Question

The average of four consecutive odd
numbers is 16. What is the product of
lowest and highest number?
(1) 247
(2) 255
(3) 221
(4) Data inadequate​

Answer 1

Given,

The average of the four consecutive odd numbers = 16

To find,

The product of the lowest and highest number.

Solution,

The common difference between any two consecutive odd numbers is 2.

(For example, 3 and 5 are two consecutive odd numbers which has a difference of 2.)

Let, the lowest odd number = x

The second odd number will be = x+2

The third odd number will be = x+4

The fourth (or, the largest) odd number will be = x+6

Sum of the four numbers = (x+x+2+x+4+x+6) = 4x+12

Average of the four numbers = (4x+12)/4 = x+3

According, to the data mentioned in the question,

x+3 = 16

x = 13

The lowest odd number = 13

The largest odd number = 13+6 = 19

Product = 13×19 = 247

Hence, the product of the highest and lowest numbers is 247.

Answer 2

$Let \: x, (x+2),(x+4) \:and \: (x+6) \:are$

$four \: consecutive \:odd \:numbers$

/* According to the problem given */

$Average \:of \: 4 \: Numbers = 16$

$\implies \frac{x+(x+2)+(x+4)+(x+6) }{4} = 16$

$\implies \frac{4x+12}{4} = 16$

$\implies \frac{4(x+3)}{4} = 16$

$\implies x + 3 = 16$

$\implies x = 16 - 3$

$\implies x = 13$

$Four \: consecutive \: odd \:numbers \: are$

$13,15,17 \:and \: 19$

$\red{ Product \:of \: lowest \:and \: Heighest \: number }$

$= 13 \times 19$

$\green { = 247}$

$Option \: \pink{ ( 1 ) } \:is \: correct$

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