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

 It is currently 16 Oct 2019, 23:22 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  In the figure above, if MNOP is a trapezoid and NOPR is a pa

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Manager  Joined: 01 Sep 2012
Posts: 114
In the figure above, if MNOP is a trapezoid and NOPR is a pa  [#permalink]

Show Tags

15
89 00:00

Difficulty:   65% (hard)

Question Stats: 61% (01:54) correct 39% (02:17) wrong based on 701 sessions

HideShow timer Statistics In the figure above, if MNOP is a trapezoid and NOPR is a parallelogram, what is the area of triangular region MNR?

(1) The ares of NOPR is 30
(2) The area of the shaded region is 5

Attachment: Capture.JPG [ 12.08 KiB | Viewed 63230 times ]

_________________
If my answer helped, dont forget KUDOS! IMPOSSIBLE IS NOTHING

Originally posted by roygush on 23 Sep 2013, 14:34.
Last edited by Bunuel on 16 Aug 2015, 11:47, edited 2 times in total.
Renamed the topic and edited the question.
Intern  Joined: 29 Jan 2013
Posts: 32
Re: In the figure above, if MNOP is a trapezoid and NOPR is a pa  [#permalink]

Show Tags

29
11
IMO B

The question asks only about area of triangle MNR

In the figure given by mick..consider the two triangles NTR and OQP

angle NRT = angle OPQ ( as NR and OP are parallel and equal also)
angle NTR = angle OQP = 90 (altitudes)
=> angle TNR = angle QOP

As two angles and the corresponding side (NR and OP) are equal the two triangles, as per ASA rule,are congruent. Hence both will have same area.

Similarly the triangles MNT and NTR are congruent (ASA rule again). Hence the area of triangle MNR = area of MNT + area of NTR = 5+5 = 10
General Discussion
Magoosh GMAT Instructor G
Joined: 28 Dec 2011
Posts: 4472
Re: In the figure above, if MNOP is a trapezoid and NOPR is a pa  [#permalink]

Show Tags

6
12
roygush wrote:
in the figure above, if MNOPis a trapzoid and NOPRis a parallelogram, what is the area of triangular regoin MNR?

(1) The are of NOPR is 30
(2) The are of OQP is 5

If someone can please explain.
Thanks.

Dear roygush,
I'm happy to help. First of all, here's a important geometry theorem to know:
http://magoosh.com/gmat/2012/isosceles- ... -the-gmat/
Triangle MNR has equal base angles --- therefore, it's isosceles, which means MN = NR. Because NOPR is a parallelogram, NR = OP, so that MN = NR = OP.

Here's a version of the graph with a new perpendicular line drawn:
Attachment: parallelogram with isosceles triangle.JPG [ 20.79 KiB | Viewed 69935 times ]

Because the bases are parallel, OQ = NT --- the distance between two parallel lines is always the same.

Statement #1: The area of NOPR is 30
From that, there's no way to determine the areas inside the triangle MNR. That statement, alone and by itself, is insufficient.

Statement #2: The area of OQP is 5
Well, if the shaded region is 5, we could figure out the pieces of the isosceles triangle. Still, we wouldn't know anything about that central part, NOQR. That would remain unknown. Therefore, this statement, alone and by itself, is insufficient.

Combined statements
Now, we know the area of NOPR is 30. We know that the two little triangles, MNT and TNR, are congruent to QOP, so each has an area of 5. That gives a total area of 30 + 5 + 5 = 40 to the whole trapezoid. With both statements, we can calculate the area, so combined, the statements are sufficient.

Does all this make sense?
Mike _________________
Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
Magoosh GMAT Instructor G
Joined: 28 Dec 2011
Posts: 4472
Re: In the figure above, if MNOP is a trapezoid and NOPR is a pa  [#permalink]

Show Tags

15
1
IMO B
The question asks only about area of triangle MNR

You are totally 100% correct. I am embarrassed to say --- I made the most boneheaded of all GMAT mistakes: was so concerned with analyzing the diagram, I lost track of exactly what the prompt was asking and assumed it was asking for the area of the whole. You are perfectly correct --- the answer has to be (B).
Mike _________________
Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
Intern  Joined: 12 Jan 2014
Posts: 1
Re: In the figure above, if MNOP is a trapezoid and NOPR is a pa  [#permalink]

Show Tags

mikemcgarry wrote:
IMO B
The question asks only about area of triangle MNR

You are totally 100% correct. I am embarrassed to say --- I made the most boneheaded of all GMAT mistakes: was so concerned with analyzing the diagram, I lost track of exactly what the prompt was asking and assumed it was asking for the area of the whole. You are perfectly correct --- the answer has to be (B).
Mike Hi Mike,

Would you mind explaining in detail why statement 1 is insufficient. I lost a lot of time on this part of the problem.

