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Math Expert V
Joined: 02 Sep 2009
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Two points, N and Q (not shown), lie to the right of point M on line ℓ  [#permalink]

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76 00:00

Difficulty:   55% (hard)

Question Stats: 66% (02:01) correct 34% (02:08) wrong based on 2134 sessions

### HideShow timer Statistics 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.

Kudos for a correct solution.

Attachment: 2015-10-26_2043.png [ 955 Bytes | Viewed 31607 times ]

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Re: Two points, N and Q (not shown), lie to the right of point M on line ℓ  [#permalink]

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Bunuel wrote: 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.

Kudos for a correct solution.

Attachment:
2015-10-26_2043.png

(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
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Re: Two points, N and Q (not shown), lie to the right of point M on line ℓ  [#permalink]

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2
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.
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Re: Two points, N and Q (not shown), lie to the right of point M on line ℓ  [#permalink]

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eshan333 wrote:
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

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
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Re: Two points, N and Q (not shown), lie to the right of point M on line ℓ  [#permalink]

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eshan333 wrote:
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.

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.

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Re: Two points, N and Q (not shown), lie to the right of point M on line ℓ  [#permalink]

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camlan1990 wrote:
Bunuel wrote: 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.

Kudos for a correct solution.

Attachment:
2015-10-26_2043.png

(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

Can you please explain how you go from "2MN = 3MQ" to "2MQ + 2QN = 3MQ"? Thank you.
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Re: Two points, N and Q (not shown), lie to the right of point M on line ℓ  [#permalink]

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7
2
Samwong wrote:
camlan1990 wrote:
Bunuel wrote: 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.

Kudos for a correct solution.

Attachment:
2015-10-26_2043.png

(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

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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Re: Two points, N and Q (not shown), lie to the right of point M on line ℓ  [#permalink]

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1
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.

-> 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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Two points, N and Q (not shown), lie to the right of point M on line ℓ  [#permalink]

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3
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

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Re: Two points, N and Q (not shown), lie to the right of point M on line ℓ  [#permalink]

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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.
Math Expert V
Joined: 02 Aug 2009
Posts: 8792
Re: Two points N and Q, not shown, be to the right of point M on line l.  [#permalink]

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HolaMaven wrote:
___________________________ line l
M
Two points N and Q, not shown, be to the right of point M on line l. What is the ratio of the length of QN to the length of MQ?

I : Twice the length of MN is three times the length of MQ.
II: Point Q is between points M and N

Hi...
Required $$\frac{QN}{MQ}$$...
Statement I..
2*MN=3*MQ....
Clearly Q is between M and N..
So 2*(MQ+NQ)=3*MQ..... 2*MQ+2*NQ=3*MQ.....
2*NQ=MQ............$$\frac{NQ}{MQ}=\frac{1}{2}$$
Sufficient
Statement II..
Q is in between M and N
Nothing much..
Insufficient

A
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Re: Two points, N and Q (not shown), lie to the right of point M on line ℓ  [#permalink]

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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.
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Re: Two points, N and Q (not shown), lie to the right of point M on line ℓ  [#permalink]

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3
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.

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

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Two points, N and Q (not shown), lie to the right of point M on line ℓ  [#permalink]

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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.

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Two points, N and Q (not shown), lie to the right of point M on line ℓ  [#permalink]

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vityakim@gmail.com wrote:
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 did we get MN=1.5MQ and why MQ+NQ equals 1.5MQ and not MN ? and how we got MQ=0.5NQ Math emergency needed:) i.e. Mathergency H ----- E-------L ------- P Anybody, somebody Manager  S
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Re: Two points, N and Q (not shown), lie to the right of point M on line ℓ  [#permalink]

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1
dave13 wrote:
vityakim@gmail.com wrote:
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 did we get MN=1.5MQ and why MQ+NQ equals 1.5MQ and not MN ? and how we got MQ=0.5NQ Math emergency needed:) i.e. Mathergency H ----- E-------L ------- P Anybody, somebody 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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Two points, N and Q (not shown), lie to the right of point M on line ℓ  [#permalink]

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Statement (1)
M, N, Q <- Not possible since MN > MQ

M, Q, N
Knowing relationship between MN and MQ, you can get QN
Sufficient

(2)
M Q N

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Re: Two points, N and Q (not shown), lie to the right of point M on line ℓ  [#permalink]

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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.

statement 1 alone is sufficient.
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Re: Two points, N and Q (not shown), lie to the right of point M on line ℓ  [#permalink]

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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 ?
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Re: Two points, N and Q (not shown), lie to the right of point M on line ℓ  [#permalink]

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UNSTOPPABLE12 wrote:
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.
_________________ Re: Two points, N and Q (not shown), lie to the right of point M on line ℓ   [#permalink] 04 Feb 2020, 23:25

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