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A computer chip manufacturer expects the ratio of the number of defect

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A computer chip manufacturer expects the ratio of the number of defect [#permalink] New post   25 Oct 2010, 07:40
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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’s the expected number of defective chips in a shipment of 60,000 chips?

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


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Re: A computer chip manufacturer expects the ratio of the number of defect [#permalink] New post   25 Oct 2010, 08:06
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Shipment --- No. of Defective Chips/shipment --- Total Chips in shipment
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 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’s the expected number of defective chips in a shipment of 60,000 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 \(\frac{60,000}{3,000}=20\).

Answer: B.
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Re: A computer chip manufacturer expects the ratio of the number of defect [#permalink] New post   11 Aug 2012, 00:45
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ASHISH3344 wrote:
Hi just require little clarification---
In the original question it says " ratio s1, s2, s3 and s4 combined"
lets disregard the question for a while
suppose there are four ratios s1=a/b , s2=c/d ,s3=e/f and s4= g/h
doesn't combined ratio mean s1+s2+s3+s4= a/b+c/d + e/f + g/h
if yes why are we using a+c+e+g/ b+d+f+h


The question says: "...ratio for shipments S1, S2, S3, and S4 combined..."

The ratio of the number of defective chips to the total number of chips for these 4 shipments is \(\frac{2+5+6+4}{5,000+12,000+18,000+16,000}\).

Hope it's clear.
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Re: A computer chip manufacturer expects the ratio of the number of defect [#permalink] New post   12 Jul 2021, 09:35
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junior 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, as shown in the table above. What’s the expected number of defective chips in a shipment of 60,000 chips?

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


Show Spoiler
Attachment:
2019-10-11_1612.png


Let's find some TOTALS for all 4 shipments combined.
There are 51,000 chips altogether
There are 17 defective chips altogether.

So, 17/51000 of the chips are defective. (notice that 17 divides nicely into 51000!)
SIMPLIFY: 1/3000 of the chips are defective

So, if we have a shipment of 60,000 chips, 1/3000 of them will be defective.
(1/3000)(60,000) = 20 defective chips

Answer: B

Cheers,
Brent
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Re: A computer chip manufacturer expects the ratio of the number of defect [#permalink] New post   25 Oct 2010, 08:16
Thanks guys! I don't why was i trying to take weighted average for both quantities!

By the way Bunuel, I have my GMAT on 27th (Wed).. Can you please suggest any last moment preparations? I was planning to go through the basic principles/formulas/tips & tricks, etc once that's it..
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Re: A computer chip manufacturer expects the ratio of the number of defect [#permalink] New post   04 Jan 2012, 03:50
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Janealams wrote:
I don't have much time left in the exam I would really appreciate explanation to following question!


for a total of 51000 chips (adding S1,S2,S3,S4) total number of defective chips is 17 ((adding defective chips of S1,S2,S3,S4) so ratio is 17/51000 or 1 every 3000 chips.

Keeping this ratio constant for 60000 chips number of defective chips will be (1/3000) * 60000 = 20
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Re: A computer chip manufacturer expects the ratio of the number of defect [#permalink] New post   04 Jan 2012, 07:01
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let X be the # of defective chips.
17/51,000=X/60,000
X= 20
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Re: A computer chip manufacturer expects the ratio of the number of defect [#permalink] New post   04 Jan 2012, 11:52
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If we sum defective chips and total chips, we get 17 : 51000. For additional 9000 total chips, which shipment makes sense to split such that we can find an easy 9000 number. S3 makes sense here since 18000/2 = 9000. Therefore, number of additional defective chips = 6/3 = 3.

Total = 17 + 3 = 20 -> B
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Re: A computer chip manufacturer expects the ratio of the number of defect [#permalink] New post   10 Aug 2012, 23:38
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Hi just require little clarification---
In the original question it says " ratio s1, s2, s3 and s4 combined"
lets disregard the question for a while
suppose there are four ratios s1=a/b , s2=c/d ,s3=e/f and s4= g/h
doesn't combined ratio mean s1+s2+s3+s4= a/b+c/d + e/f + g/h
if yes why are we using a+c+e+g/ b+d+f+h
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Re: A computer chip manufacturer expects the ratio of the number of defect [#permalink] New post   03 Jun 2013, 03:08
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Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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Re: A computer chip manufacturer expects the ratio of the number of defect [#permalink] New post   03 Jun 2013, 04:59
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the ratio of the number of defective chips to the total number of chips

i.e. (2+5+6+4) = 17 : (5,000+12,000+18,000+16,000) = 51,000

i.e. 17 : 51,000 = 1 : 3,000

which means that 1 out of every 3,000 chips is defective, so out of a total 60,000 how many are defective?

