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

It is currently 14 Nov 2018, 23:04

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • $450 Tuition Credit & Official CAT Packs FREE

     November 15, 2018

     November 15, 2018

     10:00 PM MST

     11:00 PM MST

    EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299)
  • Free GMAT Strategy Webinar

     November 17, 2018

     November 17, 2018

     07:00 AM PST

     09:00 AM PST

    Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

How many tiles of the size and shape shown above are needed to complet

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50585
How many tiles of the size and shape shown above are needed to complet  [#permalink]

Show Tags

New post 03 Oct 2017, 23:34
1
1
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

72% (01:21) correct 28% (01:21) wrong based on 39 sessions

HideShow timer Statistics

Image
How many tiles of the size and shape shown above are needed to completely cover a rectangular floor measuring 30 feet by 20 feet?

(A) 120
(B) 150
(C) 200
(D) 250
(E) 300


Attachment:
2017-10-04_1121_003.png
2017-10-04_1121_003.png [ 3.39 KiB | Viewed 857 times ]

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Senior SC Moderator
avatar
V
Joined: 22 May 2016
Posts: 2094
Premium Member CAT Tests
How many tiles of the size and shape shown above are needed to complet  [#permalink]

Show Tags

New post 04 Oct 2017, 07:57
Bunuel wrote:
Image
How many tiles of the size and shape shown above are needed to completely cover a rectangular floor measuring 30 feet by 20 feet?

(A) 120
(B) 150
(C) 200
(D) 250
(E) 300


Attachment:
2017-10-04_1121_003.png

I think we must assume that there is a large square with side length = 2, and a missing piece that is also a square, with side length = 1.

We do not know if the figure has right angles. Two adjacent equal sides, without more, cannot render, definitively, these figures as squares.

The "more" needed to be certain that, e.g., the larger figure (with half the right and bottom sides grayed out) is a square (not exhaustive):

1) it is a rectangle (rectangle with equal adjacent sides is a square), or

2) it is a parallelogram with two equal adjacent sides and one right angle at a vertex; or

3) 3 of the four vertices are right angles

Am I missing something? I cannot see a way to prove these figures are squares.

Assume the large figure is a square (which the prompt seems to suggest). Its side length = 2, its uncut area is (2*2) = 4

Asssume also that the large square has a square piece cut out.

The square piece cut out has side length = 1, area = 1

Total area of the tile is 4 - 1 = 3

The tiles are all the same shape. If the tile shown were rotated 180° (or, flipped on the diagonal, had its left lower corner where its right corner is), it would interlock with itself to form a rectangle with length = 3 and width = 2.

Area of rectangle formed by two interlocked tiles =
(2) * (tile with area 3) = 6, OR

Rectangle formed by interlocked tiles has area of LW = (2*3) = 6

Floor area = LW = (30*20) = 600

Floor area / small rectangles' area:

600/6 = 100 tiles of area 6

But it takes TWO tiles to make the rectangular area of 6

So 100 rectangles * 2 tiles per rectangle = 200 tiles

Answer C
Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3302
Location: India
GPA: 3.12
Premium Member CAT Tests
How many tiles of the size and shape shown above are needed to complet  [#permalink]

Show Tags

New post 04 Oct 2017, 08:28
Image

From the figure drawn for a tile, we can deduce that 2 such tiles will cover an area of 6 ft.
Since we need to cover a rectangular floor measuring 30 ft by 20 ft(which is 600ft),
we would need 100 such sets.

Therefore, we need exactly 200 tiles to cover the rectangular floor(Option C)
_________________

You've got what it takes, but it will take everything you've got

Senior Manager
Senior Manager
User avatar
P
Joined: 02 Jul 2017
Posts: 293
Concentration: Entrepreneurship, Technology
GMAT 1: 730 Q50 V38
GMAT ToolKit User
Re: How many tiles of the size and shape shown above are needed to complet  [#permalink]

Show Tags

New post 04 Oct 2017, 08:36
We have to find out for given tile shape, how many tiles we can fit in a rectangular floor of 30feet * 20 feet.

If we look at the tile image, we can see that by combining 2 tiles ( tile image + inverting the image) a rectangle of size 3*2 can be formed (Check the attached figure)
So we can combine 2 tiles, form a rectangle and than place it in rectangular floor

Rectangular tile size = 2*3 = 6
Area of rectangular floor = 30*20 = 600

No. of rectangular tiles that can be used on floor = 600/6 = 100

So number of give tiles = 2* number of rectangular tiles = 2* 100 = 200

Answer: C
Attachments

Tile combine.png
Tile combine.png [ 2.43 KiB | Viewed 696 times ]

Manager
Manager
avatar
G
Joined: 01 Feb 2017
Posts: 166
Re: How many tiles of the size and shape shown above are needed to complet  [#permalink]

Show Tags

New post 05 Oct 2017, 00:05
We have to combine two L-shaped tiles to form one composite unit of size 3ft x 2ft.

Now, we need 100 composite units to cover a floor of dimensions 30ft x 20ft : 10 units each along length and width respectively.

100 Composite units amount to 200 L-shaped tiles.

Hence, Answer C.

Posted from my mobile device
Intern
Intern
avatar
B
Joined: 11 Sep 2013
Posts: 19
Schools: CBS '19
Re: How many tiles of the size and shape shown above are needed to complet  [#permalink]

Show Tags

New post 18 Aug 2018, 08:32
Area to be covered => 30x20=600

Area of the given (L) shape => {area of entire shape including the missing part} - {area of the missing part} => 4-1=3

Solution: \(\frac{600}{3}\)=200

Correct answer (C)
GMAT Club Bot
Re: How many tiles of the size and shape shown above are needed to complet &nbs [#permalink] 18 Aug 2018, 08:32
Display posts from previous: Sort by

How many tiles of the size and shape shown above are needed to complet

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.