Latest TCS Aptitude Question SOLUTION: How many two-digit numbers are there which, when subtracted from the number formed by reversing its digits as well as when added to the number formed by reversing its digits, resul

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(#M40021560) TCS Numerical Ability question Keep an EYE

How many two-digit numbers are there which, when subtracted from the number formed by reversing its digits as well as when added to the number formed by reversing its digits, result in a perfect square?
option
a) 1
b) 2
c) 3
d) 4

Asked In TCS Tanu (10 years ago)

Unsolved Read Solution (5)

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Read Solution (5) :

Danish Shaikh   (10 years ago)

Only one 56,65
56+65=121
65-56=9

Is this solution Helpfull? Yes (15) | No (11)  

Ghaneshyam Solanki  (10 years ago)

10x+y be the 2 digit number then
10x+y+10Y+x(reverse) == 11(x+y)
and 10x+y - (10y+x)== 9(x-y)
solving x and y trail error method.. only one satisfies both the equations 6 and 5
ans: 1

Is this solution Helpfull? Yes (15) | No (3)  

Tanu  (10 years ago)

@DANISH But how can u say only one. Please explain.

Is this solution Helpfull? Yes (9) | No (1)  

ujjwal  (8 years ago)

Let the number xy = 10x + y
Given that, 10x+y - (10y - x) = 9(x-y) is a perfect square
So x-y can be 1, 4, 9.  -------- (1)
So given that 10x+y +(10y +x) = 11(x+y) is a perfect square.
So x+y be 11. options are (9,2), (8,3),(7,4),(6,5) hence only ( 6,5 ) satisfy the condition. .therefore ans. Is 1

Is this solution Helpfull? Yes (3) | No   

Saunak Das  (8 years ago)

there is only one such number 65. which gives 65+56=121=11^2 & 65-56=3^2.

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