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by GMATGuruNY » Tue May 22, 2018 12:31 pm
vaibhav101 wrote:A two-digit number is 18 less than the square of the sum of its digits.. how many such numbers are there?
A 1
B 2
C 3
D 4
E 5
Make a list of two-digit numbers that are 18 less than a perfect square:
36-18 = 18
49-18 = 31
64-18 = 46
81-18 = 63
100-18 = 82

Check whether each option above is equal to 18 less than the square of its digit sum:
18 = (1+8)² - 18
31 = (3+1)² - 18
46 = (4+6)² - 18
63 = (6+3)² - 18
82 = (8+2)² - 18

As the cases in blue illustrate:
63 is 18 less than the sum of the square of its digits.
82 is 18 less than the sum of the square of its digits.
No other cases are possible.

The correct answer is B.
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