Is m not equal to n? (1) m+n <0 (2) mn<0

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phoenixhazard: Senior | Next Rank: 100 Posts; Posts: 41; Joined: Thu Oct 14, 2010 1:21 pm

by phoenixhazard » Tue Oct 19, 2010 6:28 pm

Is m not equal to n?
(1) m+n <0
(2) mn<0

I can't figure this out for the life of me. If they are asking if m and n will be positive/negative I can see that but I can't see how those 2 statements can tell you if the numbers will be the same.

btw the OA is Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient
Explanation?!?!

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Source: Beat The GMAT — Data Sufficiency | Tue Oct 19, 2010 6:28 pm

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by Ian Stewart » Tue Oct 19, 2010 7:08 pm

phoenixhazard wrote:Is m not equal to n?
(1) m+n <0
(2) mn<0

I can't figure this out for the life of me. If they are asking if m and n will be positive/negative I can see that but I can't see how those 2 statements can tell you if the numbers will be the same.

btw the OA is Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient
Explanation?!?!

They are asking if you can tell whether m and n are different. So we want to come up with two scenarios, one in which m and n are different, and one in which they are equal, in order to prove that Statement 1 is not sufficient. Certainly they can be different; m could be -1 and n could be 0, for example, but they could also both be the same negative number; both could be -1, for example.

From Statement 2, if the product of m and n is negative, then one of the two numbers is positive and the other is negative. So there's no way they could be the same number, and Statement 2 is sufficient.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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phoenixhazard: Senior | Next Rank: 100 Posts; Posts: 41; Joined: Thu Oct 14, 2010 1:21 pm

by phoenixhazard » Tue Oct 19, 2010 7:13 pm

Ian Stewart wrote:
phoenixhazard wrote:Is m not equal to n?
(1) m+n <0
(2) mn<0

I can't figure this out for the life of me. If they are asking if m and n will be positive/negative I can see that but I can't see how those 2 statements can tell you if the numbers will be the same.

btw the OA is Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient
Explanation?!?!
They are asking if you can tell whether m and n are different. So we want to come up with two scenarios, one in which m and n are different, and one in which they are equal, in order to prove that Statement 1 is not sufficient. Certainly they can be different; m could be -1 and n could be 0, for example, but they could also both be the same negative number; both could be -1, for example.

From Statement 2, if the product of m and n is negative, then one of the two numbers is positive and the other is negative. So there's no way they could be the same number, and Statement 2 is sufficient.

I understand if m is negative and n is positive that definitely tells you they are not the same number. What if m = 3 and n = 2? and then another scenario that m = 3 and n = 3? Both are positive but both situations are not the same number.

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uwhusky: Legendary Member; Posts: 1172; Joined: Wed Apr 28, 2010 6:20 pmFollowed by: 4 members; Thanked: 74 times

by uwhusky » Tue Oct 19, 2010 7:34 pm

phoenixhazard,

Correct!

The question is asking: "Is m not equal to n?" There isn't any set of numbers where m is equal to n, and mn < 0.

With this information, we can answer the question as "NO," hence B is sufficient.

Yep.

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phoenixhazard: Senior | Next Rank: 100 Posts; Posts: 41; Joined: Thu Oct 14, 2010 1:21 pm

by phoenixhazard » Wed Oct 20, 2010 9:52 am

uwhusky wrote:phoenixhazard,

Correct!

The question is asking: "Is m not equal to n?" There isn't any set of numbers where m is equal to n, and mn < 0.

With this information, we can answer the question as "NO," hence B is sufficient.

Sorry maybe I'm just being dumb but I still don't understand. I know that there is no situation a set of number when multiplied would be less than 0 if they are the same, so they must be different. But you still have the situation that you can multiply two different numbers that are both positive which gives you a positive. So mn < 0 to me sounds like it will tell you if two numbers are not the same sometimes but not always, this can't be sufficient to say that's enough to answer if m and n are always diff numbers...

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uwhusky: Legendary Member; Posts: 1172; Joined: Wed Apr 28, 2010 6:20 pmFollowed by: 4 members; Thanked: 74 times

by uwhusky » Wed Oct 20, 2010 10:20 pm

If you square a number, any number, the result has to be a positive number or 0.

0^2 = 0

5^2 = 25

(1/5)^2 = 1/25

So forth...

(2) says that m x n is less than 0.

This statement means that m cannot be equal to n for the reason I have listed above. If m is equal to n, then mn must be 0 or a positive number.

Let me ask you this question. Can you come up with two numbers that are equal, and when you multiply them, the result is less than 0?

If no, then statement (2) alone is enough to answer this question.

Yep.

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phoenixhazard: Senior | Next Rank: 100 Posts; Posts: 41; Joined: Thu Oct 14, 2010 1:21 pm

by phoenixhazard » Tue Oct 26, 2010 6:45 am

uwhusky wrote:If you square a number, any number, the result has to be a positive number or 0.

0^2 = 0

5^2 = 25

(1/5)^2 = 1/25

So forth...

(2) says that m x n is less than 0.

This statement means that m cannot be equal to n for the reason I have listed above. If m is equal to n, then mn must be 0 or a positive number.

Let me ask you this question. Can you come up with two numbers that are equal, and when you multiply them, the result is less than 0?

If no, then statement (2) alone is enough to answer this question.

I was thinking this way:
m = 3, n = 2; both numbers are NOT equal but their product is greater than 0
m = 2, n = 2; both numbers are equal but their product is greater than 0

I just realized that all you have to use is mn < 0 as that statement has to be true. I was thinking more along the lines of mn <0 is just a formula you would use for any set of #s, which then it wouldn't always tell you if the 2 #s are the same. But if mn<0 HAS to be true then there is no way possible that the 2 numbers are equal. Thanks

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