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

Question

https://gmatclub.com/forum/download/file.php?id=50879 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 2019-10-11_1612.png

Bunuel · Accepted Answer

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

Show Spoiler

Attachment:

2019-10-11_1612.png [ 58.73 KiB | Viewed 32205 times ]

Show Answer

Official Answer

B

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.

Bunuel · Answer

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.

BrentGMATPrepNow · Answer

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

junior · Answer

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..

kp1811 · Answer

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

BDSunDevil · Answer

let X be the # of defective chips. 
17/51,000=X/60,000
X= 20

shinbhu · Answer

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

Total = 17 + 3 = 20 -> B

GMAT98 · Answer

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

Bunuel · Answer

Bumping for review and further discussion*. Get a kudos point for an    alternative    solution!

*New project from GMAT Club!!! Check  HERE

shivanigs · Answer

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

PareshGmat · Answer

Total defective chips expected = 60000 * \frac{(2+5+6+4)}{(5000+12000+18000+16000)} = 20

asquare097 · Answer

I think you got the division wrong 6/3 = 2 Right?

ScottTargetTestPrep · Answer

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

anairamitch1804 · Answer

(2+5+6+4)/(5000+12000+18000+16000)*60000 = 20
Answer is B

saurabhsavant · Answer

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....

Bunuel · Answer

The probability of an event = (The # of favourable outcomes)/(The total # of outcomes).

mihir0710 · Answer

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

Basshead · Answer

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.

adityasuresh · Answer

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

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards