BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

square countertop

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 274
Joined: Fri Sep 18, 2015 10:58 pm
Thanked: 12 times
Followed by:1 members
GMAT Score:530

square countertop

by vishalwin » Wed Nov 25, 2015 3:53 am
A square countertop has a square tile inlay in the center, leaving an untiled strip of uniform width around the tile. If the ratio of the tiled area to the untiled area is 25 to 39, which of the following could be the width, in inches, of the strip?

I. 1
II. 3
III. 4

A) I only
B) II only
C) I an II only
D) I and III only
E) I, II, and III
Thanks & Regards
vishalwin
------------------------------------
GMAT Score - 530
I will BEAT the GMAT!
Top
Source: — Problem Solving |
User avatar
Legendary Member
Posts: 2135
Joined: Mon Feb 03, 2014 9:26 am
Location: https://martymurraycoaching.com/
Thanked: 955 times
Followed by:140 members
GMAT Score:800

by MartyMurray » Wed Nov 25, 2015 5:05 am
This is a trick question.

You see the values and maybe get the impression that you have to calculate something, but here's the thing.

For any value of the width of the strip, you can create a strip and an inner square with the right dimensions to create the ratio of areas 25 to 39.

Basically what you have are an inner square and and outer square. The ratio of the areas of the inner square and outer square is 25:(25 + 39) or 25:64

So what you need to create are two squares such that the ratio of their sides is √25:√64 = 5:8

Any two squares such that their sides are 5x and 8x will work.

Sides of the smaller square: 5x
Sides of the larger square: 5x + 2(the width of the strip) or 8x

Using the choices given, we can create the following sets of lengths of sides.

I. 5x + 2(1) = 8x
II. 5x + 2(3) = 8x
III. 5x + 2(4) = 8x

You can plug in any positive number for width of the strip and come up with a corresponding value for x.

So any positive width is possible, and the correct answer is E.
Marty Murray
Perfect Scoring Tutor With Over a Decade of Experience
MartyMurrayCoaching.com
Contact me at [email protected] for a free consultation.
Top
GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pm
Location: East Bay all the way
Thanked: 625 times
Followed by:119 members
GMAT Score:780

by Matt@VeritasPrep » Fri Nov 27, 2015 12:42 am
I think the key here is that the width need not be an integer.

We know that the ratio of Tile : Total = 25 : 64. Hence we could think of the tile as having a width of length x, and the entire countertop as having a width of (8/5)x. That gives us a strip of width (3/5)x.

(3/5)x = 1, (3/5)x = 3, and (3/5)x = 4 all give positive values of x, so all are possible.
Top
Post new topic Post Reply
• Page 1 of 1