• 7 CATs FREE!
If you earn 100 Forum Points

Engage in the Beat The GMAT forums to earn
100 points for \$49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS
Earn 10 Points Per Post
Earn 10 Points Per Thanks
Earn 10 Points Per Upvote

## The sum of the lengths of two pieces of rope is 65 feet. How long is the shorter piece?

##### This topic has expert replies
Legendary Member
Posts: 563
Joined: 01 Mar 2018
Followed by:1 members

### The sum of the lengths of two pieces of rope is 65 feet. How long is the shorter piece?

by Gmat_mission » Wed Jun 24, 2020 8:00 am

00:00

A

B

C

D

E

## Global Stats

The sum of the lengths of two pieces of rope is 65 feet. How long is the shorter piece?

(1) The lengths of the pieces of rope are in the ratio 8:5.
(2) One piece of rope is 15 feet longer than the other piece.

[spoiler]OA=D[/spoiler]

Source: GMAT Prep

Legendary Member
Posts: 1833
Joined: 02 Mar 2018
Followed by:3 members

### Re: The sum of the lengths of two pieces of rope is 65 feet. How long is the shorter piece?

by deloitte247 » Sat Jun 27, 2020 1:47 am

00:00

A

B

C

D

E

## Global Stats

Given that: x + y = 65 feet

Target question => How long is the shorter price?

Statement 1 =>The length of the pieces of rope are 8:5
$$x+y=65............eqn1$$
$$x:y=8:5$$
$$\frac{x}{y}=\frac{8}{5}$$
$$5x=8y\ and\ x=\frac{8y}{5}$$
$$Substitute\ x\ in\ eqn\ 1$$
$$x+y=65\ \ \ \ \ where\ x=\frac{8y}{5}$$
$$\frac{8y}{5}+y=65$$
$$\frac{8y+5y}{5}=65$$
$$\frac{13y}{13}=\frac{65\cdot5}{13}$$
$$y=25\ feet$$
$$Therefore,\ x+25=65$$
$$x=65-25=40\ feet;\ shorter\ piece\ =\ y=25ft$$
$$Statement\ 1\ is\ SUFFICIENT$$

Statement 2 => One piece is 15feet longer than the other piece
i.e x + y = 65; where x = y + 15
$$Therefore,\ y+15+y=65$$
$$\frac{2y}{2}=\frac{65-15}{2}$$
$$y=\frac{50}{2}=25\ feet$$
$$x+25=65$$
$$x=65-25=40\ feet$$
$$shorter\ piece\ =\ y=25\ feet$$
$$Statement\ 2\ is\ SUFFICIENT$$

Since each statement alone is SUFFICIENT,