Two consecutive even positive integers sum of the squares of which is 1060 are ........

Quantitative Aptitiude (CLAT) Number System

Download Solution PDF

Two consecutive even positive integers, sum of the squares of which is 1060 are:

12 and 14

22 and 24

20 and 22

16 and 18

Explanation:

(x)² + (x+2)²= 1060
x²+x²+4x+4=1060
Combine like terms.
2x²+4x+4=1060
Set equal to zero so you can factor.
2x²+4x−1056=0
(2x+66)(x−16)=0
x=−66,16
x=16 because the answer must be positive according to the question.
That means x+2 is 18.
Two consecutive even positive integers are 16 and 18.
Hence, option 4 is the correct answer.