The organizers of a fair projected a 25 percent increase in

Question

The organizers of a fair projected a 25 percent increase in attendance this year over that of last year, but attendance this year actually decreased by 20 percent. What percent of the projected attendance was the actual attendance?

(A) 45%
(B) 56%
(C) 64%
(D) 75%
(E) 80%

(A) 45%
(B) 56%
(C) 64%
(D) 75%
(E) 80%

Bunuel · Accepted Answer

SOLUTION

The organizers of a fair projected a 25 percent increase in attendance this year over that of last year, but attendance this year actually decreased by 20 percent. What percent of the projected attendance was the actual attendance?

(A) 45%
(B) 56%
(C) 64%
(D) 75%
(E) 80%

(A) 45%
(B) 56%
(C) 64%
(D) 75%
(E) 80%

Last year attendance = 100 (assume);
Projected Attendance = 125;
Actual Attendance = 80.

The actual attendance therefore was (Actual)/(Project) = 80/125 *100 = 64$ of the projected attendance.

Answer: C.

sanjoo · Answer

C..

Assume last year attendence ..100====expected increased of 25%========> 125

100..actuall decreased of 20% ==================================>80

actuall/expected... 80/125=====================================16/25==64%...

64% is the ans

kinjiGC · Answer

Let "X" be the last year attendance .
Projected attendance = 1.25X
Actual attendance = 0.8X
So .8/1.25 = (4/5)/(5/4) = 16/25 hence 64% - Option C)

nutshell · Answer

Let us assume the last year attendance as 100(easiest number to pick, since all are in percent).
Projected attendance = 25% increase(of 100) = 125
Actual attendance = 20% decrease(of 100) = 80

Actual attendance/Projected attendance = (80/125) = (16/25) = (16*4)/(25*4) = 64/100 = 64%

Ans is (C).

TroyfontaineMacon · Answer

I took  \frac{80}{125}  and reduced it to  \frac{16}{25}  and couldn't figure it out past that

sooooo

I made it  \frac{15}{25}  and reduced it into  \frac{3}{5}  and then multiplied it by two to get  \frac{6}{10}=60% 
and since  16>15   \frac{16}{25} > 60%

Answer C  was the only logical answer

arunspanda · Answer

The organizers of a fair projected a 25 percent increase in attendance this year over that of last year, but attendance this year actually decreased by 20 percent. What percent of the projected attendance was the actual attendance?

(A) 45%
(B) 56%
(C) 64%
(D) 75%
(E) 80%

(A) 45%
(B) 56%
(C) 64%
(D) 75%
(E) 80%

Projected attendance:  25 %  increase  = \frac{5}{4}

Actual attendance : decreased by  20% = \frac{4}{5}

\frac{Actual}{Projected} = \frac{4}{5}/\frac{5}{4} = \frac{16}{25} =\frac{64}{100}  or  64%

Answer:  (C)

dheeraj24 · Answer

Let Last year attendance be X;
Then Projected Attendance will be 1.25x ;
 Actual attendance will be 0.8x;
Question is asking us 0.8x is what percent of 1.25x ?

0.8x/1.25x = Y/100;

y=64 %;

unceldolan · Answer

Let's pick smart numbers:

Last year's attendance: 100
projected attendance this year: 125 (+25%)
actual attendance this year : 80 (-20 %)
80/125 = 16/25 = 64/100 = 64 %. C.

damybox · Answer

we can use a smart number to solve this problem quickly.

let's say the actual attendance was 100 at the beginning.
it easy to find that the projected attendence was 125, whereas the actual attendance was 80.

\frac{80}{125} =64%

answer C

Ndkms · Answer

From MGMAT

Questions with "What is X percent of Y" translates to

"What" translates to " Unknown "
"is" translates to " = "
"X" translates to " X "
"percent" translates to " /100 "
"of" translates to multiplication sign " * "
"Y" translates to "Y"

Hence Unknown = (X/100) * Y

Use the same logic and Smart Numbers in order to decode the question and generate the formula. You should end up with

Actual = X/100 Projected ... Plug the numbers and solve with respect to X. The answer should be C

diegocml · Answer

Say ' x ' is your total attendance last year.
Projected attendance:  \cfrac { 5 }{ 4 } x 
Actual attendance:  \cfrac { 4 }{ 5 } x 
' z ' is the 'What percent of the projected attendance the actual attendance was'

\cfrac { z }{ 100 } \left( \cfrac { 5 }{ 4 } ight) x=\cfrac { 4 }{ 5 } x\ \left( \cfrac { z }{ 100 } \left( \cfrac { 5 }{ 4 } ight) x=\cfrac { 4 }{ 5 } x ight) \div x\ \left( \cfrac { z }{ 100 } \left( \cfrac { 5 }{ 4 } ight) =\cfrac { 4 }{ 5 } ight) \ast \cfrac { 100\ast 4 }{ 5 } \ z=\cfrac { 16 }{ 25 } \ast 100\ z=64%

CyberStein · Answer

last year = 75 people
this year = 60 people (20% decrease from last year)

actual= 60
projected=100 (25% increase from 75 is 100)

60/100 = 60

closest answer is 64%; they wanted you to use 100, 125, but, 75 and 100 still work

therefore, ans is (C) 64%

totaltestprepNick · Answer

C https://www.youtube.com/watch?v=BJlL0TGSpVk Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience tutoring@totaltestprep.net

shwetakoshija · Answer

Given:   
 
 The organizers of a fair projected a 25% increase in attendance this year over last year. 
 But attendance this year actually decreased by 20%

To find:    What percent of the projected attendance was the actual attendance?

Solution:  
  Approach : Since the question and the choices only have percentages and no actual values themselves, we can simply plug in a suitable value for last year's attendance and work the problem using that value. For percentages, the cleanest value to assume is 100. Let's start:

Assume that the attendance last year was = 100 
 
  Then, projected attendance this year = 125 (25% more than 100)  
  But actual attendance this year = 80 (20% less than 100)

Now, we need to find what percent of 125 (projected) was 80 (actual).  
 
  (Actual/Projected) * 100  
  (80/125) * 100  
  = 64%

Correct Answer: C

Shweta Koshija  
  GMAT, GRE, SAT Coach for 10+ years

The organizers of a fair projected a 25 percent increase in

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

The organizers of a fair projected a 25 percent increase in

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards