This year, 15% of the students who received a final grade in Professor

Question

This year, 15% of the students who received a final grade in Professor Smith's American History class received a grade higher than a 8, half the number of students who received a grade higher than a 8 last year. The number of students who received a grade higher than 8 last year is approximately what percent of the number of students who received a grade of a 8 or below this year?

A. 7%
B. 35%
C. 42%
D. 74%
E. 150%

A. 7%
B. 35%
C. 42%
D. 74%
E. 150%

Archit3110 · Answer

let total be 100 students
so 15 students got 8 or higher this year and below 8 is 85
and last year 30 students got 8 or higher
target The number of students who received a grade higher than 8 last year is approximately what percent of the number of students who received a grade of a 8 or below this year?

30/85 ; ~ 35 %
OPTION B

IanStewart · Answer

The number of students who last year got a high grade (greater than 8) would be 30% of this year's class. Since 85% of this year's class got a low grade (8 or less), we're just being asked for the approximate value of 30/85 = 6/17 as a percentage, and since that fraction is very slightly bigger than 6/18 = 1/3, the answer is approximately 35%.

BrushMyQuant · Answer

Let's solve it using 2x2 Matrix
Refer Attached Image
Now it is given to us that
 "This year, 15% of the students who received a final grade in Professor Smith's American History class received a grade higher than a 8" 
=> Value under This year and "Grade > 8" is 15% of the total value under this year. Let total Value under this year be 100.
=> Value under This year and "Grade > 8" is 15% = 15% of 100 = 0.15* 100 = 15

"half the number of students who received a grade higher than a 8 last year" 
=> Last Year students with "Grade > 8" were Twice what we have this year
=> Value under Last Year and "Grade > 8" = 2 * This Year and "Grade > 8" = 2 * 15 = 30

Now we need to  "the number of students who received a grade of a 8 or below this year"  to find the final answer.
Now we know that total grades this year = 100 and this year and grade > 8 = 15
=> This year Grades <= 8 = 100 - 15 = 85

The number of students who received a grade higher than 8 last year is approximately what percent of the number of students who received a grade of a 8 or below this year =  \frac{30}{85}  * 100 ~ 35 %

So , Answer will be B
Hope it helps!

sheldoncooper · Answer

By picking numbers :-

Let total Students = 100
8 & above this year = 15 & so 8 & below this year = 100-15 = 85
8 & above last year = 2*15 = 30

(No of students with grades above 8 last year / No of students with grade less than 8 ) *100
30*100/85 ~35%

Option B

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This year, 15% of the students who received a final grade in Professor

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