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A computer chip manufacturer expects the ratio of the number

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A computer chip manufacturer expects the ratio of the number [#permalink]

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19 Mar 2006, 03:36
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45% (medium)

Question Stats:

71% (01:05) correct 29% (01:44) wrong based on 109 sessions

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Shipment ------No. of Defective Chips/shipment---Total Chips in shipment
S1 -------------- 2 -----------------------------------------------5000
S2 -------------- 5 ------------------------ ----------------------12000
S3 -------------- 6 ----------------------------------------------- 18000
S4 -------------- 4 ----------------------------------------------- 16000

A computer chip manufacturer expects the ratio of the number of defective chips to be total number of chips in all future shipments equal to the corresponding ratio for shipmemts S1,S2,S3 and S4 comined as shown in the table above. What is the expected number of defective chips in a shipment of 60000 chips?

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

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-computer-chip-manufacturer-expects-the-ratio-of-the-number-126050.html
[Reveal] Spoiler: OA

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Last edited by Bunuel on 06 May 2012, 02:47, edited 1 time in total.
Edited the question. Topic locked.

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Re: PS from OG 11th [#permalink]

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19 Mar 2006, 08:09
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foolbox wrote:
shipment, # of defective chips, total # of chips
S1 2 5,000
S2 5 12,000
S3 6 18,000
S4 4 16,000

A computer chip manufacturer expects the ratio of the # of defective chips to the total # 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?

Say X is the number of defective ships in the shipment of 60,000

we can write out the following equation

2+5+6+4/5,000+12,000+18,000+16,000 = X/60,000

17/51,000 = X/60,000

51,000X= 1,020,000
X= 20
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19 Mar 2006, 08:10
Total # of defective chips =17
Total # of chips = 51000

# of defective chips in a shipment of 60,000 chips
= (60,000/51,000) * 17
= (60/51) * 17
= (20/17) * 17
= 20

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Re: PS from OG 11th [#permalink]

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19 Mar 2006, 09:38
foolbox wrote:
shipment, # of defective chips, total # of chips
S1 2 5,000
S2 5 12,000
S3 6 18,000
S4 4 16,000

A computer chip manufacturer expects the ratio of the # of defective chips to the total # 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?

How come we can't solve this problem like;

Viewing package S1, and using proportional

2:5,000 = X:60,000

X = 60,000 * 2 / 5,000 = 24

Doesn't that make sense, guys?

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Re: PS from OG 11th [#permalink]

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19 Mar 2006, 09:44
foolbox wrote:
foolbox wrote:
shipment, # of defective chips, total # of chips
S1 2 5,000
S2 5 12,000
S3 6 18,000
S4 4 16,000

A computer chip manufacturer expects the ratio of the # of defective chips to the total # 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?

How come we can't solve this problem like;

Viewing package S1, and using proportional

2:5,000 = X:60,000

X = 60,000 * 2 / 5,000 = 24

Doesn't that make sense, guys?

We can't just take one shipment and make and equation since the stem explicitly states .." in all future shipments to equal the corresponding ratio for shipments S1,S2,S3, and S4 combined".

So you must have all the values in the equation
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20 Mar 2006, 14:35
The generic formula for such type of ratio problems is

Part1/Part2 = New Part1/Whole

In this problem it will be

Total defective Chips/Total Chips from all shipments = X / 60000

which will be

17/51000 = x/60000
Hence, X=20

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Re: PS from OG 11th [#permalink]

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20 Mar 2008, 08:47
Why dont you have to find a common denominator before adding up the ratios? I feel like I am overlookng something easy and fundamental.

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Re: PS from OG 11th [#permalink]

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20 Mar 2008, 08:59
foolbox wrote:
shipment, # of defective chips, total # of chips
S1 2 5,000
S2 5 12,000
S3 6 18,000
S4 4 16,000

A computer chip manufacturer expects the ratio of the # of defective chips to the total # 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?

The key phrase in this question is "expects the ratio of the # of defective chips to the total # of chips in all future shipments to equal the corresponding ratio for shipments S1,S2,S3, and S4 combined".

To rephrase the sentense, if there are 17 defects to 51,000 chips, what is the proportion of defect for 60,000 chips?
=> 60,000 / 51,000 * 17 = ~ 20 (19.9999)
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25 Oct 2010, 08:04
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Summing all the defective chips in the table gives you 2 + 5 + 6 + 4 = 17.
Summing all the total number of chips in each shipment gives you 5k + 12k + 18k + 16k = 51k.

Then, setting up a ratio can help you solve the problem. Since you know there's 17 defective chips in a shipment of 51k, set that equal to x/60k and solve.

17/51k = x/60k
17/51k = 1/3k
1/3k = x/60k
60k/3k = x
x = 20

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30 Oct 2010, 01:23
I agree with your solution = 20. But the question is:

There are different combination to get 60,000 chips. For example: 1*S3 + 2*S4 + 2*S2. In this way, we ship 60,000 chips with only 6 + 4*2 + 2*2 = 18 defective chips, better than the average of 20.

The question is to find the expected number of defective chips, i guess it assume the minimum #, therefore it might not be 20.

Or i misunderstand the word "EXPECT"

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Re: Practice Test 2 Q1 [#permalink]

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31 Dec 2010, 20:10
There are (2+5+6+4 = 17) defective pieces in shipment of (5000+12000+18000+16000=51000) pieces.
That is equivalent to 1 defective piece/3000 shipment of pieces.

So, in a shipment of 60000 pieces, there will be (1/3000) * 60000 = 20 defective pieces.

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04 May 2011, 12:22
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1) Sum of chips in all shipments: 51,000
2) Sum of defects in all shipments: 17
3) So, defects:chips is 1:3000

As such, 60,000 chips x (1 defect / 3000 chips) = 20 defects

If there's any hole in my reasoning, I welcome comments. As I can benefit from it too.
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04 May 2011, 17:40
x/60000 = (2+5+6+4)/51000

=> x = (17/51000)*60000

= 20

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05 May 2011, 07:41
Ratio = 17/510000 (adding the respective columns)

17/51000 = x/60000

=> x = 20

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Re: problem solving questions..GMAT Prep [#permalink]

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15 Aug 2011, 07:04
key is to understand the meaning of "corresponding ratio for shipments S1, S2, S3, S4 combined"

first I thought it (considering r as the ratio) is equal to = r1+r2+r3+r4, however that gave me answer 84.

So correct interpretation is (take d as nbr of defective and t as nbr of total artifacts ), it is equal to = (d1+d2+d3+d4)/(t1+t2+t3+t4)

so the combined ration comes = 17/51000 = 1/3000

and nbr of defective in a shipment of 60,000 = 60,000 * 1/3000 = 20

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Re: A computer chip manufacturer [#permalink]

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05 May 2012, 08:46
This question is total bullocks. Everyone here took a simple arithmetic average (Total number of Defective)/(Total number of all shipments). I took a weighted average. Obviously the larger shipments should get more weight. Does anyone agree the wording of this question is awkward?

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Re: A computer chip manufacturer [#permalink]

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06 May 2012, 02:48
alphabeta1234 wrote:
This question is total bullocks. Everyone here took a simple arithmetic average (Total number of Defective)/(Total number of all shipments). I took a weighted average. Obviously the larger shipments should get more weight. Does anyone agree the wording of this question is awkward?

There is nothing wrong with the question or the solutions.

Shipment ------No. of Defective Chips/shipment---Total Chips in shipment
S1 -------------- 2 -----------------------------------------------5000
S2 -------------- 5 ------------------------ ----------------------12000
S3 -------------- 6 ----------------------------------------------- 18000
S4 -------------- 4 ----------------------------------------------- 16000

A computer chip manufacturer expects the ratio of the number of defective chips to be total number of chips in all future shipments equal to the corresponding ratio for shipmemts S1,S2,S3 and S4 comined as shown in the table above. What is the expected number of defective chips in a shipment of 60000 chips?

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

Set up equation: $$\frac{x}{60,000}=\frac{2+5+6+4}{5,000+12,000+18,000+16,000}$$ --> $$x=20$$;

Or: $$2+5+6+4=17$$ defective chips in $$5,000+12,000+18,000+16,000=51,000$$ chips, so $$\frac{17}{51,000}=\frac{1}{3,000}$$: 1 in 3,000. So, expected number of defective chips in a shipment of 60,000 chips is $$\frac{60,000}{3,000}=20$$.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-computer-chip-manufacturer-expects-the-ratio-of-the-number-126050.html
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Re: A computer chip manufacturer expects the ratio of the number [#permalink]

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Re: A computer chip manufacturer expects the ratio of the number   [#permalink] 12 Oct 2016, 04:06
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