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.
Nov 2211:00 AM IST
-01:00 PM IST
Do RC/MSR passages scare you? e-GMAT is conducting a masterclass to help you learn – Learn effective reading strategies Tackle difficult RC & MSR with confidence Excel in timed test environment- Nov 23
11:00 AM IST
-01:00 PM IST
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease. 
Nov 2510:00 AM EST
-11:00 AM EST
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.
26 Feb 2021, 08:03
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
62% (02:57) correct
38%
(03:13)
wrong
based on 174
sessions
History
Date
Time
Result
Not Attempted Yet
A farmer has two plots of land of different sizes, and each plot of land consists of two different crops, corn, and wheat. In one plot, the ratio of corn to wheat by land area is 7 to 3, and in the other plot, the ratio of corn to wheat by land area is 11 to 4. If the ratio of corn to wheat by land area of the two plots combined is 24 to 9, what is the ratio of the total area of the smaller plot to the total area of the larger plot?
A) 2 to 5
B) 3 to 8
C) 1 to 4
D) 2 to 9
E) 3 to 16
A) 2 to 5
B) 3 to 8
C) 1 to 4
D) 2 to 9
E) 3 to 16
26 Feb 2021, 18:52
Kudos
Bookmarks
Let the 2 plots be P1 and P2
By the theory of compound mixtures, when V1 Volume/Quantity of a mixture of X and Y which is in the ratio a : b is mixed with V2 Volume/Quantity of another mixture X and Y (i.e the constituents of the 2 mixtures are the same in the ratio p : q, then the final ratio of the constituents is given by
\(\frac{X}{Y}\) = \(\frac{X \space from \space V_1 + X \space from \space V_2 }{Y \space from \space V_1 + Y \space from \space V_2} = \frac{(\frac{a}{a + b})*V_1 + (\frac{p}{p + q})*V_2}{(\frac{b}{a + b})*V_1 + (\frac{q}{p + q})*V_2}\)
\(\frac{24}{9} = \frac{(\frac{11}{11 + 4})*P_1 + (\frac{7}{7 + 3})*P_2}{(\frac{4}{11 + 4})*P_1 + (\frac{3}{7 + 3})*P_2}\)
\(24 * (\frac{4}{15} * P_1 + \frac{3}{10} * P_2) = 9 * (\frac{11}{15} * P_1 + \frac{7}{10} * P_2)\)
\(\frac{72}{10} * P_2 - \frac{63}{10} * P_2 = \frac{99}{15} * P_1 - \frac{96}{15} * P_1 \)
\(\frac{9}{10} * P_2 = \frac{3}{15} * P_1\)
\(\frac{P_2}{P_1} = \frac{3}{15} * \frac{10}{9} = \frac{2}{9}\)
Option D
Arun Kumar
By the theory of compound mixtures, when V1 Volume/Quantity of a mixture of X and Y which is in the ratio a : b is mixed with V2 Volume/Quantity of another mixture X and Y (i.e the constituents of the 2 mixtures are the same in the ratio p : q, then the final ratio of the constituents is given by
\(\frac{X}{Y}\) = \(\frac{X \space from \space V_1 + X \space from \space V_2 }{Y \space from \space V_1 + Y \space from \space V_2} = \frac{(\frac{a}{a + b})*V_1 + (\frac{p}{p + q})*V_2}{(\frac{b}{a + b})*V_1 + (\frac{q}{p + q})*V_2}\)
\(\frac{24}{9} = \frac{(\frac{11}{11 + 4})*P_1 + (\frac{7}{7 + 3})*P_2}{(\frac{4}{11 + 4})*P_1 + (\frac{3}{7 + 3})*P_2}\)
\(24 * (\frac{4}{15} * P_1 + \frac{3}{10} * P_2) = 9 * (\frac{11}{15} * P_1 + \frac{7}{10} * P_2)\)
\(\frac{72}{10} * P_2 - \frac{63}{10} * P_2 = \frac{99}{15} * P_1 - \frac{96}{15} * P_1 \)
\(\frac{9}{10} * P_2 = \frac{3}{15} * P_1\)
\(\frac{P_2}{P_1} = \frac{3}{15} * \frac{10}{9} = \frac{2}{9}\)
Option D
Arun Kumar
27 Feb 2021, 14:33
Kudos
Bookmarks
sjuniv32
Set the ratio of the second land to the first land as x. Then to get 24/9 in the terms of the first land and second land, we need total corn over total wheat. We can treat the first land's area as 1 and the second land's area as x since the result is a ratio:
\(\frac{\frac{7}{10} + \frac{11}{15}*x}{\frac{3}{10} + \frac{4}{15}*x} = \frac{24}{9} = \frac{8}{3}\)
\(\frac{7}{10} + \frac{11}{15}*x = \frac{4}{5} + \frac{32}{45}x\)
\(\frac{1}{45}x = \frac{4}{5} - \frac{7}{10} = \frac{1}{10}\)
\(x = 9/2\).
Now we know the second land is bigger but we want the ratio of the smaller land to the bigger land, so we reverse it to get 2:9.
Ans: D
