GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 01 Jun 2020, 06:23 ### 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

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.  # The sides of rectangle A are each multiplied by x to form rectangle B

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 64155
The sides of rectangle A are each multiplied by x to form rectangle B  [#permalink]

### Show Tags

10 00:00

Difficulty:   65% (hard)

Question Stats: 65% (03:05) correct 35% (03:08) wrong based on 113 sessions

### HideShow timer Statistics

The sides of rectangle A are each multiplied by x to form rectangle B and by y to form rectangle C. When multiplied by x, the area of rectangle A equals 10, and when multiplied by y, the area of rectangle A equals 5. If the difference in area between rectangle B and C is 300, what is x−y?

A. 5
B. 20
C. 30
D. 50
E. 60

_________________
Senior Manager  G
Joined: 17 Oct 2016
Posts: 298
Location: India
Concentration: Operations, Strategy
GPA: 3.73
WE: Design (Real Estate)
Re: The sides of rectangle A are each multiplied by x to form rectangle B  [#permalink]

### Show Tags

B

Let area of rectangle A be lb.

Hence area of rectangle B is lb*x^2 and rectangle C is lb*y^2.
Also lb*x=10 and lb*y=5.
x=10/lb and y=5/lb.

Also lb(x^2-y^2)=300
Solving we get lb=1/4 and x=40 y=20
Hence x-y=20

Sent from my iPhone using GMAT Club Forum
Intern  B
Joined: 31 Dec 2017
Posts: 27
Concentration: Finance
Re: The sides of rectangle A are each multiplied by x to form rectangle B  [#permalink]

### Show Tags

3
Bunuel wrote:
The sides of rectangle A are each multiplied by x to form rectangle B and by y to form rectangle C. When multiplied by x, the area of rectangle A equals 10, and when multiplied by y, the area of rectangle A equals 5. If the difference in area between rectangle B and C is 300, what is x−y?

A. 5
B. 20
C. 30
D. 50
E. 60

Length = $$l$$, Width = $$w$$.
Area of rectangle A = $$lw$$.
Area of rectangle B = $$lx*wx = (x^2)lw$$.
Area of rectangle C = $$ly*wy = (y^2)lw$$.

$$lwx = 10, lwy = 5$$.
$$x = \frac{10}{(lw)}, y = \frac{5}{(lw)}$$
$$lw(x-y) = 10-5 = 5$$.

$$lw(x^2-y^2) = 300$$
$$lw(x+y)(x-y) = 300$$
$$5(x+y) = 300$$
$$(x+y) = 60$$.

$$\frac{10}{(lw)} + \frac{5}{(lw)} = 60$$
$$15lw = 60(lw)^2$$
$$lw = \frac{15}{60} = \frac{1}{4}.$$

$$(x-y) = 5*4 = 20$$.
Intern  B
Joined: 03 Jun 2015
Posts: 21
GMAT 1: 710 Q49 V44
GPA: 3.58
WE: Information Technology (Computer Software)
Re: The sides of rectangle A are each multiplied by x to form rectangle B  [#permalink]

### Show Tags

1
2
Assumption : Let area of rectangle A be a.b where a and b are sides of rectangle

Given : Area of B = x^2(a.b) , Area of C = y^2(a.b)
x*(a.b) = 10 ------------------ 1
y*(a.b)=5 ------------------ 2
ab(x^2-y^2) = 300 ------------------ 3

Required : x-y = ?

Solution : Add eq 2 and eq 1, we get a.b(x+y) = 15 ------------------ 4
Divide eq 3 with eq 4, we get x-y=20

_________________
A dream doesn't become reality through magic; it takes sweat, determination and hard work.
Intern  B
Joined: 13 Mar 2019
Posts: 27
Re: The sides of rectangle A are each multiplied by x to form rectangle B  [#permalink]

### Show Tags

1
If a is the area of rect A,
then xa = 10
ya = 5
=> x = 2y

Now (x^2)*a - (y^2)*a = 300
4(y^2)a - (y^2)*a = 300
(y^2)*a = 100
a y y =100
5y = 100
y =20
And hence x = 40.
Manager  G
Joined: 08 Jan 2018
Posts: 90
Re: The sides of rectangle A are each multiplied by x to form rectangle B  [#permalink]

### Show Tags

So we have three rectangles:
Let, Rectangle A = a * b
then, Rectangle B = ax * bx = $$x^2 * a * b$$
then, Rectangle C = ay * by = $$y^2 * a * b$$

Given,
When multiplied by x, the area of rectangle A equals 10 = x * a * b = 10 -> (a)
when multiplied by y, the area of rectangle A equals 5 = y * a * b = 5 -> (b)

The difference in the area between rectangle B and C is 300 = $$x^2*a*b - y^2*a*b = 300$$ => $$(x^2 - y^2) (a * b) = 300$$ => $$(x + y)(x - y)(a * b) = 300$$ ->(c)

(x + y)(a * b) = 15 -> (d)

Diving (c) by (d)
$$\frac{(x + y)(x - y)(a * b)}{(x + y)(a * b)}$$ = $$\frac{300}{15}$$
=> $$(x - y) = 20$$ Re: The sides of rectangle A are each multiplied by x to form rectangle B   [#permalink] 12 Aug 2019, 17:14

# The sides of rectangle A are each multiplied by x to form rectangle B  