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.
Apr 2808:00 AM PDT
-11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
Apr 2711:00 AM EDT
-12:00 PM EDT
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors
Apr 2912:30 AM EDT
-01:30 AM EDT
Learn how Kamakshi achieved a GMAT 675 with an impressive 96th %ile in Data Insights. Discover the unique methods and exam strategies that helped her excel in DI along with other sections for a balanced and high score.
Apr 3001:30 AM EDT
-02:30 AM EDT
At one point, she believed GMAT wasn’t for her. After scoring 595, self-doubt crept in and she questioned her potential. But instead of quitting, she made the right strategic changes. The result? A remarkable comeback to 695. Check out how Saakshi did it.
May 0111:00 AM PDT
-12:00 PM PDT
Free- full-length test + 15 concept videos + 150+ short videos + study plan!
May 0306:30 AM PDT
-08:30 AM PDT
Verbal trouble on GMAT? Fix it NOW! Join Sunita Singhvi for a focused webinar on actionable strategies to boost your Verbal score and take your performance to the next level.
13 May 2019, 21:25
Kudos
Bookmarks
D
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:
18% (02:57) correct
82%
(02:53)
wrong
based on 28
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) \(\frac{25}{27}\)
(B) \(\frac{26}{27}\)
(C) \(\frac{73}{75}\)
(D) \(\frac{145}{147}\)
(E) \(\frac{74}{75}\)
Attachment:
02cbd3882872949029f58c698cf441e7d759cc72.png [ 6.62 KiB | Viewed 4839 times ]
19 May 2019, 07:51
Kudos
Bookmarks
Hello,
Greetings for the day!
A top class question from Geometry, testing you on multiple concepts on triangles. You need to know your Pythagorean triples to figure out the length of the hypotenuse. You will also need to apply the Area formula of a triangle, but more importantly, you need to be able to apply the concept of similarity after doing a few simple constructions.
Let us name the field as PQR where PR is the hypotenuse, PQ is 3 units in length and QR is 4 units. It’s not hard to make out that PR has to be 5 units.
Let us make two constructions:
Note that UT represents the shortest distance between the square and the hypotenuse, distance being 2 units as given in the question. Also note that UT is parallel to QS since both are perpendicular to PR and hence to VW (remember, VW is parallel to PR).
The rest of the calculations is shown in the diagrams below.
19th May - Reply 3 - Part1.JPG [ 55.2 KiB | Viewed 4213 times ]
19th May - Reply 3 - Part 2.JPG [ 61.05 KiB | Viewed 4190 times ]
In the last step, you may have noticed that we subtracted \(\frac{2}{147}\) from 1. This is because, we have to find the fraction of the field that is planted. In such cases, the entire field’s area is always taken as 1.
So, the correct answer option is D.
The trap answer in this question is E. You get this answer when you extend UT to meet Q, assuming that it will be the diagonal of the small square. But, this is a wrong assumption, which will end up giving you the value of x as 2\(\sqrt{5}\), which will give you the final answer as E.
This is definitely a hard question on Geometry that you can expect once you cross the 700 level. To be able to solve questions like these, you should be able to make constructions which then enable you to use the similarity concept, else you will be stuck, beyond a certain stage in the solution. Also remember that, when there are a pair of triangles with a pair of parallel lines, more often than not, it is similarity which can help you solve the problem.
Lastly, please do not be too hard on yourself, if you were unable to solve this question within 2 minutes.
Hope this helps!
Greetings for the day!
A top class question from Geometry, testing you on multiple concepts on triangles. You need to know your Pythagorean triples to figure out the length of the hypotenuse. You will also need to apply the Area formula of a triangle, but more importantly, you need to be able to apply the concept of similarity after doing a few simple constructions.
Let us name the field as PQR where PR is the hypotenuse, PQ is 3 units in length and QR is 4 units. It’s not hard to make out that PR has to be 5 units.
Let us make two constructions:
- QS – this represents the third altitude of the right angled triangle, PQR.
VW – a line parallel to PR such that it passes through the vertex of the square, which represents the unplanted region of the field.
Note that UT represents the shortest distance between the square and the hypotenuse, distance being 2 units as given in the question. Also note that UT is parallel to QS since both are perpendicular to PR and hence to VW (remember, VW is parallel to PR).
The rest of the calculations is shown in the diagrams below.
Attachment:
19th May - Reply 3 - Part1.JPG [ 55.2 KiB | Viewed 4213 times ]
Attachment:
19th May - Reply 3 - Part 2.JPG [ 61.05 KiB | Viewed 4190 times ]
In the last step, you may have noticed that we subtracted \(\frac{2}{147}\) from 1. This is because, we have to find the fraction of the field that is planted. In such cases, the entire field’s area is always taken as 1.
So, the correct answer option is D.
The trap answer in this question is E. You get this answer when you extend UT to meet Q, assuming that it will be the diagonal of the small square. But, this is a wrong assumption, which will end up giving you the value of x as 2\(\sqrt{5}\), which will give you the final answer as E.
This is definitely a hard question on Geometry that you can expect once you cross the 700 level. To be able to solve questions like these, you should be able to make constructions which then enable you to use the similarity concept, else you will be stuck, beyond a certain stage in the solution. Also remember that, when there are a pair of triangles with a pair of parallel lines, more often than not, it is similarity which can help you solve the problem.
Lastly, please do not be too hard on yourself, if you were unable to solve this question within 2 minutes.
Hope this helps!
25 Dec 2021, 05:06
Kudos
Bookmarks
Can we take 0.4 as a diagonal of square field formed at right angle, then find the area of that square?
But the answer im getting is different. Please let me know what im missing here.
But the answer im getting is different. Please let me know what im missing here.
