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# A computer chip manufacturer expects the ratio of the number

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Joined: 23 Feb 2010
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A computer chip manufacturer expects the ratio of the number [#permalink]

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25 Oct 2010, 06:40
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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
[Reveal] Spoiler: OA
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25 Oct 2010, 07:06
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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 $$\frac{60,000}{3,000}=20$$.

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25 Oct 2010, 07:16
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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04 Jan 2012, 02:50
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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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04 Jan 2012, 06:01
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let X be the # of defective chips.
17/51,000=X/60,000
X= 20
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04 Jan 2012, 10:52
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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 [#permalink]

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10 Aug 2012, 22:38
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 [#permalink]

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10 Aug 2012, 23:45
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Expert's post
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 [#permalink]

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03 Jun 2013, 02:08
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 [#permalink]

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03 Jun 2013, 03:59
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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 [#permalink]

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24 Sep 2014, 22:40
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 [#permalink]

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28 Apr 2015, 16:35
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 [#permalink]

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14 Oct 2016, 04:56
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Expert's post
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

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

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14 Jan 2017, 13:00
(2+5+6+4)/(5000+12000+18000+16000)*60000 = 20
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Re: A computer chip manufacturer expects the ratio of the number [#permalink]

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28 Jan 2017, 09:55
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 $$\frac{60,000}{3,000}=20$$.

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 [#permalink]

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28 Jan 2017, 10:31
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 $$\frac{60,000}{3,000}=20$$.

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 [#permalink]

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08 May 2017, 00:17
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   [#permalink] 08 May 2017, 00:17
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