xy x²y ask y

Question

|m - n| > ||m| - |n|| ?

(1) m + n > 0
(2) m - n > 0

EMPOWERgmatRichC · Answer

Hi littlegirl,

You can answer this DS question by TESTing VALUES, although you could approach it with Number Properties and Algebra too.

We're asked if |M - N| > |M| - |N|. This is a YES/NO question.

Fact 1: M + N > 0

IF...
M = 1
N = 0
|1-0| is NOT > |1| - |0| and the answer to the question is NO.

IF...
M = 2
N = -1
|2 - (-1)| IS > |2| - |-1| and the answer to the question is YES.
Fact 1 is INSUFFICIENT

Fact 2: M - N > 0

The two TESTs that we used in Fact 1 also "fit" Fact 2...

IF...
M = 1
N = 0
|1-0| is NOT > |1| - |0| and the answer to the question is NO.

IF...
M = 2
N = -1
|2 - (-1)| IS > |2| - |-1| and the answer to the question is YES.
Fact 2 is INSUFFICIENT

Combined, we have the same two TESTs with different results (a NO and a YES answer).
Combined, INSUFFICIENT.

Final Answer:  E

GMAT assassins aren't born, they're made,
Rich

Bunuel · Answer

Is |m - n| > ||m| - |n|| ?

Square both sides (note that we can safely do that since both sides of the inequality are non-negative):

Is  m^2 -2mn + n^2 > m^2 - 2|mn| + n^2 ?
Is  |mn| > mn ?

So, the questions basically asks whether mn is negative.

(1) m + n > 0. Not sufficient.
(2) m - n > 0. Not sufficient.

(1)+(2) From above we can get that m is positive but n can be positive as well as negative, thus mn also can be positive as well as negative. Not sufficient.

Answer: E.

Hope it's clear.

cutegirlsimran · Answer

Alternate solution
Given equation
|m - n| > ||m| - |n|| 
must be true only when we have m as +ve and n as -ve.

So equation 1 not sufficient 
and equation 2 not sufficient

Together 1 and 2 
adding 1 and 2 we get 
2m > 0 so m is +ve 
but we are not clear about n

So Answer is E

Bunuel 
I understand the solution provided but as a alternative do we do this question in this way
is the solution I provided is correct?

Posted from my mobile device

littlegirl · Answer

Thank  rich  and  Bunuel  so much

gmatkiller88 · Answer

Hi Bunuel,
From 1+2 statements together, If we add the statements then n gets cancelled and we know that m > 0 and if we subtract the statements m will get cancelled and we can say that n > 0....hence won't these statements together tell us that m and n both are greater than 0??

Could you please help me understand where am I going wrong here? Many thanks.

Bunuel · Answer

For two inequalities, you can only apply subtraction when their signs are in the opposite directions: If a>b and c and < ) --> a-c>b-d (take the sign of the inequality you subtract from). Example: 3<4 and 5>1 --> 3-5<4-1 . So, we cannot subtract m - n > 0 from m + n > 0.. For more check: inequalities-tips-and-hints-175001.html

gmatkiller88 · Answer

oh ok. Got it....thanks a ton for your quick response and the link....Appreciate...

Temurkhon · Answer

The property is:

|m|-|n|<=|m-n|, if m and n have one sign both sides equal, but if different they are not equal.

So question is whether m and n have one sign or not

St.1 m+n>0, so m=1, n=3 or m=5, n=-2. Both scenario possible. INSUFF

St.2 m-n>0, so m=3, n=1 or m=3, n=-2. Again both scenario possible. INSUFF

St.1+St.2. Does not make clear, we still have both scenario possible. INSUFF

E

littlegirl · Answer

xy> x²y ask y <0?

(1) x> y
(2) x> 1

EMPOWERgmatRichC · Answer

Hi littlegirl,

This question can be solved with a combination of Number Properties and TESTing VALUES. You will have to be thorough with your thinking to get the correct answer.

We're told that (X)(Y) > (X^2)(Y). We're asked if Y < 0. This is a YES/NO question.

First off, from the given inequality, neither X nor Y can equal 0.

Fact 1: X > Y

IF....
X = 2
Y = -1
-2 > -4
The answer to the question is YES.

IF...
X = 1/2
Y = 1/3
1/6 > 1/12
The answer to the question is NO
Fact 1 is INSUFFICIENT

Fact 2: X > 1

Since X > 1.....X^2 will always be > X
Using the original inequality, we have...
(X)(Y) > (Bigger than X)(Y)

With this restriction, Y CANNOT be positive. Since we also know that Y CANNOT be 0, the only option that's left is for Y to be NEGATIVE EVERY TIME....

eg
IF....
X = 2
Y = -1
-2 > -4
The answer to the question is YES....and is ALWAYS YES.
Fact 2 is SUFFICIENT

Final Answer:  B

GMAT assassins aren't born, they're made,
Rich

masoomdon · Answer

i feel testing values always end up being more time consuming so here's a short way to solve this one.
we have, xy>x2y
rearranging we get,
x2y-xy<0
xy(x-1)<0......(1)
Statement 1 : x>y . it tells us nothing about th sign of x-1 or xy , so INSUFFICIENT
options left : B,C,E
Statement 2 : x>1. so (x-1) > 0 also x>0
hence y <0
SUFFICIENT

iamdp · Answer

Hi

xy - x^2y > 0
xy(1-x) > 0

Now two possible solutions are dr

xy>0 OR 1-x>0 ie x<1

Now from statement one we cannot tell whether y<0

From statement two we know x>1. Therefore solution x<1 is ruled out.
Therefore xy>0 remains

Now either xy are positive of negative but as givwn in statement two x>1 . Therefore y>0
Therefore we get a definite NO

littlegirl · Answer

Thank rich and other friends :-D

EMPOWERgmatRichC · Answer

Hi masoomdon,

One of the great aspects of the GMAT is that the questions are usually designed so that they can be solved in a variety of ways (in that way, you don't have to be a 'math expert' to score at a high level in the Quant section). If you're comfortable doing basic Arithmetic, then TESTing VALUES can be a remarkably straight-forward way to get to the correct answer on most Quant questions. I've worked with Test Takers who were "average" in every conceivable way when they began - but they were able to hit Q49+ on Test Day because they trained and got really good at TESTing VALUES. If you're not practicing IT now though (and building up that skill), then you won't be ready to use it on Test Day (when you will likely *need* it).

For Test Takers who are 'stuck' at a particular scoring level in the Quant and/or have pacing problems in the Quant, the solution almost always involves working on your TESTing VALUES skills.

GMAT assassins aren't born, they're made,
Rich

xy> x²y ask y <0?

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