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A piece of twine of length t is cut into two pieces.

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by M7MBA » Mon Apr 22, 2019 6:04 am

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Difficulty—

A piece of twine of length \(t\) is cut into two pieces. The length of the longer piece is 2 yards greater than 3 times the length of the shorter piece. Which of the following is the length, in yards, of the longer piece?

(A) \(\dfrac{t+3}{3}\)
(B) \(\dfrac{3t+2}{3}\)
(C) \(\dfrac{t-2}{4}\)
(D) \(\dfrac{3t+4}{4}\)
(E) \(\dfrac{3t+2}{4}\)

[spoiler]OA=E[/spoiler]

Source: Princeton Review
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by Brent@GMATPrepNow » Mon Apr 22, 2019 6:43 am
M7MBA wrote:A piece of twine of length \(t\) is cut into two pieces. The length of the longer piece is 2 yards greater than 3 times the length of the shorter piece. Which of the following is the length, in yards, of the longer piece?

(A) \(\dfrac{t+3}{3}\)
(B) \(\dfrac{3t+2}{3}\)
(C) \(\dfrac{t-2}{4}\)
(D) \(\dfrac{3t+4}{4}\)
(E) \(\dfrac{3t+2}{4}\)

A piece of twine of length t is cut into two pieces.
Let x = the length of the LONGER piece in yards
So, t - x = the length of the SHORTER piece in yards

The length of the longer piece is 2 yards greater than 3 times the length of the shorter piece.
In other words: (longer piece) = 3(shorter piece) + 2
In other words: x = 3(t - x) + 2

Which of the following is the length, in yards, of the longer piece?
So, we must solve for x
Take: x = 3(t - x) + 2
Expand right side: x = 3t - 3x + 2
Add 3x to both sides: 4x = 3t + 2
Divide both sides by 4 to get: x = (3t + 2)/4

Answer: E

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by [email protected] » Mon Apr 22, 2019 1:14 pm
Hi All,

We're told that a piece of twine of length T is cut into two pieces and that the length of the longer piece is 2 yards greater than 3 times the length of the shorter piece. We're asked for the length, in yards, of the longer piece. This question can be solved in a couple of different ways, including by TESTing VALUES.

IF....
the SHORTER piece = 2 yards, then...
the LONGER piece = (3)(2) + 2 = 8 yards and....
T = 2+8 = 10 yards

Thus, we're looking for an answer that equals 8 when T=10. There's only one answer that matches...

Final Answer: E

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Rich
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by Scott@TargetTestPrep » Tue Apr 23, 2019 6:54 pm
M7MBA wrote:A piece of twine of length \(t\) is cut into two pieces. The length of the longer piece is 2 yards greater than 3 times the length of the shorter piece. Which of the following is the length, in yards, of the longer piece?

(A) \(\dfrac{t+3}{3}\)
(B) \(\dfrac{3t+2}{3}\)
(C) \(\dfrac{t-2}{4}\)
(D) \(\dfrac{3t+4}{4}\)
(E) \(\dfrac{3t+2}{4}\)

[spoiler]OA=E[/spoiler]

Source: Princeton Review
We can create the equation:

L = 2 + 3S

and

L + S = t

S = t - L

Substituting, we have:

L = 2 + 3(t - L)

L = 2 + 3t - 3L

4L = 2 + 3t

L = (2 + 3t)/4

Answer: E

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[email protected]

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