The average of the numbers 5, 3, 9, 11, 29 and (p+1) is 12. The average increases by 2 when the numbers (q-5) and (q+11) are also included. Find the value of q.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 17
Average \(\times\) number of values = total, so the totals before and after the two new numbers are compared.
Total of the six numbers \(=6\times12=72\)
With two more numbers the average is \(12+2=14\), so the total of eight numbers \(=8\times14=112\)
The two new numbers: \((q-5)+(q+11)=112-72=40\)
\(2q+6=40\), so \(q=\) 17
The value of \(p\) (here 14) is not needed for \(q\).