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

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Of 200 people surveyed, 80 percent own a cellular phone and 45 percen  [#permalink]

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18 Jul 2016, 02:31
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25% (medium)

Question Stats:

79% (02:10) correct 21% (02:29) wrong based on 467 sessions

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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%

Attachment:

Screen Shot 2016-07-18 at 5.24.51 PM.png [ 840.86 KiB | Viewed 12428 times ]
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Re: Of 200 people surveyed, 80 percent own a cellular phone and 45 percen  [#permalink]

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18 Jul 2016, 02:43
1
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%.
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Re: Of 200 people surveyed, 80 percent own a cellular phone and 45 percen  [#permalink]

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18 Jul 2016, 02:58
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evannolimit wrote:
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%

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.
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Re: Of 200 people surveyed, 80 percent own a cellular phone and 45 percen  [#permalink]

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18 Jul 2016, 07:46
redundant information.
we do not need the number 200 to find oa is e.
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Re: Of 200 people surveyed, 80 percent own a cellular phone and 45 percen  [#permalink]

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13 Nov 2016, 06:15
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victory47 wrote:
redundant information.
we do not need the number 200 to find oa is e.

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.
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Re: Of 200 people surveyed, 80 percent own a cellular phone and 45 percen  [#permalink]

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13 Nov 2016, 09:23
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evannolimit wrote:
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%

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)...

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Re: Of 200 people surveyed, 80 percent own a cellular phone and 45 percen  [#permalink]

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06 Dec 2016, 11:05
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
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Re: Of 200 people surveyed, 80 percent own a cellular phone and 45 percen  [#permalink]

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14 Apr 2017, 20:20
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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!
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Re: Of 200 people surveyed, 80 percent own a cellular phone and 45 percen  [#permalink]

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18 Apr 2017, 13:38
2
Quote:
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?

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%
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Re: Of 200 people surveyed, 80 percent own a cellular phone and 45 percen  [#permalink]

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29 Jan 2018, 15:17
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%

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Of 200 people surveyed, 80 percent own a cellular phone and 45 percen  [#permalink]

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07 Jan 2019, 07:23
evannolimit wrote:
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%

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

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?
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Re: Of 200 people surveyed, 80 percent own a cellular phone and 45 percen  [#permalink]

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07 Jan 2019, 07:30
NandishSS wrote:
evannolimit wrote:
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%

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

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?

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
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Re: Of 200 people surveyed, 80 percent own a cellular phone and 45 percen  [#permalink]

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04 Apr 2019, 18:53
evannolimit wrote:
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%

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

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.

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Re: Of 200 people surveyed, 80 percent own a cellular phone and 45 percen  [#permalink]

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02 Dec 2019, 05:01
evannolimit wrote:
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%

Attachment:
The attachment Screen Shot 2016-07-18 at 5.24.51 PM.png is no longer available

We don't need to use the actual numbers since we need a percent as our answer, saving our 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%

Attachments

Image.jpeg [ 584.28 KiB | Viewed 1049 times ]

Re: Of 200 people surveyed, 80 percent own a cellular phone and 45 percen   [#permalink] 02 Dec 2019, 05:01
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