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Assemby line (ratio)

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by sofiasol » Mon Dec 12, 2016 8:38 am
On a certain assembly line, the rejection rate for Monday's production was 4 per cent, for Thursday's 8 per cent, and for the two days combined 7 per cent. What was the ratio of Tuesday's production to Moday's production?

a) 3/1
b) 2/1
c) 1/1
d) 1/2
e) 1/3

The answer is a) 3/1. Why?

Thanks in advance.
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by DavidG@VeritasPrep » Mon Dec 12, 2016 8:44 am
sofiasol wrote:On a certain assembly line, the rejection rate for Monday's production was 4 per cent, for Thursday's 8 per cent, and for the two days combined 7 per cent. What was the ratio of Thursday's production to Moday's production?

a) 3/1
b) 2/1
c) 1/1
d) 1/2
e) 1/3

The answer is a) 3/1. Why?

Thanks in advance.
The algebra:

Call total Monday production "m." If the rejection rate is 4%, .04m are rejected.
Call total Thursday production "t." If the rejection rate is 8%, .08t are rejected.
The total Monday + Thursday production = m + t. If the rejection rate is 7%, .07(m + t) are rejection.

Now .04m + .08t = .07(m +t)
,04m + .08t = .07m + .07t
.01t = .03m
t = 3m, which means there's a 3:1 ratio.
Last edited by DavidG@VeritasPrep on Mon Dec 12, 2016 8:49 am, edited 1 time in total.
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by DavidG@VeritasPrep » Mon Dec 12, 2016 8:48 am
sofiasol wrote:On a certain assembly line, the rejection rate for Monday's production was 4 per cent, for Thursday's 8 per cent, and for the two days combined 7 per cent. What was the ratio of Thursday's production to Moday's production?

a) 3/1
b) 2/1
c) 1/1
d) 1/2
e) 1/3

The answer is a) 3/1. Why?

Thanks in advance.
Or set it up on the number line.

Monday-Total-Thurs
4---------7---8
Gaps: 3 ----1

Because the overall average (7) is closer to the rate for Thursday (8), we know there's a 3:1 ratio in favor of Thursday's production.
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by [email protected] » Mon Dec 12, 2016 11:12 am
Hi sofiasol,

This question is a "weighted average" prompt - and that is a concept that you will almost certainly be tested on at least once when you take the Official GMAT. In these cases, you can always set the prompt up algebraically.

M = number of items produced on Monday
T = number of items produced on Thursday

.04M = number of rejected items on Monday
.08T = number of rejected items on Thursday

(.04M + .08T)/(M+T) = .07

.04M + .08T = .07M + .07T
.01T = .03M
T = 3M

That equation means that when M=1, then T=3. Therefore, the ratio of T to M is 3:1.

Final Answer: A

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by melguy » Wed Dec 14, 2016 12:20 am
I used the Allegation method (which is best for mixture problems) and the answer seems to be correct. Experts please confirm if the method can be used for this problem also?
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by DavidG@VeritasPrep » Wed Dec 14, 2016 6:20 am
melguy wrote:I used the Allegation method (which is best for mixture problems) and the answer seems to be correct. Experts please confirm if the method can be used for this problem also?
Sure is. Nicely done :)
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by Brent@GMATPrepNow » Wed Dec 14, 2016 6:37 am
sofiasol wrote:On a certain assembly line, the rejection rate for Monday's production was 4 per cent, for Tuesday's 8 per cent, and for the two days combined 7 per cent. What was the ratio of Tuesday's production to Moday's production?

a) 3/1
b) 2/1
c) 1/1
d) 1/2
e) 1/3
Another approach is to combine some number sense and plugging in.
Here's what I mean.
IF IT WERE THE CASE that Monday's production EQUALED Tuesday's production, then the rejection rate for the COMBINED days would be 6%, which is the average of 4% and 8%
HOWEVER, the rejection rate for the COMBINED days is 7%. This tells us that Tuesday's production (with an 8% rejection rate) has a greater influence on the total rejection rate of the combined days.
In other words, Tuesday's production must be GREATER THAN Monday's production.
This means we can conclude that the ratio of Tuesday's production to Monday's production must be greater than 1.
This allows us to ELIMINATE C, D and E.

At this point, we're going to TEST one of the two remaining answer choices.
Let's test answer choice A. If it satisfies the given information, then we know the correct answer is A.
If it doesn't satisfy the given information, then we know the correct answer is B.

Let's test answer choice A.
If the ratio of Tuesday's production to Monday's production is 3/1, let's say that Tuesday's production was 300 and Monday's production was 100.
Monday's rejection rate was 4%: 4% of 100 = 4 rejected items
Tuesday's rejection rate was 8%: 8% of 300 = 24 rejected items

The TOTAL rejected items = 4 + 24 = 28
The TOTAL production = 100 + 300 = 400
28/400 = 7% rejection rate for the two days combined.
PERFECT!

Answer: A
RELATED VIDEO
- Weighted Averages: https://www.gmatprepnow.com/module/gmat ... /video/805
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