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Last month, John rejected 0.5% of the products that...

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Last month, John rejected 0.5% of the products that...

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Last month, John rejected 0.5% of the products that he inspected and Jane rejected 0.8% of the product that she inspected. If a total of 0.75% of the products produced last month were rejected, what fraction of the products did Jane inspected?

A. 1/6
B. 1/2
C. 5/8
D. 5/6
E. 15/16

The OA is D.

I'm confused by this PS question. Experts, any suggestion about how to solve it? Thanks in advance.

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LUANDATO wrote:
Last month, John rejected 0.5% of the products that he inspected and Jane rejected 0.8% of the product that she inspected. If a total of 0.75% of the products produced last month were rejected, what fraction of the products did Jane inspected?

A. 1/6
B. 1/2
C. 5/8
D. 5/6
E. 15/16

The OA is D.

I'm confused by this PS question. Experts, any suggestion about how to solve it? Thanks in advance.
Plot the relevant figures on a number line

.5------------.75----.8
Gap-----.25----.05---

So the ratio of Jane's inspections to John's inspections is .25/.05 = 25/5 = 5/1. (The average is much closer to Jane than John, so we know that she did a disproportionate number of the inspections.)

Call Jane's inspections: 5x
Call John's inspections: x
Total: 6x

Jane/Total = 5x/6x = 5/6. The answer is D

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GMAT/MBA Expert

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Posted:
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Post
LUANDATO wrote:
Last month, John rejected 0.5% of the products that he inspected and Jane rejected 0.8% of the product that she inspected. If a total of 0.75% of the products produced last month were rejected, what fraction of the products did Jane inspected?

A. 1/6
B. 1/2
C. 5/8
D. 5/6
E. 15/16

The OA is D.

I'm confused by this PS question. Experts, any suggestion about how to solve it? Thanks in advance.
Alternatively, you could use more conventional algebra.
If Jane inspected "A" items, she'd have rejected .8A
If John inspected "N" items he'd have rejected .5N
Total rejections: .8A + .5N

Total items inspected: A + N
If 75% of the total were rejected, then: .75(A + N) = .8A + .5N

.75A + .75N = .8A + .5N
.25N = .05A
.25/.05 = A/N
5/1 = A/N
If for every 5 items Jane inspects, John inspects 1, then Jane would inspect 5 out of every 6 items. The answer is D

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LUANDATO wrote:
Last month, John rejected 0.5% of the products that he inspected and Jane rejected 0.8% of the product that she inspected. If a total of 0.75% of the products produced last month were rejected, what fraction of the products did Jane inspected?

A. 1/6
B. 1/2
C. 5/8
D. 5/6
E. 15/16
We can let the number of products inspected by John = a and the number inspected by Jane = b and create the equation:

0.005a + 0.008b = 0.0075(a + b)

50a + 80b = 75a + 75b

5b = 25a

b = 5a

Thus, Jane inspected b/(a + b) = 5a/6a = 5/6 of the products.

Answer: D

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Jeffrey Miller Head of GMAT Instruction

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