Thanks
-Chris
Magoosh GMAT Instructor G
Joined: 28 Dec 2011
Posts: 4472
Re: In the figure above, if MNOP is a trapezoid and NOPR is a pa  [#permalink]

Show Tags

3
CVarga wrote:
Hi Mike,
Would you mind explaining in detail why statement 1 is insufficient. I lost a lot of time on this part of the problem.
Thanks
-Chris

Dear Chris,
I'm happy to help. The area of a parallelogram is (base)*(height). We know nothing about the slant angle x, so we have no idea how much of the parallelogram the triangle occupies. First of all, we know b*h = 30 from Statement #1, but we don't know if we have a base of 1 and a height of 30, or a base of 30 and a height of 1, or something else. Furthermore, we don't know the slant angle x ----- perhaps x = 89°, nearly vertical, so that the side triangle is just a tall skinny sliver, or maybe x is something like 20° or 30°, so that the base of the triangle (QP) is most of the length of the base of the parallelogram (RP). Even knowing the parallelogram has an area of 30, we could design things consistent with this statement & the diagram so that the triangle OQP has an area of nearly zero or nearly half the parallelogram or anything in between.

Does all this make sense?
Mike _________________
Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
Intern  Joined: 15 Jul 2012
Posts: 32
Re: In the figure above, if MNOP is a trapezoid and NOPR is a pa  [#permalink]

Show Tags

IMO B

The question asks only about area of triangle MNR

In the figure given by mick..consider the two triangles NTR and OQP

angle NRT = angle OPQ ( as NR and OP are parallel and equal also)
angle NTR = angle OQP = 90 (altitudes)
=> angle TNR = angle QOP

As two angles and the corresponding side (NR and OP) are equal the two triangles, as per ASA rule,are congruent. Hence both will have same area.

Similarly the triangles MNT and NTR are congruent (ASA rule again). Hence the area of triangle MNR = area of MNT + area of NTR = 5+5 = 10

hey nice solution.

can you please explain the colored part it seems that NRT is exterior angle of given parallelogram, while OPQ is interior angle of the parallellogram.
how are they equal? i lack basics in these geometrical concepts.
Magoosh GMAT Instructor G
Joined: 28 Dec 2011
Posts: 4472
Re: In the figure above, if MNOP is a trapezoid and NOPR is a pa  [#permalink]

Show Tags

saggii27 wrote:
hey nice solution.

can you please explain the colored part it seems that NRT is exterior angle of given parallelogram, while OPQ is interior angle of the parallellogram.
how are they equal? i lack basics in these geometrical concepts.

Dear Saggii27,
I'm happy to respond. Because NOPR is a parallelogram, this means NR is parallel to OP. This means that RP is a line that cuts across two parallel lines --- such a line is known as a "transversal." See this blog for all the angles that must be equal in this situation:
http://magoosh.com/gmat/2013/angles-and ... -the-gmat/

Does all this make sense?
Mike _________________
Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
Manager  Joined: 05 Jul 2015
Posts: 93
Concentration: Real Estate, International Business
GMAT 1: 600 Q33 V40 GPA: 3.3
Re: In the figure above, if MNOP is a trapezoid and NOPR is a pa  [#permalink]

Show Tags

1
The official answer is B but I'm not quite understanding why we can't use A to divide the area by 3 and get 10. You can tell from the picture that it fits 3 times....
Current Student B
Joined: 23 Feb 2015
Posts: 164
Schools: Duke '19 (M)
Re: In the figure above, if MNOP is a trapezoid and NOPR is a pa  [#permalink]

Show Tags

DJ1986 wrote:
The official answer is B but I'm not quite understanding why we can't use A to divide the area by 3 and get 10. You can tell from the picture that it fits 3 times....

Never make any assumptions about figures - especially on DS

They draw them out of scale on purpose to catch people in this very trap.
Manager  Joined: 17 Sep 2015
Posts: 84
Re: In the figure above, if MNOP is a trapezoid and NOPR is a pa  [#permalink]

Show Tags

Image
In the figure above, if MNOP is a trapezoid and NOPR is a parallelogram, what is the area of triangular region MNR?

(1) The ares of NOPR is 30
(2) The area of the shaded region is 5

A) area of NOPR is 30, this is a parallelogram. It consists of two congruent triangle.

