## Sum of positive integers

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### Sum of positive integers

by piyush_nitt » Fri May 08, 2009 5:44 am
Sum of positive integers x and y is 72. What is xy?
a. x = y + 1
b. x and y have same tens digit

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by DanaJ » Fri May 08, 2009 10:30 am
This problem is wrong.
Statement 1 doesn't make sense and let me explain why. x and y are both positive integers and it says there that x = y + 1. Since x + y = 72, then it's safe to say that y + 1 + y = 2y + 1 = 72. This means that 2y = 71, with y = 35.5. As you can see, 35.5 is NOT a positive integer. This contradicts the initial assumption.

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### Re: Sum of positive integers

by Ian Stewart » Fri May 08, 2009 2:36 pm
piyush_nitt wrote:Sum of positive integers x and y is 72. What is xy?
a. x = y + 1
b. x and y have same tens digit
Agree with Dana - if x+y = 72, then either x and y are both odd, or x and y are both even. Statement 1 says that x and y are consecutive integers (i.e. one of them is odd, the other even) which contradicts information in the question.

If S1 didn't lead to a contradiction (e.g. if it said x = y+2), using it and the information in the question, you'd be able to find both x and y, and therefore answer the question. S2 alone would not be sufficient, since there are a few pairs of values of x and y with the same tens digit that add to 72 (36+36, 35+37, etc), and for each we get a different product xy.

Still, if that's the original version of the question, there's something wrong with the source.
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