• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Award-winning private GMAT tutoring
Register now and save up to $200 Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

tagged by: Vincen

# This topic has 2 expert replies and 0 member replies

Instead of walking along two adjacent sides of a rectangular field, Sabrina took a short cut along the diagonal and saved a distance equal to half the longer side. Then the ratio of the shorter side to the longer side is:

(A) 1:4
(B) 3:8
(C) 1:2
(D) 2:3
(E) 3:4

The OA is the option E.

I liked this question, but I couldn't solve it. Which is the equation that we get from the statement? Experts, may you help me? Thanks in advanced.

### GMAT/MBA Expert

Elite Legendary Member
Joined
23 Jun 2013
Posted:
9765 messages
Followed by:
487 members
2867
GMAT Score:
800
Hi Vincen,

We're told that instead of walking along two adjacent sides of a rectangular field, Sabrina took a short cut along the diagonal and saved a distance equal to HALF of the longer side. We're asked for the ratio of the shorter side to the longer side. Rather than try to approach this with a complex series of calculations, you can take advantage of the 'patterns' that exist in math (especially in Geometry) and the Answer choices to TEST THE ANSWERS.

To start, we're clearly going to be dealing with a right triangle, so the Pythagorean Theorem (A^2 + B^2 = C^2) will come into play. When using this formula, it's important to realize that in MOST cases, the 3 values will NOT all be integers. Choose 2 random numbers for A and B and the likely result will be that C is a non-integer. Here though, we're told that walking the diagonal length of the field 'saves' EXACTLY HALF the length of the long side. Mathematically-Speaking, that would be....

A + B - (1/2)(B) = C where A is the short side, B is the long side and C is the diagonal
A + (1/2)(B) = C

This equation heavily implies that A, B and C are ALL going to be INTEGERS - and if you know the common Pythagorean Triplets (3/4/5 and 5/12/13), then there's a logical answer choice to test first....

IF.... the short side is 3 and the long side is 4, then we'll have a 3/4/5 right triangle and the diagonal will be 5.
Here, the diagonal IS equal to the short side + 1/2 of the long side (re: 3 + (1/2)(4) = 3 + 2 = 5). This is an exact match for what we were told, so this MUST be the answer!

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

### GMAT/MBA Expert

GMAT Instructor
Joined
09 Apr 2015
Posted:
1461 messages
Followed by:
16 members
39
Vincen wrote:
Instead of walking along two adjacent sides of a rectangular field, Sabrina took a short cut along the diagonal and saved a distance equal to half the longer side. Then the ratio of the shorter side to the longer side is:

(A) 1:4
(B) 3:8
(C) 1:2
(D) 2:3
(E) 3:4
We can let D = the diagonal, S = the shorter side and L = the longer side. From the information in the problem, we see that:

S + L = D + L/2

S + L/2 = D

Furthermore, we can use the Pythagorean theorem:

S^2 + L^2 = D^2

If we square the equation S + L/2 = D, we have:

(S + L/2)(S + L/2) = D^2

S^2 + L^2/4 + SL = D^2

Substituting D^2 by S^2 + L^2, we have:

S^2 + L^2/4 + SL = S^2 + L^2

SL = 3L^2/4

4SL = 3L^2

4S = 3L

S/L = 3/4

_________________
Jeffrey Miller Head of GMAT Instruction

### Top First Responders*

1 Jay@ManhattanReview 81 first replies
2 Brent@GMATPrepNow 67 first replies
3 fskilnik 54 first replies
4 GMATGuruNY 37 first replies
5 Rich.C@EMPOWERgma... 13 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 fskilnik

GMAT Teacher

201 posts
2 Brent@GMATPrepNow

GMAT Prep Now Teacher

155 posts
3 Scott@TargetTestPrep

Target Test Prep

105 posts
4 Jay@ManhattanReview

Manhattan Review

97 posts
5 GMATGuruNY

The Princeton Review Teacher

91 posts
See More Top Beat The GMAT Experts