Question 1

If the average of 4 consecutive odd numbers is 92, then the least number of those numbers is:

a) 89 b) 71 c) 81 d) 91

Answer : a) 89

Solution :

Let the four consecutive odd numbers be x, x+2, x+4 and x+6

We have to find the least number i.e., x

Given that the average is 92. That is, x + x+2 + x+4 + x+6 / 4 = 92

4x + 12 = 92(4)

4x + 12 = 368

4x = 368 - 12 = 356

x = 356/4 = 89

Hence the required number is 89.

Question 2

If the sum of five consecutive even numbers is 1580, then find the average of the next five consecutive even numbers

a) 326 b) 312 c) 325 d) 318

Answer : b) 312

Solution:

Let the five consecutive even numbers be x, x+2, x+4, x+6 and x+8

The sum of the above five numbers is 1580.

i.e., x + x+2 + x+4 + x+6 + x+8 = 1580

5x + 20 = 1580

5x = 1580 - 20

x = 312

Therefore, the 5 even numbers are 312, 312+2, 312+4, 312+6 and 312+8

Or 312, 314, 316, 318 and 320

Then the next 5 consecutive even numbers are 322, 324, 326, 328 and 330

Now, the required average = 322+324+326+328+330 / 5 = 1630/5 = 326.

Hence the answer is 326.

Question 3

If the sum of the 4 consecutive even numbers is 4 more than three times the largest number, then the average of those numbers is:

a) 32 b) 12 c) 25 d) 13

Answer : d) 13

Solution :

Even numbers can be represented to have the form 2n where n = 0,1,2,3....

Based on our above understanding, any four consecutive even numbers can be represented as,

2k, 2k + 2, 2k + 4, 2k + 6

Now, adding these we get,

2k + (2k + 2) + (2k + 4) + (2k + 6) = 8k + 12

But the above sum is 4 more than 3 times the largest number(which is 2k + 6) .

i.e., 8k + 12 = 4 + 6k + 18

2k = 10

k = 5

Therefore, the sum of the numbers = 8k + 12 = 52 (by substituting the value of k)

Then the required average = 52/4 = 13