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

 It is currently 19 May 2019, 09:38

### 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

# The perimeter of a square is equal to the perimeter of a rectangle.

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
Intern
Joined: 02 Jul 2014
Posts: 1
Location: Bangladesh
Concentration: Finance, Leadership
WE: Asset Management (Commercial Banking)
The perimeter of a square is equal to the perimeter of a rectangle.  [#permalink]

### Show Tags

29 Aug 2017, 12:34
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

### HideShow timer Statistics

The perimeter of a square is equal to the perimeter of a rectangle. The length of the rectangle is three times longer than is width having total area of 1200 sq.meter. What will be the total cost if the total area of the square is covered with stones having a dimension of 50 cm.sq. each and if Rs. 50 is charged for placing a stone in the square?

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Senior SC Moderator
Joined: 22 May 2016
Posts: 2731
The perimeter of a square is equal to the perimeter of a rectangle.  [#permalink]

### Show Tags

29 Aug 2017, 14:49
Dewgmat wrote:
The perimeter of a square is equal to the perimeter of a rectangle. The length of the rectangle is three times longer than is width having total area of 1200 sq.meter. What will be the total cost if the total area of the square is covered with stones having a dimension of 50 cm.sq. each and if Rs. 50 is charged for placing a stone in the square?

Find the perimeter of the rectangle using area; then find perimeter and area of square; convert area of square into square centimeters (we have meters); and find total cost for placing some number of stones on the larger square.

1) Perimeter of rectangle

Area of rectangle, where length is three times longer than width, x = width :

$$3x * x = 1,200$$

$$3(x^2) = 1,200$$

$$x^2 = 400$$

$$x = 20$$

Rectangle length = 3x = 60m
Rectangle width = x = 20m
Rectangle perimeter = 2L + 2W = 160m

2) Perimeter and area of square, and convert to square centimeters

Perimeter of rectangle =
Perimeter of square, where
s = side of square

160 m = 4s
s = 40 m

We need big square's area in sq cm.

Side = 40m * 100cm/1m = 4,000cm
Area = $$4,000^2 = 16 * 10^6$$ sq cm

3) Total cost

We could stop here. We need to divide large square area by the area of smaller squares to see how many will fit, but then we will multiply by a unit cost that is exactly equal in value to the area, in sq cm, of the little squares.

In other words, we will divide by 50 for the area to get the number of tiles, and then multiply by 50 to get the cost of that many tiles.

The cost, therefore, is the total area in rupees -- because (* 50) then (/ 50) brings us back to original.

TOTAL COST Rs. 16,000,000

If you had not noticed that shortcut, you could rewrite area as

$$1600 * 10^4$$ sq cm (to divide by 50 easily)

$$\frac{(1600 * 10^{4})}{50} = 32 * 10^4$$ = number of smaller squares that will fit in larger square

If it costs Rs. 50 to put a stone on each small square, then the total cost is

(Rs. 50)(32)(10$$^4$$)

From above we know (32 * 50 = 1600), so total cost is Rs. 1600 * 10$$^4$$, or

Rs. 16,000,000

A few questions:

1) Do you have answer choices so that this question is more like the real GMAT?

2) What is the source of this question?

3) What is the answer and/or does anyone see a mistake in my calculations?

4) Is there a shorter way to do this problem? I don't think so. Just checking.

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________
Listen, are you breathing just a little, and calling it a life?
-- Mary Oliver

For practice SC questions go to SC Butler, here.

Please DO NOT write short answers in your verbal posts! Such answers will be deleted.
The perimeter of a square is equal to the perimeter of a rectangle.   [#permalink] 29 Aug 2017, 14:49
Display posts from previous: Sort by

# The perimeter of a square is equal to the perimeter of a rectangle.

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

 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®.