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

 It is currently 20 Oct 2019, 13:17

### 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

# In the figure above, if x and y are each less than 90 and PS

Author Message
TAGS:

### Hide Tags

Manager
Joined: 25 Jul 2010
Posts: 93
In the figure above, if x and y are each less than 90 and PS  [#permalink]

### Show Tags

05 Sep 2010, 12:50
5
26
00:00

Difficulty:

5% (low)

Question Stats:

82% (01:18) correct 18% (01:38) wrong based on 466 sessions

### HideShow timer Statistics

In the figure above, if x and y are each less than 90 and PS||QR, is the length of segment PQ less than the length of segment SR ?

(1) x > y

(2) x + y > 90

Attachment:

Figure.PNG [ 5.28 KiB | Viewed 36831 times ]
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4472
Re: In the figure above, if x and y are each less than 90 and PS  [#permalink]

### Show Tags

02 Jan 2012, 16:01
26
5
Hi there. I'm happy to help with this.

So, the lines PS & RQ are parallel, angles X & Y are each less than 90 degrees.

Statement #1 tells us angle X is greater than angle Y. In the diagram, I showed an exaggerated example of this ---- if Y is a much smaller angle, it follows a less steep diagonal, which travels a longer distance between the two lines, as shown in the diagram. Therefore, if (angle X) > (angle Y), then segment RS is longer than segment PQ. Statement #1 is sufficient.

(Notice that this logic depends on both angles staying less than 90 degrees. If X had a value greater than 90 degrees, it would start making a longer, less steep, line segment on the left side.)

Statement #2 says only that the sum (x + y) is greater than 90. The trouble with that is: it doesn't give us any way to distinguish x vs. y --- either one could be much bigger than the other, or they both could be equal. No way to distinguish x vs. y ==> no way to distinguish RS vs. PQ. Insufficient.

Does that make sense? Let me know if you have any questions on that.

Mike
Attachments

parallel lines, unequal angles.PNG [ 7.81 KiB | Viewed 36823 times ]

_________________
Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
##### General Discussion
Math Expert
Joined: 02 Sep 2009
Posts: 58434
Re: In the figure above, if x and y are each less than 90 and PS  [#permalink]

### Show Tags

05 Sep 2010, 13:15
9
12

In the figure above, if x and y are each less than 90 and PS||QR, is the length of segment PQ less than the length of segment SR ?

(1) x>y --> if the angles x and y were equal then the length of segment PQ would be equal to the length of segment SR (as PS||QR). Now, as x>y it means that point R is to the left of the position it would be if x and y were equal (previous case), or in other words, we should drag point R to the left to the position of R2 to make angle y less than x, thus making the length of segment SR bigger than the length of segment PQ. So as x>y than SR>PQ. Sufficient.

(2) x+y>90 --> clearly insufficient: if $$x=y=60$$ then the length of segment PQ would be equal to the length of segment SR but if $$x=60$$ and $$y=45$$ then the length of segment PQ would be less than the length of segment SR. Not sufficient.

Attachment:

untitled.PNG [ 38.85 KiB | Viewed 38870 times ]

_________________
Manager
Joined: 15 Apr 2010
Posts: 105
Re: In the figure above, if x and y are each less than 90 and PS  [#permalink]

### Show Tags

07 Sep 2010, 10:56
1
Exactly the explanation given by Bunuel... +1 for A
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9704
Location: Pune, India
Re: In the figure above, if x and y are each less than 90 and PS  [#permalink]

### Show Tags

08 Dec 2010, 18:02
15
2
MisterEko wrote:
Guys,
as my G-day is approaching, I am putting more and more effort in improving my Quant. However, I seem to have troubles with some basic concepts. Below are the 5 questions which I know have simple explanations but are for some reason difficult for me to understand. If you can explain the solutions for any of them, I would greatly appreciate it! Cheers!

Note that the shortest distance between two parallel lines is the perpendicular distance. As the angle keeps decreasing, the length of the line keeps increasing. So if we know that x>y, then PQ < SR. Stmnt 1 Sufficient.

Attachment:

Ques1.jpg [ 2.61 KiB | Viewed 37296 times ]

Since statement 2 doesn't give any information about relative size of x and y, nothing can be said about PQ and SR. Not sufficient.

_________________
Karishma
Veritas Prep GMAT Instructor

Manager
Joined: 10 Nov 2010
Posts: 122
Re: In the figure above, if x and y are each less than 90 and PS  [#permalink]

### Show Tags

14 Mar 2011, 23:25
If the statement didn't contain the restriction about x and y(both are less than 90),then answer would have been "E".
Am I correct in this assessment?
Math Expert
Joined: 02 Sep 2009
Posts: 58434
In the figure above, if x and y are each less than 90 and PS  [#permalink]

### Show Tags

15 Mar 2011, 04:07
4
1
vjsharma25 wrote:
If the statement didn't contain the restriction about x and y(both are less than 90),then answer would have been "E".
Am I correct in this assessment?

