data sufficiency problem

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nickhar130: Senior | Next Rank: 100 Posts; Posts: 44; Joined: Wed Nov 03, 2010 10:07 am; Thanked: 1 times

by nickhar130 » Fri Jan 07, 2011 3:37 pm

data sufficiency question

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

Please explain step by step and some rules I should know.

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Source: Beat The GMAT — Data Sufficiency | Fri Jan 07, 2011 3:37 pm

nickhar130: Senior | Next Rank: 100 Posts; Posts: 44; Joined: Wed Nov 03, 2010 10:07 am; Thanked: 1 times

by nickhar130 » Fri Jan 07, 2011 3:38 pm

sorry also below

1) x > y
2) x + y > 90

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anshumishra: Legendary Member; Posts: 543; Joined: Tue Jun 15, 2010 7:01 pmFollowed by: 3 members; Thanked: 147 times

by anshumishra » Fri Jan 07, 2011 4:10 pm

nickhar130 wrote:sorry also below

1) x > y
2) x + y > 90

Question : Is PQ < SR ?

Statement 1:
x > y
That means PQ < SR -> Sufficient (Think about x being close to 90 degree and SR being 30 degree, SR will be longer. If you want to prove you can do that as well, just draw a perpendicular line from point p and s to the parallel line below it. Then you can deduce a relationship among, x, PQ, PS and the perpendicular drawn).

Statement 2:

x+y > 90

Not sufficient (As in this case either x > y or y> x, and they affect the length of PQ and SR.

Hence, A

Thanks
Anshu

(Every mistake is a lesson learned )

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Thouraya: Master | Next Rank: 500 Posts; Posts: 112; Joined: Wed Jan 20, 2010 5:46 am; Thanked: 1 times

by Thouraya » Sat Apr 09, 2011 2:14 pm

Can someone please explain the rationale behind this problem? I didn't really understand the relation between the length of PS & QR and the measure of the angles...Thanks!

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sourabh33: Master | Next Rank: 500 Posts; Posts: 135; Joined: Tue Mar 22, 2011 12:01 pmFollowed by: 3 members; Thanked: 21 times; GMAT Score:720

by sourabh33 » Sat Apr 09, 2011 4:27 pm

Thouraya wrote:Can someone please explain the rationale behind this problem? I didn't really understand the relation between the length of PS & QR and the measure of the angles...Thanks!

Given in the Question

1. Line PS || Line QR
2. Line PQ forms angle x with line QR
3. Line SR forms angle y with line QR
4. X and y are each < 90
Question asked - Is Length of PQ smaller than SR i.e is PQ<SR

Now

Option A
x>y
If you try to visualize the change in length of line with respect to change in angle x, you could say that as the vale of x increases the length of PQ decreases (Since it is given x<90)

So if X>Y than PQ<SR, hence option 1 alone is sufficient

Evaluating Option B
since x+y>90, and considering x & y each<90, x could be greater, equal, or smaller than y....hence Option 2 not sufficient

therefore Ans is A

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Sun Apr 10, 2011 9:18 pm

nickhar130 wrote:

data sufficiency question

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

Please explain step by step and some rules I should know.

Sometimes it helps to think of real world scenarios to help you visualize what's going on in a question.

We know that the top and bottom lines are parallel, but don't know the relationship between the vertical lines (PQ and SR).

Picture a street with houses on both sides. PS is the north sidewalk and QR is the south sidewalk.

You want to cross the street. What's the shortest distance you can take? Directly across. So, if x or y were 90 degrees, we'd create the shortest possible line.

The more "diagonal" you make your crossing, the greater the distance you have to travel. If you cross from your house to the house directly opposite you, it's a short trip; if you cross from your house to the one across and 10 houses down (in a straight line), it's a much longer trip.

In geometric terms, the further the angle is away from 90 degrees, the longer the journey.

With that in mind, here's what the question is really asking:

"Is x greater than y?"

Accordingly, if we know the relationship between x and y, we can answer the question. (1) clearly gives us the relationship and (2) doesn't, so the correct answer is (A).

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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bubbliiiiiiii: Legendary Member; Posts: 979; Joined: Tue Apr 14, 2009 1:38 amFollowed by: 12 members; Location: Hyderabad, India; Thanked: 49 times; GMAT Score:700

by bubbliiiiiiii » Sun Apr 10, 2011 11:41 pm

Option 1: x>y.

if x =60; y=30, PQ < SR
if x =170 y =30 PQ > SR INSUFFICIENT.

Options 2: x+y > 90

if x = 11; y=80, PQ > RS
if x = 80; y=11, PQ < RS INSUFFICIENT.

Option 1 and 2, together: i.e., x>y and x+y>90

if x = 80; y=11, PQ < RS
if x = 170; y=30 , PQ > RS INSUFFICIENT.

Stuart, Could you please correct my approach and guide me where am I wrong? As per the approach given above I am getting E.

Regards,

Pranay

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Mon Apr 11, 2011 1:06 am

bubbliiiiiiii wrote:Option 1: x>y.

if x =60; y=30, PQ < SR
if x =170 y =30 PQ > SR INSUFFICIENT.

Options 2: x+y > 90

if x = 11; y=80, PQ > RS
if x = 80; y=11, PQ < RS INSUFFICIENT.

Option 1 and 2, together: i.e., x>y and x+y>90

if x = 80; y=11, PQ < RS
if x = 170; y=30 , PQ > RS INSUFFICIENT.

Stuart, Could you please correct my approach and guide me where am I wrong? As per the approach given above I am getting E.

Your mistake is a simple one - you didn't take into account the condition set in the question stem:

In the figure above, if x & y are each less than 90 and...

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bubbliiiiiiii: Legendary Member; Posts: 979; Joined: Tue Apr 14, 2009 1:38 amFollowed by: 12 members; Location: Hyderabad, India; Thanked: 49 times; GMAT Score:700

by bubbliiiiiiii » Mon Apr 11, 2011 1:23 am

Thanks for pointing that out.

Regards,

Pranay

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