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CAT 2015 Quantitative Ability

Question : 23 of 34

Marks: +1, -0

(106^90 - 49^90)

Solution:

x= (106^90 - 49^90)

(x^n - a^n)

is divisible by both (x - a) and (x + a) whenever n is even

⇒

(106^90 - 49^90)

is divisible by both 57 and 155

57 = 19 x 3

155 = 31 x 5

∴

(106^90 - 49^90)

will be divisible by (19 x 31) = 589 as well.

Also, note that

(106^90 - 49^90)

will be odd and options (b) and (c) are even. Hence, they can be rejected

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