.
Total number of chips: 5.000, 12.000, 18.000, 16.000

A computer chip manufacturer expects the ratio of the number of defective chips to the total number of chips in all future shipments to equal the corresponding ratio for shipments s1 s2 s3 and s4 combined as shown in the table above. What is the expected number of defective chips in a shipment of 60.000 chips?

A.14 B.20 C.22 D.24 E.25

I haven't slept on this one for two days, please help!

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Source: Beat The GMAT — Problem Solving | Sat Feb 13, 2010 1:58 pm

akahuja143: Master | Next Rank: 500 Posts; Posts: 182; Joined: Mon Apr 20, 2009 7:09 pmFollowed by: 1 member; Thanked: 1 times

by akahuja143 » Sat Feb 13, 2010 3:20 pm

I would go with C 22

I tired the varipous combination of shipments and tried substitute the answer choice.

2 shipments of 18 --36 would have deficitve 2 x6 =12
2 shipments of 12 -- 24 would have defective 2X5 = 10

Total defective 22

what is the OA?

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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Sat Feb 13, 2010 9:40 pm

cat er ina wrote:Shipment: S1, S2, S3, S4.
Number of defective chips in the shipment :2, 5, 6, 4.
Total number of chips: 5.000, 12.000, 18.000, 16.000

A computer chip manufacturer expects the ratio of the number of defective chips to the total number of chips in all future shipments to equal the corresponding ratio for shipments s1 s2 s3 and s4 combined as shown in the table above. What is the expected number of defective chips in a shipment of 60.000 chips?

A.14 B.20 C.22 D.24 E.25

I haven't slept on this one for two days, please help!

Total no of Chips in all shipments = 51.000
Total no of defectives = 17

Ratio = 17/51.000

Expected no of defective chips in 60.000 chips = 60.000*17/51.000 = 20

B

Always borrow money from a pessimist, he doesn't expect to be paid back.

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gmatmachoman: Legendary Member; Posts: 2326; Joined: Mon Jul 28, 2008 3:54 amFollowed by: 2 members; Thanked: 173 times; GMAT Score:710

by gmatmachoman » Sat Feb 13, 2010 10:46 pm

ajith wrote:
cat er ina wrote:Shipment: S1, S2, S3, S4.
Number of defective chips in the shipment :2, 5, 6, 4.
Total number of chips: 5.000, 12.000, 18.000, 16.000

A computer chip manufacturer expects the ratio of the number of defective chips to the total number of chips in all future shipments to equal the corresponding ratio for shipments s1 s2 s3 and s4 combined as shown in the table above. What is the expected number of defective chips in a shipment of 60.000 chips?

A.14 B.20 C.22 D.24 E.25

I haven't slept on this one for two days, please help!
Total no of Chips in all shipments = 51.000
Total no of defectives = 17

Ratio = 17/51.000

Expected no of defective chips in 60.000 chips = 60.000*17/51.000 = 20

B

@ajith,

How did u count the ratio's with out taking common divisor?

R&D on GMAT algorithm:

https://www.beatthegmat.com/r-d-on-gmat- ... tml#305739

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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Sat Feb 13, 2010 11:16 pm

cat er ina wrote:
A computer chip manufacturer expects the ratio of the number of defective chips to the total number of chips in all future shipments to equal the corresponding ratio for shipments s1 s2 s3 and s4 combined[/b] as shown in the table above. What is the expected number of defective chips in a shipment of 60.000 chips?

See the Highlighted part of the sentence, It asks to consider the combined ratio rather than the individual ratios.

Combined ratio = (Defectives in S1 +Defectives in S2 +Defectives in S3 +Defectives in S4)/(Total chips in S1+Total chips in S2+Total chips in s3+Total chips in S4)

= 17/51.000= 1/3.000

Always borrow money from a pessimist, he doesn't expect to be paid back.

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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Sat Feb 13, 2010 11:24 pm

gmatmachoman wrote:
@ajith,

How did u count the ratio's with out taking common divisor?

We want to find the combined ratio;combined ratio is not the same as sum of the ratios.

For example, say, I am making 10 mistakes in 100 and if you are making 5 mistakes in 100 -
The ratio of mistakes we make together is not 10/100+5/100 = 15/100 = 15% rather, it is (10+5)/(100+100) = 15/200 = 7.5%

We sum the fractions, finding a common divisor etc... Here we are not summing them.

Always borrow money from a pessimist, he doesn't expect to be paid back.

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cat er ina: Junior | Next Rank: 30 Posts; Posts: 23; Joined: Sat Feb 13, 2010 1:36 pm

by cat er ina » Mon Feb 15, 2010 7:43 am

i GOT IT!! thank you everybody, the correct answer is 20!

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n2739178: Junior | Next Rank: 30 Posts; Posts: 17; Joined: Wed May 26, 2010 11:25 pm

by n2739178 » Tue Nov 08, 2011 1:54 pm

the wording of the question is a bit confusing hey!

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8137; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

hi

by Scott@TargetTestPrep » Tue Dec 05, 2017 6:24 pm

cat er ina wrote:Shipment: S1, S2, S3, S4.
Number of defective chips in the shipment :2, 5, 6, 4.
Total number of chips: 5.000, 12.000, 18.000, 16.000

A computer chip manufacturer expects the ratio of the number of defective chips to the total number of chips in all future shipments to equal the corresponding ratio for shipments s1 s2 s3 and s4 combined as shown in the table above. What is the expected number of defective chips in a shipment of 60.000 chips?

A.14 B.20 C.22 D.24 E.25

We need to first determine the ratio of the defective chips to the total number of chips for shipments S1, S2, S3, and S4.

Defective Chips = 2 + 5 + 6 + 4 = 17 chips[spoiler]
[/spoiler]
Total Chips = 5,000 + 12,000 + 18,000 + 16,000 = 51,000

Thus the ratio of defective chips to total chips is 17/51,000 = 1/3000. We interpret this ratio as: we would expect 1 defective chip out of every 3,000 chips in the shipment.

To determine the number of defective chips in a shipment of 60,000 chips we can use the following proportion, in which x is the expected number of defective chips in the shipment of 60,000 chips:

1/3,000 = x/60,000

60,000 = 3,000x

x = 20

Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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