Question: If the average (arithmetic mean) of the four numbers 3, 15, 32, and (N + 1) is 18, then N =
(A) 19
(B) 20
(C) 21
(D) 22
(E) 29
“If the average (arithmetic mean) of the four numbers 3, 15, 32, and (N + 1) is 18, then N =”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide 2022”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.
Solution and Explanation:
Approach Solution 1:
As per the question, average (arithmetic mean) of the four numbers 3, 15, 32, and (N + 1) is 18.
Candidates need to find the value of “N”
The average (arithmetic mean) of the four numbers 3, 15, 32, and (N + 1) is 18
Average Sum of all 4 numbers is 3+15+32+(N+1) = 18
So, (sum of all 4 numbers)/4 = 18
= (3+15+32+(N+1))/4 = 18
We need to multiply both sides by 4 to get the sum of all 4 numbers
Hence, the equation stands:
(3+15+32+(N+1))/4*4 = 18*4
This means that 3 + 15 + 32 + (N+1) = 72
If we simplify the equation, it stands at : N + 51 = 72
N = 72-51
If we solve, we get, N = 21
Correct Answer: C
Approach Solution 2:
As per the question, average (arithmetic mean) of the four numbers 3, 15, 32, and (N + 1) is 18.
Candidates need to find the value of “N”
The average (arithmetic mean) of the four numbers 3, 15, 32, and (N + 1) is 18
We will consider a different way for practice.
Let us consider how far each number is from the average of 18:
The first number is 3 which is (-15) far from 18.
The second number is 15 which is (-3) far from 18.
The third number is 32 which is 14 far from 18.
Hence, the equation stands at:
(-15) + (-3) + 14 + (N+1) = 18
-18+14+(N+1) = 18
-4 + (N+1) = 18
N - 3 = 18
N = 18+3
N = 21
Correct Answer: C
Approach Solution 3:
Mean is the sum of the values divided by the total number of values in the data set.
Given data set is 3,15,32,(N+1)
Total number of values is 4
Given that arithmetic mean is 18
⟹3+15+32+N+1/4=18
⟹3+15+32+N+1=18×4
⟹51+N=72
⟹N=72−51=21
Correct Answer: C
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