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In a town, 25% families own a phone and 15% own a car, 65% families ow

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In a town, 25% families own a phone and 15% own a car, 65% families ow  [#permalink]

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New post 31 May 2018, 12:13
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  95% (hard)

Question Stats:

47% (01:49) correct 53% (02:16) wrong based on 134 sessions

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In a town, 25% families own a phone and 15% own a car, 65% families own neither a phone nor a car. 2000 families own both a car and a phone. Consider the following statements in this regard:

I. 10% families own both a car and a phone.
II. 35% families own either a car or a phone.
III. 40,000 families live in the town.

Which of the above statements are correct?


A) Only I
B) II and III
C) Only III
D) I and III
E) Only II

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Re: In a town, 25% families own a phone and 15% own a car, 65% families ow  [#permalink]

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New post Updated on: 31 May 2018, 20:48
Bunuel wrote:
In a town, 25% families own a phone and 15% own a car, 65% families own neither a phone nor a car. 2000 families own both a car and a phone. Consider the following statements in this regard:

I. 10% families own both a car and a phone.
II. 35% families own either a car or a phone.
III. 40,000 families live in the town.

Which of the above statements are correct?


A) Only I
B) II and III
C) Only III
D) I and III
E) Only II


Ans: E
From the stem we know that
Total = Phone + Car - both + None
100 % = 25% + 15% + both% - 65%
both= 5% (I wrong)
(II correct)
Edited: Since 5% = 2,000 ; 100% = 40,000 (III Correct)

Ans: B
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Originally posted by D3N0 on 31 May 2018, 15:52.
Last edited by D3N0 on 31 May 2018, 20:48, edited 1 time in total.
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Re: In a town, 25% families own a phone and 15% own a car, 65% families ow  [#permalink]

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New post 31 May 2018, 20:43
dkumar2012 wrote:
Bunuel wrote:
In a town, 25% families own a phone and 15% own a car, 65% families own neither a phone nor a car. 2000 families own both a car and a phone. Consider the following statements in this regard:

I. 10% families own both a car and a phone.
II. 35% families own either a car or a phone.
III. 40,000 families live in the town.

Which of the above statements are correct?


A) Only I
B) II and III
C) Only III
D) I and III
E) Only II


Ans: E
From the stem we know that
Total = Phone + Car - both + None
100 % = 25% + 15% + both% - 65%
both= 5% (I wrong)
(II correct)
Since 5% = 20,000 ; 100% = 400,000 (III wrong)

Ans: E


Hi dkumar2012

you seems to have miss-read the value for 5%. Its 2000 not 20,000

so, Since 5% = 2000 ; 100% = 40,000 (III right)

Ans: B
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Re: In a town, 25% families own a phone and 15% own a car, 65% families ow  [#permalink]

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New post 31 May 2018, 20:50
GMATisLovE wrote:
Hi dkumar2012

you seems to have miss-read the value for 5%. Its 2000 not 20,000

so, Since 5% = 2000 ; 100% = 40,000 (III right)

Ans: B


Yes, Thank you for pointing out. Edited the explanation and answer.

thank you !
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Re: In a town, 25% families own a phone and 15% own a car, 65% families ow  [#permalink]

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New post 01 Jun 2018, 05:48
3

Solution



Given:
    • In a town, 25% families own a phone, 15% own a car, 65% own neither a phone nor a car
    • 2000 families own both a car and a phone

To find:
    • Which of the given statements in the option are true?

Approach and Working:
If we assume that 2000 families, which own both a car and a phone, are b% of the total population, we can show all the information in the following venn diagram:

Image

As per the diagram, we can say
    • Percentage of people who have only phone = 25 – b
    • Percentage of people who have only car = 15 – b
    • Percentage of people who have none = 65

As the total percentage is 100, we can write
    • 25 – b + b + 15 – b + 65 = 100
    Or, 105 – b = 100
    Or, b = 5%
    • Therefore, people with only phone is 20% and people with only car is 10%

Now considering the statements individually,
    1. 10% families own both a car and a phone.
This is wrong as we know b represents this population, which is equal to 5%
Therefore, statement 1 is wrong

    2. 35% families own either a car or a phone.
The families who own either a car or a phone = total – the families who own none = 100 – 65 = 35%
Therefore, statement 2 is correct

    3. 40,000 families live in the town.
As 5% of total is 2000, total population will be 40000
Therefore, statement 3 is correct

Hence, the correct answer is option B.

Answer: B
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Re: In a town, 25% families own a phone and 15% own a car, 65% families ow  [#permalink]

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New post 03 Jun 2018, 18:21
Bunuel wrote:
In a town, 25% families own a phone and 15% own a car, 65% families own neither a phone nor a car. 2000 families own both a car and a phone. Consider the following statements in this regard:

I. 10% families own both a car and a phone.
II. 35% families own either a car or a phone.
III. 40,000 families live in the town.

Which of the above statements are correct?


A) Only I
B) II and III
C) Only III
D) I and III
E) Only II


We can create the equation from the given percentages:

total = phone + car - both + neither

100 = 25 + 15 - both + 65

100 = 105 - both

both = 5 percent

We see that I is false.

If we let n = the total number of families, then:

0.05n = 2000

n = 40,000

The percent who own either a car or a phone is 25 + 15 - 5 = 35 percent.

Thus, II and III are true.

Answer: B
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Re: In a town, 25% families own a phone and 15% own a car, 65% families ow  [#permalink]

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New post 14 Jun 2018, 17:05
1
Bunuel wrote:
In a town, 25% families own a phone and 15% own a car, 65% families own neither a phone nor a car. 2000 families own both a car and a phone. Consider the following statements in this regard:

I. 10% families own both a car and a phone.
II. 35% families own either a car or a phone.
III. 40,000 families live in the town.

Which of the above statements are correct?


A) Only I
B) II and III
C) Only III
D) I and III
E) Only II


Is the answer B or C? I see some experts getting B as the answer but the OA is marked as C
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Re: In a town, 25% families own a phone and 15% own a car, 65% families ow  [#permalink]

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New post 14 Jun 2018, 20:12
GMATSkilled wrote:
Bunuel wrote:
In a town, 25% families own a phone and 15% own a car, 65% families own neither a phone nor a car. 2000 families own both a car and a phone. Consider the following statements in this regard:

I. 10% families own both a car and a phone.
II. 35% families own either a car or a phone.
III. 40,000 families live in the town.

Which of the above statements are correct?


A) Only I
B) II and III
C) Only III
D) I and III
E) Only II


Is the answer B or C? I see some experts getting B as the answer but the OA is marked as C

_________________________
The OA is B. Edited. Thank you.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: In a town, 25% families own a phone and 15% own a car, 65% families ow  [#permalink]

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New post 14 Jun 2018, 23:15
The answer should be C. Option II says that 35% of the families own either a phone or a car, whereas, 35% families own either a phone or a car or both. There are 5% families which own both phone and a car and that is included in 35%.
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Re: In a town, 25% families own a phone and 15% own a car, 65% families ow &nbs [#permalink] 14 Jun 2018, 23:15
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