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# If x and y are positive integers, what is the value of (x + y)?

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If x and y are positive integers, what is the value of (x + y)?
(1) (x + y - 1)! < 100
(2) y = x^2 - x + 1

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commented Jun 9, 2015 by Guru (5,808 points)

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Both x and y are +ve integers i.e. they shall be 1,2,3,4,5 ...... n
Let us pick up statement #1
(x+y-1)! < 100
Let us write the factorials of 1,2,3,4 and see when does it exceed 100.
1! = 1
2! = 2
3! = 6
4! = 24
5! = 120
So the max value of x+y-1 can be 4 because when it is 5 it exceeds 100.
So x+y-1 = 1,2,3,4 or
x+y = 2, 3, 4, 5
But does not give us 1 solution. Not Sufficient
Let us Pick up Statement #2
y = x^2 -x + 1
This quadratic has no integer solutions, hence we cannot solve it for answer. Not Sufficient
Umm. Combine them replace y from in statement #1 from #2
x+x^2-x+1 = 2,3,4,5
=> x^2+1 = 2,3,4,5
=> x^2 = 1,2,3,4
this will 2 solutions +ve x = 1,2
corresponding +ve y can be 1,3
The answer should be e, the oa is debatable here. please check again.
answered Jun 9, 2015 by Guru (5,808 points)
Student Speaks Jyotsna Mehta

Indian School of Business, Co'18

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