Last visit was: 19 Nov 2025, 22:22 It is currently 19 Nov 2025, 22:22
Close
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
Your Progress

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.
Close
Request Expert Reply
Confirm Cancel
User avatar
GMATBusters
User avatar
GMAT Tutor
Joined: 27 Oct 2017
Last visit: 14 Nov 2025
Posts: 1,924
Own Kudos:
6,647
 [5]
Given Kudos: 241
WE:General Management (Education)
Expert
Expert reply
Posts: 1,924
Kudos: 6,647
 [5]
1
Kudos
Add Kudos
4
Bookmarks
Bookmark this Post
User avatar
GMATBusters
User avatar
GMAT Tutor
Joined: 27 Oct 2017
Last visit: 14 Nov 2025
Posts: 1,924
Own Kudos:
Given Kudos: 241
WE:General Management (Education)
Expert
Expert reply
Posts: 1,924
Kudos: 6,647
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
ashwini2k6jha
Joined: 11 Jun 2014
Last visit: 27 Jan 2025
Posts: 93
Own Kudos:
98
 [2]
Given Kudos: 48
Location: India
Schools: ISB '23
GMAT 1: 700 Q49 V37
Schools: ISB '23
GMAT 1: 700 Q49 V37
Posts: 93
Kudos: 98
 [2]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
Archit3110
User avatar
Major Poster
Joined: 18 Aug 2017
Last visit: 19 Nov 2025
Posts: 8,422
Own Kudos:
4,982
 [1]
Given Kudos: 243
Status:You learn more from failure than from success.
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1: 545 Q79 V79 DI73
GMAT Focus 2: 645 Q83 V82 DI81
GPA: 4
WE:Marketing (Energy)
GMAT Focus 2: 645 Q83 V82 DI81
Posts: 8,422
Kudos: 4,982
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
PQR is a right triangle in the xy plane. If the coordinate of point P is (-5,2), what is the area of the shaded region?
1) The coordinate of point R is (3,8)
2) The coordinate of point Q is (3,2)

#1
The coordinate of point R is (3,8)
but we do not have the coordinate of point Q ; so insufficient

#2
The coordinate of point Q is (3,2)
but we do not have the coordinate of point R ; so insufficient
using 1 & 2
we have the points of ∆ PQR and shaded region area can be determined
OPTION C
User avatar
Raxit85
Joined: 22 Feb 2018
Last visit: 02 Aug 2025
Posts: 766
Own Kudos:
Given Kudos: 135
Posts: 766
Kudos: 1,177
Kudos
Add Kudos
Bookmarks
Bookmark this Post
PQR is a right triangle in the xy plane. If the coordinate of point P is (-5,2), what is the area of the shaded region?
Distance of base of shaded region is 5.

1) The coordinate of point R is (3,8) - No information about height of shaded region. So insufficient.

2) The coordinate of point Q is (3,2) - Base of shaded region is 2 point above from origin. Still insufficient.

1) + 2)

No exact information about height of shaded region. So insufficient.
Ans. E
User avatar
Kinshook
User avatar
Major Poster
Joined: 03 Jun 2019
Last visit: 19 Nov 2025
Posts: 5,794
Own Kudos:
Given Kudos: 161
Location: India
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Products:
GMAT 1: 690 Q50 V34
Posts: 5,794
Kudos: 5,514
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Given: PQR is a right triangle in the xy plane.
Asked: If the coordinate of point P is (-5,2), what is the area of the shaded region?

Attachment:
Screenshot 2020-04-26 at 9.05.30 AM.png
Screenshot 2020-04-26 at 9.05.30 AM.png [ 30.37 KiB | Viewed 8623 times ]
1) The coordinate of point R is (3,8)
Since it is not provided that PQ is parallel to x-axis
Multiple right-triangles can be formed with P(-5,2) & R(3,8).
Area of shaded region = 1/2 * Base * height
Since k & m may vary and are unknown
NOT SUFFICIENT

Attachment:
Screenshot 2020-04-26 at 8.56.36 AM.png
Screenshot 2020-04-26 at 8.56.36 AM.png [ 30.31 KiB | Viewed 8532 times ]
2) The coordinate of point Q is (3,2)
Now PQ is parallel to x-axis
But since coordinate of R(3,y) is unknown
and correspondingly ordinate of A(0,k) is also unknown
NOT SUFFICIENT

Attachment:
Screenshot 2020-04-26 at 8.54.51 AM.png
Screenshot 2020-04-26 at 8.54.51 AM.png [ 32.02 KiB | Viewed 8421 times ]
(1) + (2)
1) The coordinate of point R is (3,8)
2) The coordinate of point Q is (3,2)
Now PQ is parallel to x-axis
Angle Q is right-angle
Since triangle PAB & PQR are similar triangles;
AB/PB = RQ/PQ
(x-2)/5 = (8-2)/(3+5) = 6/8 = 3/4
x = 2 + 15/4 = 5.75
Area of shaded region = 1/2 * 5 * (x-2) = 2.5(x-2) = 2.5*(5.75-2) = 2.5 * 3.75 = 9.375
SUFFICIENT

IMO C


Attachments

GMATBusters Quant Quiz 26042020 Q#6.mp4 [4.67 MiB]
Downloaded 118 times

User avatar
uc26
User avatar
INSEAD School Moderator
Joined: 19 Sep 2018
Last visit: 11 Nov 2021
Posts: 89
Own Kudos:
Given Kudos: 945
Posts: 89
Kudos: 71
Kudos
Add Kudos
Bookmarks
Bookmark this Post
We know that point P is (-5,2) and PQR is a right triangle. Let the points where the y-axis cuts the triangle PQR be A (on side PR) and C (on side PQ) respectively. If P and Q have the same Y co-ordinate and R and Q have the same X co-ordinate, then triangles PQR and PCA will become similar triangles since all the 3 angles in the two triangles will be equal. If we know the co-ordinates of points R and Q, we can figure out the side lengths of triangle PQR. PC=5 since the x co-ordinate of P is -5. For similar triangles, we know that the ratios of the lengths of the corresponding sides are equal. And since we know one side of PCA, we can figure out the side AC and find the area of triangle PCA i.e the area of the shaded region.

