|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
03 May 2020, 10:57
Kudos
Bookmarks
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
58% (01:55) correct
42%
(02:36)
wrong
based on 38
sessions
History
Date
Time
Result
Not Attempted Yet
In the figure above, M and N are two points on the side PQ and PR of a triangle PQR, respectively such that MNQR is a trapezium and MN:QR = 2:5. What is the ratio of the area of triangle PMN to the area of trapezium MNQR?
A. 4:25
B. 4:21
C. 4:10
D. 4:9
E. 1:2
Are You Up For the Challenge: 700 Level Questions
Attachment:
Untitled.png [ 5.7 KiB | Viewed 19111 times ]
Bunuel
Given: In the figure above, M and N are two points on the side PQ and PR of a triangle PQR, respectively such that MNQR is a trapezium and MN:QR = 2:5.
Asked: What is the ratio of the area of triangle PMN to the area of trapezium MNQR?
Attachment:
Screenshot 2020-05-03 at 11.42.06 PM.png [ 21.27 KiB | Viewed 15699 times ]
Let PLO be perpendicular drawn from P to line QR meeting line QR at O and line MN at L.
If MNQR is a trapezium -> MN & QR are parallel
Since triangles PMN & PQR are similar triangles
MN:QR = PL:PO = 2:5
Ratio of area of triangle PMN to the area of triangle PQR = MN * PL : QR : PO = 2^2 : 5^2 = 4:25
Since area of trapezium MNQR = Area of triangle PQR - Area of triangle PMN
Ratio of the area of triangle PMN to the area of trapezium MNQR = 4:(25-4) = 4: 21
IMO B
firas92
Current Student
Joined: 16 Jan 2019
Last visit: 24 Jul 2026
Posts: 616
Own Kudos:
Given Kudos: 142
Location: India
Concentration: General Management
Schools: Tepper '23 (M$) Foster '23 (D)
GMAT 1: 740 Q50 V40
WE:Sales (Other)
Products:
03 May 2020, 11:12
Kudos
Bookmarks
If MNQR is a trapezium, then MN||QR which means PMN and PQR are similar triangles
By property, if the corresponding sides of two similar triangles are in the ratio \(a:b\), then their areas are in the ratio \(a^2:b^2\)
So the areas of PMN and PQR are in the ratio 4:25 and therefore the area of MNQR and PQR must be in the ratio 21:25
Therefore PMN and MNQR have their areas in the ratio 4:21
Answer is (B)
Posted from my mobile device
By property, if the corresponding sides of two similar triangles are in the ratio \(a:b\), then their areas are in the ratio \(a^2:b^2\)
So the areas of PMN and PQR are in the ratio 4:25 and therefore the area of MNQR and PQR must be in the ratio 21:25
Therefore PMN and MNQR have their areas in the ratio 4:21
Answer is (B)
Posted from my mobile device
