GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 23 Jun 2018, 00:50

### 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

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# A board of length L feet is cut into two pieces such that the length

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 46291
A board of length L feet is cut into two pieces such that the length [#permalink]

### Show Tags

22 Sep 2017, 00:44
00:00

Difficulty:

45% (medium)

Question Stats:

75% (01:35) correct 25% (00:46) wrong based on 24 sessions

### HideShow timer Statistics

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

_________________
Senior Manager
Joined: 02 Jul 2017
Posts: 294
GMAT 1: 730 Q50 V38
Re: A board of length L feet is cut into two pieces such that the length [#permalink]

### Show Tags

22 Sep 2017, 01:26
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 => $$x+\frac{x-1}{2} = L$$ => $$\frac{3x-1}{2}= L$$ => $$3x-1= 2L$$ => $$x= \frac{2L+1}{3}$$

SC Moderator
Joined: 22 May 2016
Posts: 1759
Re: A board of length L feet is cut into two pieces such that the length [#permalink]

### Show Tags

23 Sep 2017, 08:47
Bunuel wrote:
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.

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.

Sidenote: If the short piece = anything from 1 to 10, in all but one case, the result is three non-integer answers, one integer answer that does not match, and E as the correct answer.

The one exception: if the shorter piece = 1. 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.

_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

Re: A board of length L feet is cut into two pieces such that the length   [#permalink] 23 Sep 2017, 08:47
Display posts from previous: Sort by