GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 16 Dec 2018, 07:43

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

## Events & Promotions

###### Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### Free GMAT Prep Hour

December 16, 2018

December 16, 2018

03:00 PM EST

04:00 PM EST

Strategies and techniques for approaching featured GMAT topics
• ### FREE Quant Workshop by e-GMAT!

December 16, 2018

December 16, 2018

07:00 AM PST

09:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 51227
In the diagram below, what is the length of RS?  [#permalink]

### Show Tags

17 Jul 2017, 22:25
1
6
00:00

Difficulty:

75% (hard)

Question Stats:

45% (02:38) correct 55% (01:21) wrong based on 93 sessions

### HideShow timer Statistics

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 2163 times ]

_________________
Senior Manager
Joined: 14 Oct 2015
Posts: 250
GPA: 3.57
Re: In the diagram below, what is the length of RS?  [#permalink]

### Show Tags

18 Jul 2017, 00:50
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.
_________________

Please hit Kudos if this post helped you inch closer to your GMAT goal.
Procrastination is the termite constantly trying to eat your GMAT tree from the inside.
There is one fix to every problem, working harder!

Director
Joined: 21 Mar 2016
Posts: 521
Re: In the diagram below, what is the length of RS?  [#permalink]

### Show Tags

18 Jul 2017, 21:21
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
Manager
Joined: 05 Dec 2016
Posts: 244
Concentration: Strategy, Finance
GMAT 1: 620 Q46 V29
Re: In the diagram below, what is the length of RS?  [#permalink]

### Show Tags

18 Jul 2017, 22:51
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.
Manager
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]

### Show Tags

25 Jul 2017, 11:30
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: 10
Re: In the diagram below, what is the length of RS?  [#permalink]

### Show Tags

02 Dec 2018, 08:06
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: 10
Re: In the diagram below, what is the length of RS?  [#permalink]

### Show Tags

02 Dec 2018, 08:06
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: 45
Re: In the diagram below, what is the length of RS?  [#permalink]

### Show Tags

02 Dec 2018, 10:22
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
Intern
Joined: 28 Apr 2016
Posts: 41
Location: United States
GMAT 1: 780 Q51 V47
GPA: 3.9
Re: In the diagram below, what is the length of RS?  [#permalink]

### Show Tags

02 Dec 2018, 10:40
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!
_________________

Online GMAT tutor with a 780 GMAT score. Harvard graduate.

Re: In the diagram below, what is the length of RS? &nbs [#permalink] 02 Dec 2018, 10:40
Display posts from previous: Sort by