In a class of 40 students, each student received a distinct score on a final examination. … — GMAT

In a class of $40$ students, each student received a distinct score on a final examination. If a particular student's score is at the $85\text{th}$ percentile of the class scores, how many students scored lower than this student?

$34$ Answer
B
$85$
C
$6$
D
$35$
E
$33$

Answer

34 students scored lower than this student.

The 85th percentile of a group of 40 students means that 85% of the class scored below this student. Calculating

85\%

40

yields

0.85 \times 40 = 34

. Therefore, exactly 34 students scored lower.

Step-by-Step Solution

Understand the definition of percentile rank.

Being at the

85\text{th}

percentile means that the student's score is strictly higher than

85\%

of the other scores in the dataset.

By definition, the

p\text{th}

percentile of a set of distinct values separates the lower

p\%

of the data from the rest.

Calculate

85\%

of the total number of students (

40

0.85 \times 40 = 34

Multiplying the percentage by the sample size gives the exact count of students below the percentile threshold.

Key Concept

Percentile Rank

Question

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