If average of 7 consecutive even numbers is 21, what is the difference

Question

If average of 7 consecutive odd numbers is 21, what is the difference between the smallest and the largest numbers ?

A. 10
B. 11
C. 12
D. 13
E. 14

globaldesi · Answer

the first term be x
so 7th term will be x+ (7-1)* 2= x+12 x +(n-1)d where difference is 2 and 7 th term 
difference x+12-x= 12

answer C

CrackverbalGMAT · Answer

Hi Bunuel, the data given should be for consecutive odd numbers and not consecutive even numbers.

Let the numbers be x, x+2, x+4, x+6, x+8, x+10 and x+12

The difference between the largest and the smallest numbers = x + 12 - x = 12

Therefore Option C is the correct answer.

In terms of actual calculations.

Since the average of these 7 numbers is 21, the sum = 7 * 21 = 147

Therefore x + x + 2 + x + 4 + x + 6 + x + 8 + x + 10 + x + 12 = 147

7x + 42 = 147

7x = 105

x = 15 and the largest number would be x + 12 = 15 + 12 = 27

The difference is 27 - 15 = 12

Option C

Arun Kumar

Bunuel · Answer

_______________
Edited. Thank you!

Nipungupta9081 · Answer

IMO C

Consecutive ODD Integers = 2n - 5 + 2n - 3 + 2n -1 + 2n +1 + 2n + 3 + 2n + 5 + 2n + 7

= 14n + 7 / 7 = 21
= 14n + 7 = 147 
= 14n = 140

N = 10.

Lowest odd Number = 2n - 5 = 2*10 - 5 = 15
Highest Odd Number = 2n + 7 = 2*10 + 7 = 27

Difference = 27 - 15 = 12.

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