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22 Sep 2017, 00:44
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
72% (02:11) correct
28%
(02:20)
wrong
based on 72
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A board of length L feet is cut into two pieces such that the length of one piece is 1 foot more than twice the length of the other piece. Which of the following is the length, in feet, of the longer piece?
(A) (L + 2)/2
(B) (2L + 1)/2
(C) (L – 1)/2
(D) (2L + 3)/3
(E) (2L + 1)/3
(A) (L + 2)/2
(B) (2L + 1)/2
(C) (L – 1)/2
(D) (2L + 3)/3
(E) (2L + 1)/3
22 Sep 2017, 01:26
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let two piece length be x and y
=> x+y =L
Given x=2y+1 <= longer piece
=> y=\(\frac{x-1}{2}\)
x+y = L => \(x+\frac{x-1}{2} = L\) => \(\frac{3x-1}{2}= L\) => \(3x-1= 2L\) => \(x= \frac{2L+1}{3}\)
Answer: E
=> x+y =L
Given x=2y+1 <= longer piece
=> y=\(\frac{x-1}{2}\)
x+y = L => \(x+\frac{x-1}{2} = L\) => \(\frac{3x-1}{2}= L\) => \(3x-1= 2L\) => \(x= \frac{2L+1}{3}\)
Answer: E
23 Sep 2017, 08:47
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Bunuel
A board of length L feet is cut into two pieces such that the length of one piece is 1 foot more than twice the length of the other piece. Which of the following is the length, in feet,
of the longer piece?
(A) (L + 2)/2
(B) (2L + 1)/2
(C) (L – 1)/2
(D) (2L + 3)/3
(E) (2L + 1)/3
Choosing numbers here works well: the answer choices do not require lengthy calculation. The algebra here can be time-consuming. of the longer piece?
(A) (L + 2)/2
(B) (2L + 1)/2
(C) (L – 1)/2
(D) (2L + 3)/3
(E) (2L + 1)/3
It's probably easiest to pick the length of the short piece first.
Short piece = 2
Long piece, ((2*short)+1) = 5
L = (2 + 5) = 7
Using L = 7, go through the answer choices until one of them yields the answer 5, the length of the longer piece.
(A) (L + 2)/2 is (7+2)/2 = 4.5, not an integer, NOT a match
(B) (2L + 1)/2 is (14+1)/2 = not an integer, NOT a match
(C) (L – 1)/2 is (7-1)/2 = 3: NOT a match
(D) (2L + 3)/3 is (14+3)/3: not an integer, NOT a match
(E) (2L + 1)/3 is (14+1)/3 = 5. This IS a match.
Answer E
Sidenote: With experience, you learn when not to use 1. (I rarely use it, except for number properties
in which the range -2 < x < 2 is probably at issue. (Test 1, 0, -1, 1/2, and -1/2 in such cases.)
If the short piece = anything from 2 to 10, the result is three non-integer answers, one integer answer that does not match, and E as the correct answer.
If you choose "shorter piece = 1," two answers are correct. The longer piece is 3, and L = 4. In that case alone, answers A and E both work. But assigning any other single-digit length to the short piece will quickly distinguish A as incorrect and E as correct.
