Number Properties

[zahrahooda]

If x and y are positive even numbers and have a sum of 36, how many pairs of x and y that can let x>y are possible?

[srcc25anu]

X + Y = 36 where x and y are both even and positive. also x > y

36/2 = 18 so the largest value of x can be 20 (X can't be 18 as then y must also be 18 and condition of x > y is violated). and x should be less than 36 as both x and Y must be positive. (Thanks for pointing this out)

so x can be any even number from 18 to 34 and y can be the complement that together adds to give 36
How many even numbers between 20 and 34 inclusive?

[(34 - 20) / 2] + 1 = 8 possible combinations of X and Y possible

[fcabanski]

The previous solution is incorrect. If x is 36, y is 0. 0 isn't positive.

Equations can be hard. Common sense isn't. Set up the problem correctly, think for a moment, and write things down. It isn't hard to solve this without any equations.

Write down what you know and the given info:

Given: Positive even numbers with x>y where x+y=36. (x and y add up to 36).

What you know: Have to be integers, because fractions aren't even or odd. 2,4,6,8...36.

18+18 = 36. x has to be larger than 18 because it has to be larger than y. 20, 22, 24, 26, 28, 30, 32, 34 x can't be 36, because then y would be 0. 0 isn't positive.

How many numbers/combinations is that? 8: 20+16, 22+14, 24+12, 26+10, 28+8, 30+6, 32+4, 34+2

[Jim@StratusPrep]

Yep, keep things simple, just count the even numbers between 18 and 36. There are 8.