The average age of an adult class is 40 years. 12 new students with an

Question

The average age of an adult class is 40 years. 12 new students with an average of 32 years join the class, thereby decreasing the average by 4 years. The original strength of the class was :

A. 10 
B. 11
C. 12 
D. 15
E. 15

Archit3110 · Answer

sum of n/ n = 40
40n= sum
x+384/n+12 = 36
40n+384=36n+432
n= 12
IMO C

CrackverbalGMAT · Answer

Average = \frac{Sum \space of \space observations}{Total \space Observations}

Therefore Sum of Observations = Average * Total Observations

Let the number of students of the original class = x

Their average age = 40 years

Sum of their Ages = 40x

Sum of ages of the 12 students of average age 32 years = 32 * 12 = 384

Total Students = x + 12

Total Sum of ages = 40x + 384

Average age = original average - 4 = 40 - 4 = 36

Therefore  \frac{40x \space + \space 384}{x \space + \space 12} = 36

Cross multiplying, we get: 40x + 384 = 36x + 432

4x = 432 - 384 = 48

x = 12

Option C

Arun Kumar

MathRevolution · Answer

Average:  \frac{Sum }{ Total}

Let the original strength be 'x'.

=> 40:  \frac{Sum }{ x}

=> Sum = 40x

=> 12 new students with an average of 32 years joins the class: 12 * 32 = 384.

=> New sum: 40x + 384 ; New Total: x + 12 ; New average: 40 - 4 = 36

=> 36 =  \frac{(40x + 384) }{ (x + 12)}

=> 36x + 432 = 40x + 384

=> 48 = 4x

=> x = 12

Answer C

Abhishek009 · Answer

40n + 12*32 = ( n + 12 )36

Or,  40n + 384 = 36n + 432

Or,  4n = 48

Or,  n = 12 , Hence Answer must be (C)

ScottTargetTestPrep · Answer

Solution:

We can let the original number of students in the class be x and create the equation:

(40x + 32 * 12) / (x + 12) = 36

40x + 384 = 36(x + 12)

40x + 384 = 36x + 432

4x = 48

x = 12

Answer: C

Dereno · Answer

Can be done using alligations. New average = 40-4 = 36

40. . 32

. 36

4. : 4

12 corresponds to 4. Then the other value remains same as 4. So, 12.

Alternate approach:

If the new students who entered have the all their averages equal 40. Then average drop doesn’t occur.

But, they are 8 down per student. Total cumulative amount down is 12*8 = 96 down.

When this 96 value is split among the total students (n+12)

We take the original number of students to be n.

96/(n+12) = 4

4n = 48

n = 12.

egmat · Answer

Think of it this way: The new students (average 32) are  younger  than the original class (average 40), so they  pull the average down .

The original group is  4 years above  the new average (40 - 36 = 4).
The new group is  4 years below  the new average (36 - 32 = 4).

Since both groups deviate by the  same amount  from the combined average, they must be  equal in size !

Original class = 12 students ✓

The average age of an adult class is 40 years. 12 new students with an

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

The average age of an adult class is 40 years. 12 new students with an

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