Cross multiply : (60,000 *1)/3,000 = 20 chips are defective
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Re: A computer chip manufacturer expects the ratio of the number of defect [#permalink] New post   24 Sep 2014, 23:40
Total defective chips expected\(= 60000 * \frac{(2+5+6+4)}{(5000+12000+18000+16000)} = 20\)
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Re: A computer chip manufacturer expects the ratio of the number of defect [#permalink] New post   28 Apr 2015, 17:35
shinbhu wrote:
If we sum defective chips and total chips, we get 17 : 51000. For additional 9000 total chips, which shipment makes sense to split such that we can find an easy 9000 number. S3 makes sense here since 18000/2 = 9000. Therefore, number of additional defective chips = 6/3 = 3.

Total = 17 + 3 = 20 -> B



I think you got the division wrong 6/3 = 2 Right?
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Re: A computer chip manufacturer expects the ratio of the number of defect [#permalink] New post   14 Oct 2016, 05:56
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junior wrote:
Shipment --- No. of Defective Chips/shipment --- Total Chips in shipment
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 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’s 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

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
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Re: A computer chip manufacturer expects the ratio of the number of defect [#permalink] New post   14 Jan 2017, 14:00
(2+5+6+4)/(5000+12000+18000+16000)*60000 = 20
Answer is B
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Re: A computer chip manufacturer expects the ratio of the number of defect [#permalink] New post   28 Jan 2017, 10:55
Bunuel wrote:
Shipment --- No. of Defective Chips/shipment --- Total Chips in shipment
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 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’s the expected number of defective chips in a shipment of 60,000 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 \(\frac{60,000}{3,000}=20\).

Answer: B.



HI..Thanx Buneul....but are we not supposed to add the ratios as 2/5000 + 5/12000 + 6/18000 + 4/16000 thereby giving 7 defectives in 5000...WHAT PART OF THE PROB ACTUALLY INDICATES THAT WE NEED TO ADD THE DEFECTIVES DIVIDED BY OTAL SHIPMENTS.
PL HELP....
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Re: A computer chip manufacturer expects the ratio of the number of defect [#permalink] New post   28 Jan 2017, 11:31
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saurabhsavant wrote:
Bunuel wrote:
Shipment --- No. of Defective Chips/shipment --- Total Chips in shipment
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 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’s the expected number of defective chips in a shipment of 60,000 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 \(\frac{60,000}{3,000}=20\).

Answer: B.



HI..Thanx Buneul....but are we not supposed to add the ratios as 2/5000 + 5/12000 + 6/18000 + 4/16000 thereby giving 7 defectives in 5000...WHAT PART OF THE PROB ACTUALLY INDICATES THAT WE NEED TO ADD THE DEFECTIVES DIVIDED BY OTAL SHIPMENTS.
PL HELP....


The probability of an event = (The # of favourable outcomes)/(The total # of outcomes).
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Re: A computer chip manufacturer expects the ratio of the number of defect [#permalink] New post   08 May 2017, 01:17
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They need the ratio to be same as the ratio of S1+S2+S3+S4 (combined)..
So for S1+S2+S3+S4 (combined), the # defective pieces are 2+5+6+4 = 17
And S1+S2+S3+S4 (combined) Total pieces are = 5000+12000+18000+16000 = 51000

So, if there 17 defective pieces per 51000 total pieces then for a total of 60000, how many defective pieces (X) shall be there …

X = 60000 x 17 / 51000 = 20
Option B
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Re: A computer chip manufacturer expects the ratio of the number of defect [#permalink] New post   16 Oct 2020, 15:53
The 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.

In this question we need to add the total number of chips in all the shipments and determine the ratio of defective chips to total number of ships.

5,000 + 12,000 + 18,000 + 16,000 = 51,000

2+5+6+4 = 17

51,000 / 17 = 3000 / 1

60,000 chips: 20 defective chips

Answer is B.
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Re: A computer chip manufacturer expects the ratio of the number of defect [#permalink] New post   06 Aug 2022, 00:59
Shipment --- No. of Defective Chips/shipment --- Total Chips in shipment
S1 ---------------------- 2 ------------------------------------------ 5,000
S2 ---------------------- 5 ------------------- ---------------------- 12,000
S3 ---------------------- 6 ------------------------------------------ 18,000
S4 ---------------------- 4 ------------------------------------------ 16,000

Hi I simply used the unitary method,

No of defective chips Total No of chips
2+5+6+4 = 17 5000+12000+18000+16000 = 51000
? 60000
60/51* 17 = 20

Kindly correct my approach if wrong
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Re: A computer chip manufacturer expects the ratio of the number of defect [#permalink]
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