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If x, y and z are integers

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If x, y and z are integers

by melguy » Tue Aug 27, 2013 9:05 am
Hello All

I am just confused with a property. When adding and subtracting can we freely move variables without knowing the signs (positive or negative?)

Does this property applies to multiplication and division only?

Thanks
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by Brent@GMATPrepNow » Tue Aug 27, 2013 9:34 am
Hey Melguy,

If you're referring to working with inequalities, then we can:
- add and subtract the same value from both sides of the inequality, and the direction of the inequality remains the same.
- multiply or divide both sides of the inequality by a POSITIVE VALUE, and the direction of the inequality remains the same.

If we multiply or divide both sides of the inequality by a NEGATIVE VALUE then we must REVERSE the direction of the inequality.

So, at one point in your example, we have 33x + 11z < 22y
So, if we divide both sides by POSITIVE 11, we get 3x + z < 2y

The tricky part comes when we want to multiply or divide both sides of the inequality by a some VARIABLE. If we don't know the sign of that variable, we won't know whether to reverse the direction of the inequality or leave it as is.

For example, if we know that xy < 3x, we cannot divide both sides by x and conclude that y < 3.
TAKEAWAY: Do not multiply or divide both sides of the inequality by a VARIABLE unless you are certain of the sign of that variable.

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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