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sampath: Senior | Next Rank: 100 Posts; Posts: 49; Joined: Thu May 19, 2011 9:20 pm

Numbers

by sampath » Fri Aug 05, 2011 11:22 am

Is x+y positive?
1. x -y is positive
2. x/y is positive

Thanks.

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Source: Beat The GMAT — Data Sufficiency | Fri Aug 05, 2011 11:22 am

gmatboost: Master | Next Rank: 500 Posts; Posts: 312; Joined: Tue Aug 02, 2011 3:16 pm; Location: New York City; Thanked: 130 times; Followed by:33 members; GMAT Score:780

by gmatboost » Fri Aug 05, 2011 11:45 am

Statement 1:
x - y is positive means x - y > 0
Or, x > y ....... Rewriting it this way makes it much easier to think about the situation in my opinion
Knowing that x > y definitely does not allow us to determine if their sum is positive.

You could plug in numbers to show this, but I think it's useful to try thinking through this at this slightly higher level.

Statement 2:
x/y is positive
For the product of two numbers to be positive, the two must have the same sign. They both could be positive (in which case the sum is positive). They both could be negative (in which case the sum is negative).

Again, You could plug in numbers to show this, but here as well I think it's useful to try thinking through this at this slightly higher level.

Combined:
[spoiler]The two numbers must have the same sign. And one of them (x) has to be bigger than the other one(y). It's still true that they both could be positive (in which case the sum is positive), or that they both could be negative (in which case the sum is negative).[/spoiler]

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