Average of 75 students is 82, out of which average of 42 students is 7

Question

Average of 75 students is 82, out of which average of 42 students is 79. What is the average of the remaining 33 students rounded to the nearest integer?

A. 84
B. 85
C. 86
D. 87
E. 88

The average marks of 75 students is 82, out of which the average of 42 students is 79. What is the average of the remaining 33 students?

Archit3110 · Answer

sum for 75 students ; 75*82 = 6150
sum of 42 students ; 42 * 79 = 3138
so for 33 students sum = 6150-3138 ; 2832
avg ; 2832/33; 85.8 ~ 86 IMO C

eabhgoy · Answer

All 75 students have an average of 82

but 42 students have an average of 79. 
Therefore these 42 students are of the average by 3 points each and this difference has to be adjusted to the remaining 33 students.
Hence 42*3 = 126

These 126 points will be adjusted to the average of the remaining 33 students
=> 126/33 = 3.81 = approx 4

Now the average for the 33 students = 82 + 4 = 86.

Hence the correct answer is 86.

ScottTargetTestPrep · Answer

The sum of the 75 students is 75 x 82 = 6,150.

The sum of the 42 students is 42 x 79 = 3,318.

Thus, the sum of the remaining 33 students is 6,150 - 3,3318 = 2,832, and their average is 2,832/33 = 85.8, rounded to 86.

Answer: C

nandini14 · Answer

Is this the right procedure to solve such questions cause looks very easy!

egmat · Answer

nandini14  Yes, it is. You can use it for weighted average problems like this.

Why This Works: 
The fundamental relationship is:  	ext{Average} = \frac{	ext{Sum}}{	ext{Count}} , which means  	ext{Sum} = 	ext{Average} 	imes 	ext{Count} . When you know the overall average and one subgroup's average, you can isolate the remaining subgroup's sum through subtraction. This is the most efficient approach for this problem type.

What to watch for: 
 
 Some problems give you individual values instead of subgroup averages—then you'd add those values directly to your sum calculations 
 Watch for problems asking for the average of combined groups (different formula needed) 
 Always verify that subgroup counts add up to the total count

Average of 75 students is 82, out of which average of 42 students is 7

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Average of 75 students is 82, out of which average of 42 students is 7

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards