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On each lab that René completed he received either 100

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On each lab that René completed he received either 100

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Source: Magoosh

On each lab that René completed he received either 100 points or 85 points. On how many labs did he score 100 points?

1) René's scores for his completed labs totaled 1140 points.
2) René completed a total of twelve labs.

The OA is A

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Junior | Next Rank: 30 Posts Default Avatar
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On each lab that René completed he received either 100 points or 85 points. On how many labs did he score 100 points?

1) René's scores for his completed labs totaled 1140 points.
We have 60 points less for 1200, which is 15*4
In have 15 points less than 100 in 85
So there are total 4 lab with a score of 85
1140 - 4*85 = 800
implies we have 8 labs with 100 score
Sufficient

2) René completed a total of twelve labs.
We can strictly say the number of labs with 100 point, may be 6,7,8,..or all 12
Insufficient

Option A is correct



Last edited by Manasa3190 on Thu Jan 03, 2019 12:02 am; edited 1 time in total

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BTGmoderatorLU wrote:
Source: Magoosh

On each lab that René completed he received either 100 points or 85 points. On how many labs did he score 100 points?

1) René's scores for his completed labs totaled 1140 points.
2) René completed a total of twelve labs.
Let x = the number of 100-point labs and y = the number of 85-point labs.
Question stem, rephrased:
What is the value of x?

Statement 1:
100x + 85y = 1140
20x + 17y = 228
The value in blue implies the following:
Since 20x will have a units digit of 0, 17y must have a UNITS DIGIT OF 8.
Thus, y=4, with the result that 17y = 17*4 = 68.
Substituting 17y=68 into 20x+17y=228, we get:
20x + 68 = 228
20x = 160
x = 8.
SUFFICIENT.

Statement 2:
Here, x can be any value between 0 and 12, inclusive.
INSUFFICIENT.

The correct answer is A.

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Statement 1: Rene's scores for his completed labs totalled 1140 points
Let 100 points = x
Let 85 points = y
100x + 85y =1140
divide through by 5; we have
$$20x+17y=228$$
There is only one unique solution to this; x=8 and y=4
Rene's scored 100 points in 8 labs; STATEMENT 1 IS SUFFICIENT

Statement 2: Rene's completed a total of 12 labs. There are so many variants for this.
100 points in 1 lab and 85 points in 11 labs
100 points in 4 labs and 85 points in 8 labs etc

STATEMENT 2 IS INSUFFICIENT

ANSWER IS A

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