# 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

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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