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Jolene began building a picket fence by planting stakes in a
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08 Feb 2020, 05:54
08 Feb 2020, 05:54
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Jolene began building a picket fence by planting stakes in a row; the stakes were evenly spaced. After planting the first 10 stakes, Jolene measured the length of the row and found that the row was 27 feet long. She continued the row by planting another 10 stakes, then measured the length of the entire row. How many feet long was the row of stakes Jolene had planted?
(A) 37
(B) 54
(C) 57
(D) 60
(E) 81
(A) 37
(B) 54
(C) 57
(D) 60
(E) 81
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Official Answer
A,B,D,E
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Re: Jolene began building a picket fence by planting stakes in a
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09 Feb 2020, 08:24
09 Feb 2020, 08:24
GeminiHeat wrote:
Jolene began building a picket fence by planting stakes in a row; the stakes were evenly spaced. After planting the first 10 stakes, Jolene measured the length of the row and found that the row was 27 feet long. She continued the row by planting another 10 stakes, then measured the length of the entire row. How many feet long was the row of stakes Jolene had planted?
(A) 37
(B) 54
(C) 57
(D) 60
(E) 81
(A) 37
(B) 54
(C) 57
(D) 60
(E) 81
Let each stake be x feet wide and the gap between 2 stakes be y feet
For the first 10 stakes, there are 9 gaps: \(10x + 9y = 27\) ... (i)
After planting another 10 stakes, there are a total of 20 stakes, having 19 gaps.
Thus, total length = \(20x + 19y\)
Observe that, the total length for 20 stakes
\(20x + 19y = 2(10x + 9y) + y = 2 * 27 + y = 54 + y\)
Thus, the total length is 54 (if y = 0) or greater than 54
Working with the options B, C, D, E:
Option B: 54 + y = 54 => y = 0, i.e. there is no gap between the stakes - possible
Option C: 54 + y = 57 => y = 3
=> From (i): x = 0, which implies that the stakes have zero width - not possible
For options D and E, the value of y will be greater than 3 and hence, x will be negative - not possible
Thus, the only possible answer is B
I feel there is a mistake in the data given - kindly check once
gmatclubot
Re: Jolene began building a picket fence by planting stakes in a [#permalink]
09 Feb 2020, 08:24
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