OG 108
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OG 108
Source: Beat The GMAT — Problem Solving |
You have already posted this question here >> https://www.beatthegmat.com/og-108-t213839.html
Anju Agarwal
Quant Expert, Gurome
Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.
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Quant Expert, Gurome
Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.
§ GMAT with Gurome § Admissions with Gurome § Career Advising with Gurome §
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We can plug in the answers, which represent the original number of trees.Each year for 4 years, a farmer increased the number of trees in a certain orchard by 1/4 of the number of trees in the orchard of the preceding year. If all of the trees thrived and there were 6250 trees in the orchard at the end of 4 year period, how many trees were in the orchard at the beginning of the 4 year period?
A. 1250
B. 1563
C. 2250
D. 2560
E. 2752
Since the number of trees increases by 1/4 each year, the correct answer must be a multiple of 4.
The last 2 digits of a multiple of 4 must themselves form a multiple of 4.
Eliminate A (1250) and C (2250), since 50 is not a multiple of 4.
Eliminate B (1563), since 63 is not a multiple of 4.
Answer choice D: 2560
After the 1st year, the number of trees = 2560 + (1/4)2560 = 3200.
After the 2nd year, the number of trees = 3200 + (1/4)3200 = 4000.
After the 3rd year, the number of trees = 4000 + (1/4)4000 = 5000.
After the 4th year, the number of trees = 5000 + (1/4)5000 = 6250.
Success!
The correct answer is D.
Note that we had to try only ONE answer choice -- a very efficient way to solve the problem.
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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
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These types of qstns can be approached by reverse tracking-
At the end of 4th year no. of tree- 6250
Let n, be the no. of trees at the end of 3rd year.
so n+(1/4)n= 6250
5n/4=6250
n= 5000
similarly let n, be the trees at the end of second year
5n/4= 5000
n=4000
and let n be the tress at the end of first year
5n/4= 4000
n=3200
Therefore trees at the beginning will be : 5n/4= 3200
n= 2560
At the end of 4th year no. of tree- 6250
Let n, be the no. of trees at the end of 3rd year.
so n+(1/4)n= 6250
5n/4=6250
n= 5000
similarly let n, be the trees at the end of second year
5n/4= 5000
n=4000
and let n be the tress at the end of first year
5n/4= 4000
n=3200
Therefore trees at the beginning will be : 5n/4= 3200
n= 2560
