square countertop

Expert replies

vishalwin: Master | Next Rank: 500 Posts; Posts: 274; Joined: Fri Sep 18, 2015 10:58 pmFollowed by: 1 member; Thanked: 12 times; GMAT Score:530

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!

Like this post

Source: Beat The GMAT — Problem Solving | Wed Nov 25, 2015 3:53 am

MartyMurray: Legendary Member; Posts: 2135; Joined: Mon Feb 03, 2014 9:26 amFollowed by: 140 members; Location: https://martymurraycoaching.com/; Thanked: 955 times; 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 âˆš25:âˆš64 = 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.

Like this post

Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; 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.

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review