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GMATPrep Test 1 - Geometry - Triangles

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by citystatekate » Mon Jul 19, 2010 6:34 pm
Oh geometry....I've stared at this for a really long time and still can't figure it out...

Image

In the figure shown, the measure of angle PRS is how many degrees greater than the measure of angle PQR?

(1) The measure of angle QPR is 30 degrees.
(2) The sum of the measures of angles PQR and PRQ is 150 degrees.

I understand the statements are saying the same thing, so it's got to be D or E. OA is D. Why?
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Source: — Data Sufficiency |

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by Rahul@gurome » Mon Jul 19, 2010 6:55 pm
citystatekate wrote:Oh geometry....I've stared at this for a really long time and still can't figure it out...

Image

In the figure shown, the measure of angle PRS is how many degrees greater than the measure of angle PQR?

(1) The measure of angle QPR is 30 degrees.
(2) The sum of the measures of angles PQR and PRQ is 150 degrees.

I understand the statements are saying the same thing, so it's got to be D or E. OA is D. Why?
(1) angle QPR = angle SPQ - angle SPR = 30º

Now in two triangles PQS and PRS one angle is 90 implies that sum of other two angles would also be 90º.

angle SQP + angle SPQ = 90º
angle SPR + angle SRP = 90º

Increase in one of the angles would decrease the other angle by same degree. Therefore, the difference among the angles should be 30º.
So, (1) is SUFFICIENT.

(2) Same explanation as above. So, (2) is SUFFICIENT.

The correct answer is (D).
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by citystatekate » Mon Jul 19, 2010 7:52 pm
Thanks! Based on the question I immediately thought this required finding specific values for each angle, but this makes more sense (and requires less work! :) )
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by aloneontheedge » Tue Jul 20, 2010 1:22 am
citystatekate wrote:Oh geometry....I've stared at this for a really long time and still can't figure it out...

Image

In the figure shown, the measure of angle PRS is how many degrees greater than the measure of angle PQR?

(1) The measure of angle QPR is 30 degrees.
(2) The sum of the measures of angles PQR and PRQ is 150 degrees.

I understand the statements are saying the same thing, so it's got to be D or E. OA is D. Why?
Other way would be to create a rectangle by extending point Q horizontally and P vertically.
then line PQ acts as a transversal line cutting 2 parallel lines.
Using this All angles can be found.

2) Stmnt 2 is same as 1 in which QPR wil be again 30
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by outreach » Tue Jul 20, 2010 7:32 am
angle PRS = angle QPR + angle PQR (exterior angle of a triangle is equal to sum of two interior angles)
PRS - PQR = QPR = 30.
(1) is sufficient.
(2) same as (1)
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by GMATGuruNY » Tue Jul 20, 2010 11:19 am
A very useful approach when a DS question asks for the value of an angle (or, in this case, the difference between 2 angles):

Plug in twice, following the rules of geometry.

Why twice? So we can see what happens to the value of PRS-PQR.

If the value of PRS-PQR stays the same, the statement is sufficient.
If the value of PRS-PQR changes, the statement is insufficient.

As we plug in, we have to follow the rules of geometry. If angles are inside a triangle, their sum must be 180. If angles form a straight line, their sum must be 180. You get the idea.

The attached .pdf shows two combinations of angle measurements in which QPR=30. In each case, PRS-PQR=30. Since the value of PRS-PQR stays the same, statement 1 is sufficient.

Hope this helps!
Attachments
BTG_triangle_plugging in.pdf
(36.99 KiB) Downloaded 195 times
Last edited by GMATGuruNY on Wed Jul 21, 2010 2:39 am, edited 1 time in total.
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by raul_200485 » Tue Jul 20, 2010 8:38 pm
A very useful approach for determining how the angles in a figure affect each other:

Plug in twice, following the rules of geometry.

Why twice? So we can see what happens to the value of PRS-PQR.

If the value of PRS-PQR stays the same, the statement is sufficient.
If the value of PRS-PQR changes, the statement is insufficient.

As we plug in, we have to follow the rules of geometry. If angles are inside a triangle, their sum must be 180. If angles form a straight line, their sum must be 180. You get the idea.

The attached .pdf shows two combinations of angle measurements in which QPR=30. In each case, PRS-PQR=30. Since the value of PRS-PQR stays the same, statement 1 is sufficient.

Hope this helps!

Great approach sir.
Could u provide us with some more sums to practice with this approach. It would help us to apply it better at places.
Regards,
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by raul_200485 » Tue Jul 20, 2010 8:44 pm
citystatekate wrote:Oh geometry....I've stared at this for a really long time and still can't figure it out...

Image

In the figure shown, the measure of angle PRS is how many degrees greater than the measure of angle PQR?

(1) The measure of angle QPR is 30 degrees.
(2) The sum of the measures of angles PQR and PRQ is 150 degrees.

I understand the statements are saying the same thing, so it's got to be D or E. OA is D. Why?
Another way is

We know QPR is 30, so anglePRQ +ANGLE PQR=150,(STATEMENT 1)
NOW, PRS+PRQ=180(STATEMENT 2)
SO, PRQ=180-PRS(STATEMENT 3)

SUBSTITUTE
STATEMENT 3 IN STATEMENT 1

180-PRS+PRQ=150
SO PRS-PRQ=180-150=30

SIMILARLY WE GET THE SAME RESULT WITH STATEMENT 2 OF THE QUESTION, HENCE OPTION D.
REGARDS
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