by: gmataccount123
11 mins
by: WA
12 mins
Events & Promotions
|
|
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.
Sep 1507:00 PM EDT
-09:00 PM EST
Elite scores are possible when you enroll in a powerful GMAT course, taught live online + 6 months access to TTP OnDemand video courses included! Class starts Tues/Thurs Sept. 15, 2026 - Nov. 15, 2027, 7:00pm-9:00pm EST
Sep 2107:00 PM EDT
-10:00 PM EDT
Boost your GMAT score in less than one month in a live online class + 6 months access to TTP OnDemand video courses included! Class starts Mon, Tues, Wed, Thur, Fri Sept. 21, 2026 - Oct. 9, 2027, 7:00pm-10:00pm EST
Posts: 1,926
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
32% (02:20) correct
68%
(03:39)
wrong
based on 25
sessions
History
Date
Time
Result
Not Attempted Yet
Farmer Pythagoras has a field in the shape of a right triangle. The right triangle's legs have lengths 3 and 4 units. In the corner where those sides meet at a right angle, he leaves a small unplanted square S so that from the air it looks like the right angle symbol. The rest of the field is planted. The shortest distance from S to the hypotenuse is 2 units. What fraction of the field is planted?
A) 25/27
B) 26/27
C) 73/75
D) 145/147
E) 74/75
Attachment:
Ques.jpg [ 9.82 KiB | Viewed 4014 times ]
Posts: 1,926
Official Solution
Attachment:
2.jpg [ 14.98 KiB | Viewed 3851 times ]
Attachment:
1.jpg [ 111.1 KiB | Viewed 3884 times ]
General Discussion
Posts: 14
Since the shortest distance is the perpendicular to hypotenuse say x,
1/2(5)(x)= 1/2(3)(4)
Thus x= 12/5= 2.4
Thus length of diagonal of square= 2.4-2= 0.4
Thus area of square= 0.4x0.4= 0.16
Thus area left for farming= 6-0.16= 5.84
Fraction= 5.84/6= 73/75
1/2(5)(x)= 1/2(3)(4)
Thus x= 12/5= 2.4
Thus length of diagonal of square= 2.4-2= 0.4
Thus area of square= 0.4x0.4= 0.16
Thus area left for farming= 6-0.16= 5.84
Fraction= 5.84/6= 73/75
From the image attached, we have found diagonal of square=(2/5)
2(side^2)=(diagonal^2) (In a square, relation between diagonal and side)
side^2= area of square S =2/25
total area of the field=(1/2)*4*3=6 ((1/2*base*height))
area planted=6-(2/25)=148/25
fraction of the field planed=(148/25)/6=74/75
IMO:OPTION E
2(side^2)=(diagonal^2) (In a square, relation between diagonal and side)
side^2= area of square S =2/25
total area of the field=(1/2)*4*3=6 ((1/2*base*height))
area planted=6-(2/25)=148/25
fraction of the field planed=(148/25)/6=74/75
IMO:OPTION E
Attachments
GMATbuster's Weekly Quant Quiz#9 Ques 6 ANSWER.pdf [844.76 KiB]
Downloaded 85 times
| To download please login or register as a user |
Let the side of square S be x. Hypotenuse is 5 from Pythagoras theorem. Draw lines from top right upper vertex of S to two end points of the hypotenuse of the triangle. So, now we have divided this into square S + 1 thin triangle with base x and height (3-x) + one thin triangle with base x and height (4-x) + one triangle with base 5 and height 2. All this must add up to total area of 0.5*3*4 = 6
Hence, \(x^2 + 0.5*x*(3-x) + 0.5*x*(4-x) + 0.5*2*5 = 6\), which gives
\(x^2 + 1.5*x - 0.5*x^2 + 2*x - 0.5*x^2 + 5 = 6\)
\(3.5*x = 1\) or \((7/2)*x = 1\) or x = 2/7
Area of S = \((2/7)^2\) = 4/49
Area of planted region = 6 - (4/49)
Fraction needed = [6 - (4/49)]/6 = 1 - \(\frac{4}{(49*6)}\) = 1 - \(\frac{2}{147}\) = 145/147
Hence Option D
Hence, \(x^2 + 0.5*x*(3-x) + 0.5*x*(4-x) + 0.5*2*5 = 6\), which gives
\(x^2 + 1.5*x - 0.5*x^2 + 2*x - 0.5*x^2 + 5 = 6\)
\(3.5*x = 1\) or \((7/2)*x = 1\) or x = 2/7
Area of S = \((2/7)^2\) = 4/49
Area of planted region = 6 - (4/49)
Fraction needed = [6 - (4/49)]/6 = 1 - \(\frac{4}{(49*6)}\) = 1 - \(\frac{2}{147}\) = 145/147
Hence Option D
Notice that the incorrect responses assume that the diagonal of the square is the continuation of the perpendicular from the hypotenuse.
The correct responses avoid this assumption by terminating the perpendicular at the vertex of box S and then dealing with the resulting triangles.
Posted from my mobile device
The correct responses avoid this assumption by terminating the perpendicular at the vertex of box S and then dealing with the resulting triangles.
Posted from my mobile device
Moderator:
Announcements
Monday, Sep 14, 2026
11:30am NY / 3:30pm London / 9pm Mumbai
Subscribe to GMAT Club for New Podcast Episodes, Debriefs, & Insightful Sessions on GMAT Preparation
Tuck at Dartmouth
AI at Dartmouth Tuck: How the School Is Preparing Leaders for the Age of Artificial Intelligence
Inside the courses, research, and hands-on learning defining wise, decisive leadership in an AI-driven world.
Read More
Inside the courses, research, and hands-on learning defining wise, decisive leadership in an AI-driven world.
Read More
Top 5 GMAT Debrief Videos
Success stories and strategies from high-scoring candidates.