Arithmetic MCQ 9 (Numbers and average problem)
Arithmetic MCQ 9: The average of 1st 3 of 4 numbers is 16 and of the last 3 is 15. If the sum of the first and the last number is 13. What is the last numbers?
a) 8 b) 6 c) 5 d) 2
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Solution:
Let the 4 numbers be A,B,C and C .
We know average is calculated by taking sum of entries and dividing it by the number of entries.
i-e
\[ Average = \frac{Sum of Entries}{Number of Entries} \]
According to given condition average of the first four numbers is 16.
Hence,
\[ 16= \frac{A+B+C}{3} \]
from this we get,
\[ A+B+C=48 —–(1) \]
Also given that average of last three numbers is 15.
Hence,
\[ 15=\frac{B+C+D}{3} \]
From this we get,
\[ B+C+D=45 ——-(2) \]
Subtracting eq 2 from eq 1, we get;
\[ A-D=3 —–(3) \]
Also we have been told that sum of first and the last numbers is 13,
i-e
\[ A+D= 13 ——(4) \]
Subtracting eq 3 from eq 4, we get;
\[ (A+D)-(A-D)=13-3 \]
So,
\[ 2D=10 \]
This gives;
\[ D=5 \]
So the last number is 5 — option c is correct!
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