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(#M40157087) CAT Numerical Ability question number Keep an EYE

Find the two digit no.which exceeds by 12 the sum of squares of digits and by 16 the doubled product of its digits.?

Asked In CAT arun sawaiyan (8 years ago)

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Devendra Marghade  (8 years ago)

Ans= 64

Let the digits of a two-digit number be x and y and the number be 10x+y, then
According to first condition: 10x+y= (x^2+y^2)+ 12 ----(i) and
According to second condition: 10x+y= 2xy+16 ----(ii)
Comparing (i) & (ii), (x^2+y^2)+ 12 = 2xy+16
=> x^2+y^2-2xy =4
=> (x-y)^2 = 4 or x-y= 2
Now checking for the combinations of x,y with difference of 2, and satisfying 1st and 2nd condition, we have x=6, y=4 , where 64= 6^2+4^2+12 and 64=2*6*4+16

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Abhishek Shaw  (8 years ago)

yes,it is 64

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