A right proved by others : triangle OPR is congruent to triangle NTR (or half of triangle NMR)

so basically triangle OPR is one of the two congruent triangles which makes up the parallelogram. Since OPR = NTR.

hence half the area of the parallelogram is the area of the req triangle MNR -----> sufficient

Im sure Im going wrong somewhere but this is what i figured in the test. Can someone please point out where am i going wrong in my logic?

Geometry is my weakest area. Thanks in advance
_________________
You have to dig deep and find out what it takes to reshuffle the cards life dealt you
Magoosh GMAT Instructor G
Joined: 28 Dec 2011
Posts: 4472
Re: In the figure above, if MNOP is a trapezoid and NOPR is a pa  [#permalink]

Show Tags

aniketm.87@gmail.com wrote:
Image
In the figure above, if MNOP is a trapezoid and NOPR is a parallelogram, what is the area of triangular region MNR?

(1) The ares of NOPR is 30
(2) The area of the shaded region is 5

A) area of NOPR is 30, this is a parallelogram. It consists of two congruent triangle.

A right proved by others : triangle OPR is congruent to triangle NTR (or half of triangle NMR)

so basically triangle OPR is one of the two congruent triangles which makes up the parallelogram. Since OPR = NTR.

hence half the area of the parallelogram is the area of the req triangle MNR -----> sufficient

Im sure Im going wrong somewhere but this is what i figured in the test. Can someone please point out where am i going wrong in my logic?

Geometry is my weakest area. Thanks in advance

Dear aniketm.87,

I'm happy to respond. My friend, either diagonal of a parallelogram will indeed divide the parallelogram into two congruent triangles. Do you understand exactly what the the word "congruent" means? It means totally matching in every way: every side in one triangle is exactly equal to the corresponding side in the other, and every angle in one triangle is exactly equal to the corresponding angle in the other. It's absolutely impossible for two triangles to be congruent if one has a right angle and the other doesn't.

In parallelogram NOPR, it's true that triangle OPR is congruent to triangle NOR, but that doesn't help us answer the prompt question at all.

Triangle NTR, the right triangle that is half of triangle NMR, is not even pretending to be congruent to either OPR or NOR. Triangle NTR has a right angle, and neither OPR or NOR has a right angle.

Does all this make sense?
Mike _________________
Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
Manager  B
Joined: 01 Nov 2016
Posts: 58
Concentration: Technology, Operations
Re: In the figure above, if MNOP is a trapezoid and NOPR is a pa  [#permalink]

Show Tags

3
1
- Shape NOPR is a parallelogram so that means lines NR and OP are parallel.
- If those lines are parallel, then angle R and angle P are equal. So angle P = x.
- If angle R and angle P are equal then triangle QOP is half of triangle MNR, because triangle MNR base angles are both x.
- You can imagine a line straight down the middle of triangle MNR to create a perpendicular angle, and since the two base angles are both x then triangle MNR is basically just two of triangle QOP.

1. Not sufficient because have no base or height information.
2. Sufficient because we know triangle QOP is half or triangle MNR. Since triangle QOP is area 5, then triangle MNR must be area 10.
Manager  B
Joined: 20 Jan 2016
Posts: 175
Re: In the figure above, if MNOP is a trapezoid and NOPR is a pa  [#permalink]

Show Tags

"As two angles and the corresponding side (NR and OP) are equal the two triangles, as per ASA rule,are congruent. Hence both will have same area."

Is this theory true ? can someone please confirm this.
Magoosh GMAT Instructor G
Joined: 28 Dec 2011
Posts: 4472
Re: In the figure above, if MNOP is a trapezoid and NOPR is a pa  [#permalink]

Show Tags

1
1
pra1785 wrote:
"As two angles and the corresponding side (NR and OP) are equal the two triangles, as per ASA rule,are congruent. Hence both will have same area."

Is this theory true ? can someone please confirm this.

Dear pra1785,

I'm happy to respond. Yes, that's 100% correct. For more detail, see:
GMAT Data Sufficiency: Congruence Rules

Let me know if you have further questions after reading that blog.

Mike _________________
Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
Non-Human User Joined: 09 Sep 2013
Posts: 13204
Re: In the figure above, if MNOP is a trapezoid and NOPR is a pa  [#permalink]

Show Tags

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: In the figure above, if MNOP is a trapezoid and NOPR is a pa   [#permalink] 14 Oct 2019, 04:24
Display posts from previous: Sort by

In the figure above, if MNOP is a trapezoid and NOPR is a pa

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  