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Math Expert V
Joined: 02 Sep 2009
Posts: 55266
In the diagram below, what is the length of RS?  [#permalink]

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6 00:00

Difficulty:   75% (hard)

Question Stats: 46% (02:00) correct 54% (01:43) wrong based on 107 sessions

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In the diagram below, what is the length of RS? (1) PQ = 28 and TU = 21.
(2) PQ, RS and TU are parallel lines.

Attachment: 2017-07-18_1022.png [ 7.72 KiB | Viewed 2570 times ]

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Joined: 14 Oct 2015
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Re: In the diagram below, what is the length of RS?  [#permalink]

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Bunuel wrote:
In the diagram below, what is the length of RS? (1) PQ = 28 and TU = 21.
(2) PQ, RS and TU are parallel lines.

Attachment:
2017-07-18_1022.png

It appears to be C.

Statement 1: Insufficient.

We do not know the actual height from the base.

Statement 2: Insufficient.

We do not know lengths.

Combining, if the lines are parallel, their intersection should be the half of the average of the two lengths.
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Director  S
Joined: 21 Mar 2016
Posts: 518
Re: In the diagram below, what is the length of RS?  [#permalink]

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jedit wrote:
Bunuel wrote:
In the diagram below, what is the length of RS? (1) PQ = 28 and TU = 21.
(2) PQ, RS and TU are parallel lines.

Attachment:
2017-07-18_1022.png

It appears to be C.

Statement 1: Insufficient.

We do not know the actual height from the base.

Statement 2: Insufficient.

We do not know lengths.

Combining, if the lines are parallel, their intersection should be the half of the average of the two lengths.

to me it luks like E...
the two big triangles are similar and we will get the ratio not the absolute values,....
any help on this is appreciated..
thanks
Manager  S
Joined: 05 Dec 2016
Posts: 241
Concentration: Strategy, Finance
GMAT 1: 620 Q46 V29 Re: In the diagram below, what is the length of RS?  [#permalink]

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I presume that it's E, because from (1) + (2) we cannot deduce whether RS is the mid-section of triangles or not.
PQ/TU=4/3 hence we have 1 and 2 for RS, and it is still possible for RS to be 7 or 14.
It also can be visualized if we make it wider ot thinner the overlapping of 2 triangles PQU & TQU.
Current Student B
Joined: 06 Nov 2016
Posts: 103
Location: India
GMAT 1: 710 Q50 V36 GPA: 2.8
Re: In the diagram below, what is the length of RS?  [#permalink]

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jedit wrote:
Bunuel wrote:
In the diagram below, what is the length of RS? (1) PQ = 28 and TU = 21.
(2) PQ, RS and TU are parallel lines.

Attachment:
2017-07-18_1022.png

It appears to be C.

Statement 1: Insufficient.

We do not know the actual height from the base.

Statement 2: Insufficient.

We do not know lengths.

Combining, if the lines are parallel, their intersection should be the half of the average of the two lengths.

please explain how you came to the conclusion.
Intern  B
Joined: 09 Nov 2018
Posts: 11
Re: In the diagram below, what is the length of RS?  [#permalink]

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jedit wrote:
Bunuel wrote:
In the diagram below, what is the length of RS? (1) PQ = 28 and TU = 21.
(2) PQ, RS and TU are parallel lines.

Attachment:
2017-07-18_1022.png

It appears to be C.

Statement 1: Insufficient.

We do not know the actual height from the base.

Statement 2: Insufficient.

We do not know lengths.

Combining, if the lines are parallel, their intersection should be the half of the average of the two lengths.

Is this a theorem? Do u have any explaination?
Intern  B
Joined: 09 Nov 2018
Posts: 11
Re: In the diagram below, what is the length of RS?  [#permalink]

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sonikavadhera wrote:
jedit wrote:
Bunuel wrote:
In the diagram below, what is the length of RS? (1) PQ = 28 and TU = 21.
(2) PQ, RS and TU are parallel lines.

Attachment:
2017-07-18_1022.png

It appears to be C.

Statement 1: Insufficient.

We do not know the actual height from the base.

Statement 2: Insufficient.

We do not know lengths.

Combining, if the lines are parallel, their intersection should be the half of the average of the two lengths.

please explain how you came to the conclusion.

Were you able to find an answer to this?
Intern  B
Joined: 10 Sep 2018
Posts: 44
Re: In the diagram below, what is the length of RS?  [#permalink]

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Hmm well its a nice question,

I chose E thinking on the lines that the only way C can be the answer would be if the bigger triangles are also similar ie if PQU is similar to TQU

Stmt 1 - only gives the value of PQ and TU and tells that they are not congruent. Fair enough
Stmt 2 says - RUS is similar to PUQ and that RQS is similar to TQU . no dimensions no answer

so if statement two also means PUQ and TUQ similar then we have our answer
RS/21= RS/28

RS=1/7
i want to believe it but since i am not sure i wont advocate it and wait for some expert to comment on it
Intern  B
Joined: 28 Apr 2016
Posts: 42
Location: United States
GMAT 1: 780 Q51 V47 GPA: 3.9
Re: In the diagram below, what is the length of RS?  [#permalink]

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1
RK007 wrote:
jedit wrote:
Bunuel wrote:
In the diagram below, what is the length of RS? (1) PQ = 28 and TU = 21.
(2) PQ, RS and TU are parallel lines.

Attachment:
2017-07-18_1022.png

It appears to be C.

Statement 1: Insufficient.

We do not know the actual height from the base.

Statement 2: Insufficient.

We do not know lengths.

Combining, if the lines are parallel, their intersection should be the half of the average of the two lengths.

Is this a theorem? Do u have any explaination?

I'm not going to worry about whether this is a theorem or not, since approaching this problem from basic principles will be more relevant for the GMAT anyway.

I would start by re-drawing the diagram, and labeling the lengths of segments with variables as I have done below: Note that we are solving for c in the above diagram. Now, based on statement 2, if we see that triangle RSU is similar to triangle PQR, and triangle RSQ is similar to triangle TUQ, we can write the ratios of sides as the following equations:

$$\frac{c}{e} = \frac{a}{d+e}$$ and $$\frac{c}{d} = \frac{b}{d+e}$$

If we cross-multiply these equation we get:

$$c(d+e) = ae$$ and $$c(d+e) = bd$$

This tells us that:

$$ae=bd$$

Now, statement 1 tells us that a = 28 and b = 21, which turns the equation above into:

$$28e = 21d$$

Thus, we have the ratio of e to d, which means that we also can calculate the ratio of e to d+e. We can rearrange the equation $$c(d+e) = ae$$ to be:

$$c = a*\frac{e}{d+e}$$

Finally, since we know a = 28 and we can calculate the ratio $$\frac{e}{d+e}$$, this is sufficient to calculate c, and thus answer the question.

Please let me know if you have any questions!
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# In the diagram below, what is the length of RS?

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