(1) We have no information on the co-ordinates of point Q. Not sufficient.

(2) We have no information on the co-ordinates of point R. Not sufficient.

(1)+(2) Since we have the co-ordinates of points R and Q, we can find the area of the shaded region= Area of triangle PCA. Sufficient.

Answer: C.
avatar
Tommy6e
Joined: 24 Jan 2018
Last visit: 05 Apr 2024
Posts: 19
Own Kudos:
Given Kudos: 79
GMAT 1: 710 Q49 V38
GMAT 2: 740 Q49 V41 (Online)
GPA: 3.85
Products:
GMAT 2: 740 Q49 V41 (Online)
Posts: 19
Kudos: 10
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Choice C is correct
PQR is a right triangle in the xy plane. If the coordinate of point P is (-5,2), what is the area of the shaded region?

Statement 1:
1) The coordinate of point R is (3,8)
We do not have enough information to find the area of the shaded area (triangle PAB)

Statement 2:
2) The coordinate of point Q is (3,2)
We do not have enough information to find the area of the shaded area

Both statements:
Since P and Q are located at y=2 and R and Q are located at X=3, we can find that PQ = 3-(-5) = 8 and RQ = 8-2 = 6

The area of triangle PRQ is 8*6/2 = 24

Triangles APB and RPB are similar because RQ is parallel to the Y-axis.
Since triangles APB and RPB are similar and we have the area of PRQ(=24), we can find the area of the shaded area PAB
Attachments

Screenshot_960.png
Screenshot_960.png [ 9.71 KiB | Viewed 8213 times ]

User avatar
1BlackDiamond1
Joined: 26 Sep 2016
Last visit: 24 Feb 2022
Posts: 61
Own Kudos:
292
 [1]
Given Kudos: 35
Posts: 61
Kudos: 292
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
This question is easier said than done.

Just use number sense and geometry common sense. We need all points P, Q R to find the area. Solving this question is very difficult. But in DS we do not need to solve the question hence the answer is C.
User avatar
kapilagarwal
Joined: 29 Jul 2018
Last visit: 11 Jun 2021
Posts: 15
Own Kudos:
Given Kudos: 9
Concentration: Finance, Economics
WE:Project Management (Finance: Investment Banking)
Posts: 15
Kudos: 1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ANS: E BOTH INSUFFICIENT , SINCE WE CAN'T FIND HEIGHT OF THE SHADED REGION

Posted from my mobile device
avatar
SR71Blackbird
Joined: 26 Nov 2019
Last visit: 26 Mar 2022
Posts: 15
Own Kudos:
Given Kudos: 189
Location: United Arab Emirates
GMAT 1: 640 Q48 V31
GPA: 3.96
GMAT 1: 640 Q48 V31
Posts: 15
Kudos: 15
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Statement 1 is sufficient to answer the question.

slope is rise / run = (8-2)/(3+5) = 3/4. => for every 4 units forward, the line goes up by 3 unit. we know the distance of P from Y axis, we can find the height of the triangle and find the area.

One doubt might arise, what if the line PQ is not parallel to X-axis, since right angle triangle at q, we can drop perpendiculars from P and R and find the location of Q
Kudos
Add Kudos
Bookmarks
Bookmark this Post
PQR is a right triangle in the xy plane. If the coordinate of point P is (-5,2), what is the area of the shaded region?
1) The coordinate of point R is (3,8)
2) The coordinate of point Q is (3,2)

Statement 1 - R is (3,8) , which mean q will be (3,2)
we can get equation of line PR as we know two end point coordinates, using equation of line

we can also use similar triangle property to find length of base of SHADED area
hence sufficient

Statement - 2
does not give info on R and we cannot find coordinates of shaded triangle, hence not sufficient.

Answer- A
User avatar
lacktutor
Joined: 25 Jul 2018
Last visit: 23 Oct 2023
Posts: 659
Own Kudos:
Given Kudos: 69
Posts: 659
Kudos: 1,396
Kudos
Add Kudos
Bookmarks
Bookmark this Post
PQR is a right triangle in the xy plane. If the coordinate of point P is (-5,2), what is the area of the shaded region?

(Statement1): The coordinate of point R is (3,8)
—> We cannot make sure whether the coordinate of point Q is (3,2) or not.
Insuffcient

(Statement2): The coordinate of point Q is (3,2).
—> the point of Q could be (3,8), (3.9) or any other points (3, y)
Insuffcient

Taken together 1&2,
PQ = 8
QR= 6
—> we can find the area of shaded region by using similar triangles:
5/8 = x/ 6
—> x= 30/8 = 15/4 = 3.75
Area of shaded region = 5*3.75/2 = 9.375
Sufffient

Answer (C)

Posted from my mobile device
User avatar
jrk23
Joined: 26 Sep 2017
Last visit: 29 Oct 2021
Posts: 300
Own Kudos:
Given Kudos: 29
Posts: 300
Kudos: 80
Kudos
Add Kudos
Bookmarks
Bookmark this Post
i think " c" is the answer. two triangle are similar than the ratio of their sides are equal.

So we need both co-ordinates.

so "C" is the answer.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,590
Own Kudos:
Posts: 38,590
Kudos: 1,079
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
Moderators:
Math Expert
105390 posts
496 posts