Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 16 Jul 2019, 12:09

### 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

# If the radius of a circle is decreased by 10%, by what percent is its

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 56244
If the radius of a circle is decreased by 10%, by what percent is its  [#permalink]

### Show Tags

08 Mar 2018, 02:18
00:00

Difficulty:

15% (low)

Question Stats:

88% (00:42) correct 13% (01:00) wrong based on 54 sessions

### HideShow timer Statistics

If the radius of a circle is decreased by 10%, by what percent is its area decreased?

(A) 10

(B) 19

(C) 21

(D) 79

(E) 81

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 56244
Re: If the radius of a circle is decreased by 10%, by what percent is its  [#permalink]

### Show Tags

08 Mar 2018, 02:18
Bunuel wrote:
If the radius of a circle is decreased by 10%, by what percent is its area decreased?

(A) 10

(B) 19

(C) 21

(D) 79

(E) 81

For other subjects:
ALL YOU NEED FOR QUANT ! ! !
_________________
examPAL Representative
Joined: 07 Dec 2017
Posts: 1074
Re: If the radius of a circle is decreased by 10%, by what percent is its  [#permalink]

### Show Tags

08 Mar 2018, 02:25
Bunuel wrote:
If the radius of a circle is decreased by 10%, by what percent is its area decreased?

(A) 10

(B) 19

(C) 21

(D) 79

(E) 81

We'll pick an easy number which can help us make the calculation.
This is an Alternative approach.

Say the original radius was 10. Then the original area is pi*10^2 = 100pi
If the radius decreases by 10% it is now 9. Then the new area is pi*9^2 =81pi
This is a decrease of 100pi - 81pi = 19pi.
Since 19pi 19% of 100pi, our answer is 19%.

_________________
Senior SC Moderator
Joined: 22 May 2016
Posts: 3063
If the radius of a circle is decreased by 10%, by what percent is its  [#permalink]

### Show Tags

08 Mar 2018, 10:58
Bunuel wrote:
If the radius of a circle is decreased by 10%, by what percent is its area decreased?

(A) 10

(B) 19

(C) 21

(D) 79

(E) 81

Scale factor:
All changes in dimension of a figure have to do with length. Length is increased or decreased by a scale factor, $$k$$

Decrease in one length only (one dimension) = multiply by $$k$$

Decrease in area?
Area = length*length (two dimensions)
Multiply by $$(k*k)= k^2$$

Original area = A
New area = (original area)*($$k^2$$)
(.9)*(.9)*(A) = .81A

Percent decrease: $$\frac{New-Old}{Old}*100$$

$$(\frac{-.81A-A}{A}*100) =\frac{|-.19|}{1}*100= 19$$
% decrease

* Decrease in volume, e.g. cube, if change is uniform = (length * length * length) = multiply by $$(k*k*k) = k^3$$
_________________
SC Butler has resumed!
Get two SC questions to practice, whose links you can find by date, here.

Tell me, what is it you plan to do with your one wild and precious life? -- Mary Oliver
If the radius of a circle is decreased by 10%, by what percent is its   [#permalink] 08 Mar 2018, 10:58
Display posts from previous: Sort by