Xavier Aptitude Test 2018 Paper

Question : 62 of 99

Marks: +1, -0

X and Y are the digits at the unit’s place of the numbers

(408X)^{63}

and

(789Y)^{85}

where X ≠ Y. However, the digits at the unit’s place of the numbers

(408X)^{63}

and

(789Y)^{85}

are the same. What will be the possible value(s) of (X + Y)?

Solution:

Any number raised to power by the multiple of 4 givesthe numbers whose units places are same.
∴ We divide the powers 63 and 85 by 4.
⇒

{63}/4

⇒ Quotent =15, Remainder = 3

{85}/4

⇒ Q = 21 , R = 1
∴ X and Y are such numbers which when raised to power by 3 and 1 respectively give same units digits numbers.
⇒

X^3

2^3

= 8 or

X^3

3^3

= 27

Y^12

8^1

= 8 or

Y^1

7^1

= 7
∴ X + Y = 8 + 2 = 10 or X + Y = 7 + 3 = 10

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