Question

The sum of 7 consecutive numbers is 84. The difference between the largest and smallest is:
A)7
B)6
C)14
D)21

Answer 1

$\huge{\mathcal{Hi\: there!}}$

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Let the seven consecutive numbers be x, x + 1, x + 2, x + 3, x + 4, x + 5, and x + 6.

A / Q,

x + x + 1 + x + 2 + x + 3 + x + 4 + x + 5 + x + 6 = 84.

⇒ 7x + 21 = 84

⇒ 7x = 84 - 21

⇒ 7x = 63

⇒ x = 63 / 7

⇒ x = 9

So,

Numbers are ;

1st no = x = 9

2nd no = x + 1 = 10

3rd no = x + 2 = 11

4th no = x + 3 = 12

5th no = x + 4 = 13

6th no = x + 5 = 14

7th no = x + 6 = 15

Here,

Smallest number = 9

Largest number = 15.

Now ,

Difference between largest and the smallest number = ( 15 - 9 )

⇒ 6.

Hence, the required answer is 6.

( Option B) is correct.

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Thanks for the question!

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Answer 2

Solutions :-


Given :

The sum of 7 consecutive numbers is 84


Let the first consecutive number be x
Second = x + 1
Third = x + 2
Fourth = x + 3
Fifth = x + 4
Sixth = x + 5
Seventh = x + 6



A/q

=> x + x + 1 + x + 2 + x + 3 + x + 4 + x + 5 + x + 6 = 84
=> 7x + 21 = 84
=> 7x = 84 - 21
=> 7x = 63
=> x = 63/7 = 9



Therefore,
First number = x = 9
Second number = x + 1 = 9 + 1 = 10
Third number = x + 2 = 9 + 2 = 11
Fourth number = x + 3 = 9 + 3 = 12
Fifth number = x + 4 = 9 + 4 = 13
Sixth number = x + 5 = 9 + 5 = 14
Seventh number = x + 6 = 9 + 6 = 15


Here,
Largest number = 15
Smallest number = 9


Find the difference between the largest and smallest number :-

Largest number - Smallest number
= 15 - 9
= 6


Hence,
Option 'B' = 6 is the right answer.