Yes, if we were not given that x and y are each less than 90 then PQ and SR could be mirror images of each other and thus have equal length.
Attachments

untitled.PNG [ 38.85 KiB | Viewed 5989 times ]

_________________
Intern
Joined: 27 Dec 2014
Posts: 4
Re: In the figure above, if x and y are each less than 90 and PS  [#permalink]

### Show Tags

06 Feb 2015, 02:58
Hi guys,

I went through the task and argued similar we would have argued in a triangle.
The side which is opposite the smaller angle is also the smaller side. (in a triangle)
But here in a polygon this argumentation doesnt hold.

Because I thought SR is smaller than PQ because angle x is smaller than (180-y).

After reading your explanations I totally get your point, but I dont understand why we can't argue the same way we do with
triangles.

Thanks !
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9704
Location: Pune, India
Re: In the figure above, if x and y are each less than 90 and PS  [#permalink]

### Show Tags

06 Feb 2015, 04:38
1
gmatstrong wrote:
Hi guys,

I went through the task and argued similar we would have argued in a triangle.
The side which is opposite the smaller angle is also the smaller side. (in a triangle)
But here in a polygon this argumentation doesnt hold.

Because I thought SR is smaller than PQ because angle x is smaller than (180-y).

After reading your explanations I totally get your point, but I dont understand why we can't argue the same way we do with
triangles.

Thanks !

First of all, think, which side of the quadrilateral is the opposite side to any given angle. Look at the diagram, the angle has 2 sides opposite to it (which don't form the angle). You can make one of the opposite sides smaller and the other greater at whim. So there is no defined relation between the angle and the opposite sides.

Attachment:

Ques3.jpg [ 4.6 KiB | Viewed 29775 times ]

_________________
Karishma
Veritas Prep GMAT Instructor

Intern
Joined: 02 Oct 2017
Posts: 20
Re: In the figure above, if x and y are each less than 90 and PS  [#permalink]

### Show Tags

16 Jan 2018, 22:41
VeritasPrepKarishma Can you elaborate this explanation from scratch. Not able to understand what all rules it is using concerning the parallel lines given. Cannot understand Bunuel's post.

Thanks!

ucb2k7

VeritasPrepKarishma wrote:
MisterEko wrote:
Guys,
as my G-day is approaching, I am putting more and more effort in improving my Quant. However, I seem to have troubles with some basic concepts. Below are the 5 questions which I know have simple explanations but are for some reason difficult for me to understand. If you can explain the solutions for any of them, I would greatly appreciate it! Cheers! :war

Note that the shortest distance between two parallel lines is the perpendicular distance. As the angle keeps decreasing, the length of the line keeps increasing. So if we know that x>y, then PQ < SR. Stmnt 1 Sufficient.

Attachment:
Ques1.jpg

Since statement 2 doesn't give any information about relative size of x and y, nothing can be said about PQ and SR. Not sufficient.

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9704
Location: Pune, India
Re: In the figure above, if x and y are each less than 90 and PS  [#permalink]

### Show Tags

18 Jan 2018, 08:28
1
ucb2k7 wrote:
VeritasPrepKarishma Can you elaborate this explanation from scratch. Not able to understand what all rules it is using concerning the parallel lines given. Cannot understand Bunuel's post.

Thanks!

ucb2k7

VeritasPrepKarishma wrote:
MisterEko wrote:
Guys,
as my G-day is approaching, I am putting more and more effort in improving my Quant. However, I seem to have troubles with some basic concepts. Below are the 5 questions which I know have simple explanations but are for some reason difficult for me to understand. If you can explain the solutions for any of them, I would greatly appreciate it! Cheers! :war

Note that the shortest distance between two parallel lines is the perpendicular distance. As the angle keeps decreasing, the length of the line keeps increasing. So if we know that x>y, then PQ < SR. Stmnt 1 Sufficient.

Attachment:
Ques1.jpg

Since statement 2 doesn't give any information about relative size of x and y, nothing can be said about PQ and SR. Not sufficient.

You are given that PS is parallel to QR. The shortest distance between these two lines will be the perpendicular distance as shown by the solid line between them in the diagram above (https://gmatclub.com/forum/in-the-figur ... ml#p829762)

Now as you turn the line towards the right (as shown by dotted lines above) the angle at the base keeps reducing. Consider two such lines PQ and SR. If the angle x is greater than angle y, it means PQ is less tilted than SR. So PQ is closer to the perpendicular line than is SR. So PQ is shorter than SR.

Does this help?
_________________
Karishma
Veritas Prep GMAT Instructor

Non-Human User
Joined: 09 Sep 2013
Posts: 13316

### Show Tags

04 Oct 2019, 23:48
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: DS: Lines (GMATPrep)   [#permalink] 04 Oct 2019, 23:48
Display posts from previous: Sort by