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Question

If the difference between two natural numbers is 2 and the sum of their squares is 244, then the sum of the smaller number and the square of the larger number is

A
154
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B
112
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C
109
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D
180
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Solution

The correct option is A 154
Let the two natural numbers be x and y, x > y.
xy=2 and x2+y2=244
(xy)2+2xy=244 [x2+y)2+2xy
2xy=2444=240
xy=120
y=120x

Now, x - y = 2

x120x=2
x2120=2x
x22x120=0
x212x+10x120=0
x(x12)+10(x12)=0
(x12)(x+10)=0
y=12012=10 (Neglecting x=10,as it is a natural number
y+x2=10+122=154
Hence, the correct answer is option (1).

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