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# 100 residents of a city were surveyed and each one read at least one

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100 residents of a city were surveyed and each one read at least one  [#permalink]

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08 Dec 2019, 22:58
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45% (medium)

Question Stats:

57% (01:19) correct 43% (01:11) wrong based on 67 sessions

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Competition Mode Question

100 residents of a city were surveyed and each one read at least one of the town's two newspapers, the Times and the Post. How many residents read the Post?

(1) The number of residents who read no newspapers is zero.

(2) The number of residents who read only the Times was 46.

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Re: 100 residents of a city were surveyed and each one read at least one  [#permalink]

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09 Dec 2019, 00:02
1
100 residents of a city were surveyed and each one read at least one of the town's two newspapers, the Times and the Post. How many residents read the Post?
Let T = number of residents reading the Times
P = number of residents reading the Post
Since no resident is a non-reader of the two newspapers, number of residents reading no paper is zero.
P + T - P(intersection)T = 100
P = ?
(1) The number of residents who read no newspapers is zero.
Accordingly, P + T - P(intersection)T = 100
50 + 55 - 5 = 100
or
60 + 55 - 15 = 100

INSUFFICIENT.

(2) The number of residents who read only the Times was 46.
So, T - P(intersection)T = 46
Hence P = 100 - 46 = 54

SUFFICIENT.

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100 residents of a city were surveyed and each one read at least one  [#permalink]

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Updated on: 10 Dec 2019, 18:18
solve using 2x2 matrix

---RT--NRT--total
RP--0--54--54
NRP--46--0----46
total--46--54--100
IMO B

100 residents of a city were surveyed and each one read at least one of the town's two newspapers, the Times and the Post. How many residents read the Post?

(1) The number of residents who read no newspapers is zero.

(2) The number of residents who read only the Times was 46.

Originally posted by Archit3110 on 09 Dec 2019, 00:20.
Last edited by Archit3110 on 10 Dec 2019, 18:18, edited 2 times in total.
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Re: 100 residents of a city were surveyed and each one read at least one  [#permalink]

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09 Dec 2019, 00:58
1
Total Residents: 100
Assume:
Nos of residents who read times & post: a
Only Post: b
Only Time: c
So, we need to find out: a+b(people who read both and who only read post)
1) St 1: We already know from question each read atleast one. Hence, inconsequential. Insufficient
2) St 2: c=46. We also know that a+b+c(only times + only post + both)=100. Solving, we find (a+b). Sufficient.
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100 residents of a city were surveyed and each one read at least one  [#permalink]

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Updated on: 09 Dec 2019, 23:06
Q. How many (out of 100) residents read the Post?

(1) No new information is given from this statement. This is just a rephrase from "each one read at least one of the town's two newspapers, the Times and the Post."
NOT SUFFICIENT

(2) 100-46=54
SUFFICIENT.

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Originally posted by chondro48 on 09 Dec 2019, 01:22.
Last edited by chondro48 on 09 Dec 2019, 23:06, edited 1 time in total.
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Re: 100 residents of a city were surveyed and each one read at least one  [#permalink]

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09 Dec 2019, 03:33
1
Quote:
100 residents of a city were surveyed and each one read at least one of the town's two newspapers, the Times and the Post. How many residents read the Post?

(1) The number of residents who read no newspapers is zero.

(2) The number of residents who read only the Times was 46.

(1) The number of residents who read no newspapers is zero. insufic

………TIMES……NOT……TOTAL
POST
NOT ………………0………
TOT…………………………100

(2) The number of residents who read only the Times was 46. sufic

………TIMES……NOT……TOTAL
POST…………………………[54]
NOT …[46]…………[0]……[46]
TOT…………………………100

Post = 54

Ans (B)
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Re: 100 residents of a city were surveyed and each one read at least one  [#permalink]

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09 Dec 2019, 10:10
1
From the question stem, we know that the total number of people in the town, S=100.
We also know that each person in the town read at least one of the two newspapers, the Times and the Post. This implies none=0.

We are to determine how many residents read the Post.

Statement 1: The number of residents who read no newspapers is zero.
This is insufficient. Statement 1 is a distraction. We have already inferred statement 1 from the information provided in the question stem. It is a trick because it might make you think that you already don't have this information given in the question stem.

Statement 2: The number of residents who read only the Times was 46.
This is sufficient. We know that the number of people who read the post = S - those who read only the Times
so The number who read the Times can be determined as = 100-46 = 54.

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Re: 100 residents of a city were surveyed and each one read at least one  [#permalink]

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09 Dec 2019, 14:03
1
Total = 100 residents
—> Each one read at least one of the town's two newspapers, the Times and the Post. —> neither =0

—> Post =???

(Statement1): Neither= 0
Clearly insufficient. —> it is already mentioned above.

(Statement2): Only Times = 46
100 = only Post + only Times + both
—> only Post + both= 100 —46 = 54
Sufficient

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Re: 100 residents of a city were surveyed and each one read at least one  [#permalink]

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09 Dec 2019, 17:29
1
(1) The number of residents who read no newspapers is zero......it's already mentioned in the question

(2) The number of residents who read only the Times was 46..... clearly sufficient=100-46=54

OA:B

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Re: 100 residents of a city were surveyed and each one read at least one  [#permalink]

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09 Dec 2019, 19:26
100 residents of a city were surveyed and each one read at least one of the town's two newspapers, the Times and the Post. How many residents read the Post?

(1) The number of residents who read no newspapers is zero.

(2) The number of residents who read only the Times was 46.

1) This is just another expression of the line "each one read at least one of the town's two newspapers, the Times and the Post" > not sufficient.

2) The other 54 read the Post or both. > Sufficient.

IMHO B is the answer. But if there is other newspapers read by the 100 residents of the city other than the mentioned 2, then E will be answer. So I'm confused regarding this.
Re: 100 residents of a city were surveyed and each one read at least one   [#permalink] 09 Dec 2019, 19:26
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