(1) Twice the length of MN is 3 times the length of MQ.
=> MN>MQ
=> Because both N, Q lie on the right of M
=> Q is between M and N

2MN = 3MQ
=> 2MQ + 2QN = 3MQ
=> MQ = 2QN
=> QN/MQ = 1/2

Sufficient

(2) Point Q is between points M and N.
Insufficient

Ans: A

Ans is C , as we do not know the exact positions of N and Q , in the question it is given that both lie to the right of M however we do not know whether N lie to the right of Q or Q lie to the right of N , so without knowing the exact position of N and Q we cannot ans the question. Therefore both statements are necessary for the conclusion.

From statement 1 we know that "Twice the length of MN is 3 times the length of MQ" -> 2MN = 3MQ it means that MN>MQ -> hence the position of Q is between M and N.
ans:A

Hi eshan333,

While you ARE correct that we don't know the exact positions of N and Q, the question does NOT ask us for them (so you have to be careful about when you choose to stop working). The prompt asks for the RATIO of two lengths, NOT the exact measure of either of them. With a bit of 'playing around' and TESTing VALUES, you might find that you change your answer.

GMAT assassins aren't born, they're made,
Rich
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Can you please explain how you go from "2MN = 3MQ" to "2MQ + 2QN = 3MQ"? Thank you.

You are given that 2MN=3MQ ---> MN=1.5MQ

Now, this should tell you that the arrangement becomes:

M-------Q-------N such that MN = MQ+QN

Again, as MN = 1.5 MQ ---> MQ+QN=1.5 MQ (as MN = MQ+QN )

Thus, you get, QN = 0.5 MQ ---> clearly you can now calculate the ratio QN/MQ . Thus this statement is sufficient.

Hope this helps.
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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Two points, N and Q (not shown), lie to the right of point M on line ℓ. What is the ratio of the length of QN to the length of MQ?

(1) Twice the length of MN is 3 times the length of MQ.
(2) Point Q is between points M and N.



------|---------------------------------- line L

M

When you modify the original condition and the question, the que is ratio of QN:MQ, which is for 1) ratio and for 2) number(equation). In a case like this, it is most likely that ratio is the answer.

In 1),

------|--------|--------------------------|----- line L

M Q N

If MQ=2d, 2MN=3*2d, MN=3d and QN=d. Therefore, the que, QN:MQ=d:2d=1:2 is derived, which is unique and sufficient.
Therefore, the answer is A.


-> Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.
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I solved this by picking numbers (I know it may look like a overkill on DS but it helped me to know the positions of N and Q )

S1:

I see 2 and 3 in the statement and pick a Number 6 for MN.
2(MN) = 3(MQ)
2(6) = 3(MQ) => MQ = 4
MQ=4 and MN=6 => QN = 2
QN/MQ = 2/4 = 1/2

S1 Suff.

S2:

Insuff. since we don't know the exact location of Q

Answer : A
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how can we know Q is between MN,
Can it be like Q-----M------------N ? then MN still longer than QM.

Hello pclawong,

It is not possible for the line to be Q-----M------------N. Here's why.

Stem says that N and Q are to the the right of M. Two cases are possible

Case 1: M-----------Q---------------N

Case 2: M-----------N---------------Q

Lets see which of the above two cases holds true

S1 says - Twice the length of MN is 3 times the length of MQ. Algebraically this means

\(2MN = 3MQ\)

\(MN = \frac{3}{2}* MQ\)

Since \(\frac{3}{2}\) is a number greater than 1, we get

\(MN > MQ\)

This clearly means the Line HAS to look like this M-------Q-----------N

Do let me know in case I was unable to give an answer.



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Hello guys ,
a prompt question does "Point Q is between points M and N" mean that QM=QN , or is Q just at a random place between M and N ?

Point Q is between points M and N does NOT mean that QM = QN. If it were so, the answer would be D, not A.
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Statement 1:
\(2(MN)=3(MQ)\)
\(\frac{2}{3}=\frac{MQ}{MN}\)

Let \(MQ=2d\) and \(MN=3d\).
The result is the following number line:
M<--2d-->Q<--d-->N

Thus:
\(\frac{QN}{MQ}=\frac{d}{2d}=\frac{1}{2}\)
SUFFICIENT.

Statement 2:
No information about any lengths.
INSUFFICIENT.


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Is it ok if, after having understood the positions of Q and N on the line and found that we had a ratio between them, I stopped?

I then looked at the statement (2) and I saw that it was superfluous.

I didn't calculate but I picked answer A. Is it a good habit?

Hi Genoa2000,

DS questions are interesting because they're built to 'test' you on a variety of skills (far more than just your 'math' skills), including organization, accuracy, attention-to-detail, thoroughness and the ability to prove that your answer is correct. DS questions also have no 'safety net' - meaning that if you make a little mistake, then you will convince yourself that one of the wrong answers is correct.

If you choose to select an answer after just reading the information in Fact 2 (and not do any work to PROVE what the correct answer is), then one of two outcomes is likely... You might understand the information perfectly and have the correct answer.... OR.... you have made some type of silly/little mistake and you are about to let some easy points slip away. Doing work "in your head" is the WORST way to approach a GMAT question - so the more often you take that approach, the more likely you lose some 'gettable' points on Test Day.

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

Question Stem Analysis:

We need to determine the value of QN/MQ. We can let MQ = x, QN = y. If Q is between M and N, then MN = x + y. If N is between M and Q, then MN = x - y. In any case, we need to determine the value of y/x.

Statement One Alone:

With statement one, we see that N is further to the right of M than Q is. Therefore, Q is between M and N. In that case, MN = x + y and MQ = x, and we have:

2(x + y) = 3x

2x + 2y = 3x

2y = x

y/x = 1/2

Statement one alone is sufficient.

Statement Two Alone:

Knowing only that Q is between M and N is not sufficient to answer the question. For example, if Q is exactly the midpoint of M and N, then the ratio QN/MQ = 1. However, if Q is closer to M than it is to N, then the ratio is greater than 1.

Answer: A
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Video solution from Quant Reasoning:
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_________________

Answer: Option A

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