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# In the diagram below, what is the length of RS?

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

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17 Jul 2017, 23:25
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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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Re: In the diagram below, what is the length of RS?  [#permalink]

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18 Jul 2017, 01:50
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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Re: In the diagram below, what is the length of RS?  [#permalink]

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18 Jul 2017, 22:21
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
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Re: In the diagram below, what is the length of RS?  [#permalink]

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18 Jul 2017, 23:51
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.
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Re: In the diagram below, what is the length of RS?  [#permalink]

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25 Jul 2017, 12:30
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
Joined: 09 Nov 2018
Posts: 11
Re: In the diagram below, what is the length of RS?  [#permalink]

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02 Dec 2018, 09:06
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
Joined: 09 Nov 2018
Posts: 11
Re: In the diagram below, what is the length of RS?  [#permalink]

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02 Dec 2018, 09:06
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
Joined: 10 Sep 2018
Posts: 44
Re: In the diagram below, what is the length of RS?  [#permalink]

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02 Dec 2018, 11:22
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
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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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02 Dec 2018, 11:40
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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Re: In the diagram below, what is the length of RS?   [#permalink] 02 Dec 2018, 11:40
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