Latest Book Aptitude Question SOLUTION: The sum of the digits of a two-digit number X is Y. The sum of the digits of X^2 is Y^2. Find X.

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(#M40034986) BOOK Numerical Ability question solve Keep an EYE

The sum of the digits of a two-digit number X is Y. The sum of the digits of X^2 is Y^2. Find X.

Asked In Book pranshu goyal (10 years ago)

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Ann Theressa  (10 years ago)

X = 10,20 or 30

When X = 10
sum of digits = 1+0 = 1=Y
X^2 = 100
sum of digits of 100 = 1+0+0 = 1 = Y^2

When X = 20
sum of digits = 2+0 = 2=Y
X^2 = 400
sum of digits of 400 = 4+0+0 = 4 = Y^2

When X = 30
sum of digits = 3+0 = 3=Y
X^2 = 900
sum of digits of 900 = 9+0+0 = 9 = Y^2

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Saraswathy  (10 years ago)

Let X be "ab" ... first digit is a, 2nd digit is b

(a+b) = y -->(1)
(ab)^2 = y^2 -->(2)
ab = y

so
ab= a+b

a+b-ab = 0
a+b(1-a) = 0

a != 1 ... it ll produce b=0
So when a=2
2+b(-1) = 0
b=2

a = 2, b = 2 , X="ab" = 22
sub in (1) and (2)
2+2 = y => y=4
(22)^2 = 4^2 => 484 = 16
Given sum of digits of x^2 = Y^2
x^2 = 484 => 4+8+4 = 16 = y^2

Ans : x=22, y=4

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