CRE 1 - Average Basics

Since, age of every member of the family will increase by 3 years, the average of the whole family will also increase by 3 years.

Hence, option (b).

Mean rainfall = $\frac{\mathrm{89+95+70+102+29+79+63+85}}{10}$ = 73.4 cm

Hence, option (b).

Average = $\frac{621+679+697+603+649+651}{6}$ = 650

Alternately,

All these numbers are around 650.

Assume the base to be 650 and add the average deviation.

Average = Assumed average + average deviation

Average = 650 + $\frac{\left(621-650\right)+(679-650)+(697-650)+(603-650)+(649-650)+(651-650)}{6}$

Average = 650 + $\frac{-29+29+47-47-1+1}{6}$

Average = 650 + 0 = 650

Hence, option (b).

Given, Mon to Thur, (4 days) avg. Temp = 48°C

Thus, cumulative temp = 48 × 4 = 192°C.

Since temp, on Mon was 42°C

∴ Tue to Thur, (3 days), cumulative temp = 192 – 42 = 150°

Let temp. on Friday be x° C. 

Then from the problem, (150 + x)/4 = 47

⇒ x = 38°C

Hence, option (b).

Sum of the numbers = $32\frac{1}{3}+32\frac{1}{4}+31\frac{2}{3}+33\frac{3}{4}$

= 32 + 32 + 31 + 33 + $\left[\frac{1}{3}+\frac{1}{4}+\frac{2}{3}+\frac{3}{4}\right]$

= 128 + $\left[\frac{1}{4}+\frac{3}{4}+\frac{1}{3}+\frac{2}{3}\right]$

= 128 + 2 = 130.

Average = $\frac{130}{4}$ = $32\frac{1}{2}$.

Hence, option (a).

Cumulative score of 8 numbers = 8 × 23

New cumulative score = 8 × (8 × 23)

Avg. score of new set = (8 × 8 × 23)/8 = 184.

Alternately,

Since each number is multiplied with 8, the average also will become 8 times.

∴ New average = old average × 8 = 23 × 8 = 184.

Hence, option (d).

We know that average of average of all possible sets of 3 (or any other number) would always be equal to the average of initial numbers.

Hence, over here the average of 20 weights is 72 kg. Hence, their sum = 72 × 20 = 1440 kg.

Hence, option (c).

Sum of the ages immediately after the birth of 1^st child = 16 × 3 = 48

Sum of the ages immediately after the birth of 2^nd child = 15 × 4 = 60

The difference between the sum of the ages = 60 – 48 = 12 is due to 3 persons growing by same number of years. Hence, the gap between birth of 1^st child and 2^nd child = 12/3 = 4 years.

Similarly, the difference between the birth of 2^nd and 3^rd child = (16 × 5 – 15 × 4)/4 = 5 years

Similarly, the difference between the birth of 3^rd child and 4^th child = (15 × 6 – 16 × 5)/5 = 2 years

Hence, when the 4^th child was born, the 1^st child would be = 4 + 5 + 2 = 11 years old. 

When 4^th child was born the average age of the family was 15 years and current average age is 16 which implies that each of the family member grows 1 year. Hence, the current age of the 1^st child = 11 + 1 = 12 years

Hence, option (b).

Let the first odd number be x.

∴ The numbers are: x, x + 2, x + 4, x + 6. x + 8, x + 10, x + 12 and x + 14.

Since these numbers are in Arithmetic Progression the average of these 8 numbers will be same as average of first and the last number.

∴ (x + x + 14)/2 = 36

⇒ 2x + 14 = 72

⇒ x = 29

∴ The highest number = x + 14 = 43.

Alternately,
Since consecutive odd numbers will be in Arithmetic Progression and there avereage is 36 which will also be the average of 4^th and 5^th numbers.

∴ The 4^th term will be 35 and 5^th will be 37. Now, the 6^th number will be 39, 7^th will be 41 and 8^th will be 43.

Hence, 43.