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
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