If the average of 15, 25, 19, 20, 23, 18 and \((x-3)\) is 20, then find the average of \(x\), \((x+6)\), \((2x-1)\) and 23.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 30
Average \(\times\) number of values = sum of the values, so the first average gives the sum of the seven numbers and hence \(x\).
Finding \(x\) (seven numbers with average 20):
Sum of the seven numbers \(=7\times20=140\)
Sum of the six known numbers \(=15+25+19+20+23+18=120\)
\(x-3=140-120=20\), so \(x=23\)
The new average:
The four numbers: \(x=23\), \(x+6=29\), \(2x-1=45\) and 23
Average \(\displaystyle=\frac{23+29+45+23}{4}=\frac{120}{4}=30\)