Problem Solving

Shipment / Number of Defective Chips in the Shipment / Total number of Chips in the 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 the future shipments to equal the corresponding rate for shipments S1, S2, S3, and S4 combined, as shown in the table above. What is the expected number of defective chips in the shipment of 60,000 chips?

A) 14

B) 20

C) 22

D) 24

E) 25

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

sanju09 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 following table (read in order). What is the expected number of defective chips in a shipment of 60,000 chips?

Shipment: S1 S2 S3 S4
Number of defective chips in the shipment: 2 5 6 4
Total number of chips in the shipment: 5,000 12,000 18,000 16,000
A. 14
B. 20
C. 22
D. 24
E. 25

We are given the following:

S1: 2 defective chips out of 5,000 total

S2: 5 defective chips out of 12,000 total

S3: 6 defective chips out of 18,000 total

S4: 4 defective chips out of 16,000 total

The ratio of the number of defective chips to total chips is:

(2 + 5 + 6 + 4)/(5,000 + 12,000 + 18,000 + 16,000)

17/51,000 = 1/3,000

We see that we would expect 1 chip out of every 3,000 chips to be defective.

We can set up a proportion to determine the number of defective chips that we would expect in a 60,000 shipment of chips.

1/3,000 = x/60,000

60,000 = 3,000x

x = 20 chips

Answer: B