(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

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

Can you please explain how you go from "2MN = 3MQ" to "2MQ + 2QN = 3MQ"? Thank you.

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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Image
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.


My 2 cents.
I think the difficulty of this question comes from uniqueness.
We can solve this with simple algebra.

From con 1, we learn that
1) MQ + NQ = MN AND
2) 2MN = 3MQ

From here we can get MN
MN=1.5MQ, now plug it back to 1)

MQ+NQ=1.5MQ
MQ=0.5NQ and this is sufficient, hence A.

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

Given that N and Q are to the right of M, we can either have M---N---Q or M---Q----N. say MN=a, MQ= b and QM=c

Statement 1 says 2MN = 3MQ, i.e 2a=3b, therefore a > b and our line is M---Q----N. By observation, the line may look 1---3---4. This gives us 1/2 as the ratio of QN TO MQ.---Sufficient

Statement 1 says M---Q----N, we already know this somewhat in the prompt and its is not sufficient by itself without the info given in statement 1, for instance.

Hence the answer is A.

From statement 1:
\(2*MN = 3*MQ\) --> \(MN = \frac{3*MQ}{2}\) --> \(MN= 1.5* MQ\) (I)
Since Q is between M and N, we have \(MN = MQ+QN\) (II)
Combine equations (I) and (II)
\(1.5*MQ = MQ+QN\) --> \(1.5*MQ-MQ = QN\) --> \(0.5*MQ=QN\)

Hope it's clear.
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OA explanation is pretty straight forward for this question:

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

(1) Given that twice the length of MN is
3 times the length of MQ , it follows that
the points are ordered from left to right as
M , Q , and N . Thus, letting MQ = x and
QN = y , it is given that 2(x + y) = 3x and
the value of y
x is to be determined. The given
equation can be rewritten as 2 x + 2 y = 3 x , or
2y = x , or y/x=1/2= ; SUFFICIENT.
(2) Given that Q is between M and N , the ratio
of QN to MQ can be close to zero (if Q and
N are close together and both far from M )
and the ratio of QN to MQ can be large (if
M and Q are close together and both far
from N ); NOT sufficient.

The correct answer is A;
statement 1 alone is sufficient.

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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