Of 200 people surveyed, 80 percent own a cellular phone and 45 percen

Question

Of 200 people surveyed, 80 percent own a cellular phone and 45 percent own a pager. If all 200 people surveyed own a cellular phone, or a pager, or both, what percent of those surveyed either do not own a cellular phone or do not own a pager?

(A) 35%
(B) 45%
(C) 55%
(D) 65%
(E) 75%

Show Spoiler

Attachment:

Screen Shot 2016-07-18 at 5.24.51 PM.png

msk0657 · Accepted Answer

This is how I tried.

Since this is percentage and number type, converting all into percentages. Here we are asked the percentage of people who don't have neither CP or Pager.

We are given 80% hold CP i.e. 20% does't have CP. Similarly for the pager.

Hence 75%. Option E.

gauz · Answer

we can...

80% who own cellular phone = 160
45% own pager = 90

total who own cellular phone = 160+90=250. However total number of people is 200 so 250-200=50 people own both..

now we need people who either own a cp or a pager (but not both), so we substract the 50 from 200=150 is our required population.

(150\200)*100 = 75.

HARRY113 · Answer

My option E) Straight forward answer if you follow 2x2 matrix method..

cell , not cell Pag - - 90 N. pag - - 110 160 40 200 Required = 110+90 = 150 therefore, 150/200 = 75%.

thangvietname · Answer

redundant information.
we do not need the number 200 to find oa is e.

Abhishek009 · Answer

n ( C ∪ P ) = n ( C ) + n ( P ) - n ( C ∩ P )

200 = 160 + 90 - n ( C ∩ P )

Or, n ( C ∩ P ) = 250 - 200

Or, n ( C ∩ P ) = 50

So, Percentage of people owning both a Cell Phone & Pager is 25% and 75% owns a Cell Phone + Pager...

Thus , 75% either do not own a cellular phone or do not own a pager..
  
Hence, answer will be (E)...

Revant · Answer

We know : T (total) - N (neither)= A + B - K(both)
Total : 100% (given)
Neither : 0 % (given)

100- 0 = 80 + 45 + K
=> K = 125-100= 25

Now we know that A= A1 + K i.e. A= Own cellular phone, K = own cellular phone and pager, A1= own's cellular phone only and not pager , => 80=A1 + 25 =>A1= 55
Similarly B=B1 + K, => B1= 20

So A1 + B1 = 55+20 = 75

Ans : E

Cez005 · Answer

The 80% (160) that own a cell phone and 45% (90) that own a pager also include those that own both. If c=cell phone owners only, p=pager owners only and b=both, then: Total=(c+b)+(p+b)-b
So, 200=160+90-b
b=50, so 150 own only one of either a pager or cell. 75%.

If you like and/or agree then kudos. If you have a better method, please comment!

sid117 · Answer

80% own cell phone, 20% do not.
45% own pager, 55% do not.
So percent of those who either do not own cell phone or do not own pager is 20% + 55% = 75%

EMPOWERgmatRichC · Answer

Hi All,

This question is a modified version of a typical Overlapping Sets question. You can solve it with the tic-tac-toe board or the Overlapping Sets Formula:

Total = (Group 1) + (Group 2) - Both + Neither

In this prompt, we're told that ALL 200 people own at least one of the two items, so the 'Neither' group would be 0.

80% of 200 = 160 people own a cell phone 
45% of 200 = 90 people own a pager

Plugging that data into the formula, we have...

200 = 160 + 90 - Both

200 = 250 - Both 
Both = 50

Since 50 of the 200 people have both items, the other 200 - 50 = 150 people have just one item. As a percentage of the total, that is 150/200 = 75%

Final Answer:  E

GMAT assassins aren't born, they're made, 
Rich

NandishSS · Answer

HI  Bunuel ,  niks18 ,  Gladiator59 ,

either do not own a cellular phone or do not own a pager  Does it mean only a cellular phone and only pager?

niks18 · Answer

Hi  NandishSS

yes your understanding is correct. You can visualize the question as

Those who do not own cellular phone = Those who own pagers only

Those who do not own pager = Those who own cellular phones only

So those who do not own a cellular phone or a pager = Those who own only cellular phone + those who own only pager

ScottTargetTestPrep · Answer

We can use the formula for overlapping sets for this problem:

Total = #Cell + #Pager - Both + Neither

200 = 160 + 90 - x + 0

200 = 250 - x

50 = x

We see that 50 individuals own both a cell phone and a pager. Thus, the number of people who own a cell phone and not a pager is 160 - 50 = 110.
 
Similarly, of the 90 individuals who own a pager, there are 90 - 50 = 40 who own a pager and not a cell phone.

Thus, there are 110 + 40 = 150 who either do not own a cell phone or do not own a pager. 
This number represents 150/200 = 3/4 x 100% = 75% of the people surveyed.

Answer: E

dabaobao · Answer

We don't need to use the actual numbers since we need a percent as our answer, saving us some calculations.

Most efficient way to do this Q is to use a double-set matrix as shown in the attachment.

"either do not own a cellular phone or do not own a pager" => ~C + ~P = 20 + 55 = 75%

ANSWER: E

alessandro77 · Answer

I don't know why all answers were extremely complicated, this is the simplest solution.

80% own a cell phone, so 20% do not own a cellphone.
45% own a pager, so 55% do not own a pager
20%+55%=75%

v12345 · Answer

Percent who do not own a cellular phone = 100 - 80 = 20%
Percent who do not own a pager = 100 - 45 = 55%
Percent of those surveyed either do not own a cellular phone or do not own a pager = 20 + 55 = 75%

Hence, the OA is (E).

Birthday109 · Answer

Pag 
 Pag' 
 Total 
 
  Phone

80 
 
  Phone'

20 
 
  Total 
 45 
 55 
 100%

I believe this question can be solved using the double matrix method. The question asks for do NOT own a phone OR do NOT own a pager, so I did 20+55=75%

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Of 200 people surveyed, 80 percent own a cellular phone and 45 percen

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

GMAT Problem Solving (PS) Questions

Of 200 people surveyed, 80 percent own a cellular phone and 45 percen

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