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1/m - 1/n =6

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Source: — Data Sufficiency |
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by killer1387 » Sat Mar 17, 2012 3:23 am
pappueshwar wrote:If mn != 0, is 1/m - 1/n =6 ?

1. n - m = 6mn
2. n = 4m

OA IS A WHY IS STMNT 2 INCORRECT?
1) SUFFICIENT

YES
2) INSUFFICIENT

u cant say anything about the
1/m - 1/n =3m/4m^2 we dont know "m"

hence A
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by pappueshwar » Sat Mar 17, 2012 3:49 am
Hey,

sorry i did not understand the way u solved.

i did it this way:

1/m - 1/n = 6
substitute the value of n=4m and u get M = 1/8 from which 1/n can be found .
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by Anurag@Gurome » Sat Mar 17, 2012 4:03 am
pappueshwar wrote:If mn != 0, is 1/m - 1/n =6 ?

1. n - m = 6mn
2. n = 4m

OA IS A WHY IS STMNT 2 INCORRECT?
(1) n - m = 6mn
Dividing both sides by mn, we get,
n/mn - m/mn = 6mn/mn
1/m - 1/n = 6; SUFFICIENT.

(2) n = 4m
1/m - 1/n = 1/m - 1/4m = 4/4m - 1/4m = 3/4m; NOT sufficient.

The correct answer is A.
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by GMATGuruNY » Sat Mar 17, 2012 4:03 am
pappueshwar wrote:If mn != 0, is 1/m - 1/n =6 ?

1. n - m = 6mn
2. n = 4m

OA IS A WHY IS STMNT 2 INCORRECT?
Rephrase the question:
1/m - 1/n = 6
n/(mn) - m/(mn) = 6
(n-m)/mn = 6.

Question rephrased: Does (n-m)/mn = 6?

Statement 1: n - m = 6mn
Thus, (n-m)/mn = 6.
SUFFICIENT.

Statement 2: n = 4m.
Substituting n=4m into 1/m - 1/n = 6, we get:
1/m - 1/(4m) = 6
4/(4m) - 1/(4m) = 6
3/(4m) = 6
3 = 24m
m = 3/24 = 1/8, implying that n = 4/8 = 1/2.
Thus, if m=1/8 and n=1/2, then 1/m - 1/n = 6.
But if m and n are OTHER VALUES -- if m=1 and n=4, for example -- then 1/m - 1/n ≠ 6.
INSUFFICIENT.

The correct answer is A.
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by [email protected] » Sat Mar 17, 2012 4:11 am
mn != 0

The solution is very well known but what does the above statement mean. there is no factorial (positive number) that is equal to 0.

Even 0! is 1 and not 0.

So could anybody explain the above statement.
If we ignore that statement, we get the answer as A. The answer might change if that statement does mean something...

Anurag! what does that statement mean really...
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by [email protected] » Sat Mar 17, 2012 4:33 am
I very well understood that why Anurag said that the answer is A and not D.

I will try to explain to you the statement 2.

Lets assume that something is given in statement 2: When something is given, either it will prove that the equation 1/m - 1/n = 6 or it will not. But if it does both then the statement is insufficient alone.

When you put in different values of n and m, you get both the answers.

Do not try to put the equation n = m in the original equation otherwise it will give the answer that we want the equation to prove that 1/m - 1/n = 6.

The reality is that no values of m and n are given and so we have to put in. And when we put in the same values in the main equation we get different answers.

Eg: When I put n = 1 and m =2 I get

1/2 - 1 = - 1/2 and not 6

Now when I put the values as m = 1/8 and n = 1/2, I get...

8 - 2 = 6. It does prove to be yes...



Hence not sufficient... This was a very simple but a very tricky question... Even I slipped in between the two equations but he answer is only A and not D....


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by Anurag@Gurome » Sat Mar 17, 2012 4:36 am
[email protected] wrote:mn != 0

The solution is very well known but what does the above statement mean. there is no factorial (positive number) that is equal to 0.

Even 0! is 1 and not 0.

So could anybody explain the above statement.
If we ignore that statement, we get the answer as A. The answer might change if that statement does mean something...

Anurag! what does that statement mean really...
It is actually mn is not equal to zero, and not mn! = 0

I hope that helps.
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by [email protected] » Sat Mar 17, 2012 4:44 am
Thanks Anurag, for that correction... Also could please tell me whether my explanation is correct or no...

Really worked hard on this one...

Even I felt the answer to be D but really something was not feeling right when I solved the equations...

please help...
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by tomada » Sat Mar 17, 2012 11:04 am
Hi Amit,

I think that excellent explanations have already been given, but I like to throw in my 2 cents (I guess we're near a dollar now...)

I think we all agree that Statement (1) is sufficient, so I won't bother with that.

Statement (2) says that n=4m.

Question: Is knowing that n=4m enough to prove that, without exception, 1/m - 1/n = 6 ?

So, we substituted '4m' for 'n', and the question becomes:

Can we prove,without exception, that 1/m - 1/(4m) = 6?

You then showed that this equation is true when m=1/8.
However, that is the only value for 'm', which makes the equation true.

Since any value of 'm' other than 1/8 would make the equation false, we can't say that Statement (2) is sufficient.



[email protected] wrote:Thanks Anurag, for that correction... Also could please tell me whether my explanation is correct or no...

Really worked hard on this one...

Even I felt the answer to be D but really something was not feeling right when I solved the equations...

please help...
I'm really old, but I'll never be too old to become more educated.
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