When 2/3 of the garments in a shipment were inspected

[agha79]

When 2/3 of the garments in a shipment were inspected, 18 of the garments passed inspection and the remaining 2 garments failed. How many of the uninspected garments must pass inspection in order that 90% of the garments in the shipment pass?

A. 10
B. 9
C. 8
D. 7
E. 5

I thought that 2/3 of x (taking x as the total garments) got 18 garments passed and 2 failed. 1/3 of x were uninspected. I could not follow the question then.
OA is B

[girish_ns]

Dear Agha:

Let us start by noting that of the garments that were inspected, 18 passed the inspection and the other 2 failed. This means:

Total number of garments inspected = 18 + 2 = 20

The question also says that only 2/3rd of the total number of garments were inspected. So, if "x" is the total number of garments, we can write this equation:

(2/3)x = 20
So, x = 30

This means that there are 30 total garments, out of which 20 were inspected, and 10 left to be inspected.

The question asks how many remaining garments have to pass the inspection to have a 90% of total garments pass the test.

Lets calculate what is 90% of the total garments. This can be found out with the following formula:

(90/100)(total num. of garments) = (90/100)30 = 27.

So a total of 27 garments should pass the inspection to have 90% of total garments pass the inspection.

Of this 27, 18 has already passed the inspection (provided in the problem).

So, the number of garments that have to pass the inspection = 27 -18 = 9.

So the answer is B

Hope this helps

[agha79]

thanks Girish!! wonderful explanation.

[jnelson0612]

Yes, very nice work girish! Thank you.