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Of 41 reviews of a particular restaurant, 20 cited good service, 7 cit

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Bunuel
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Of 41 reviews of a particular restaurant, 20 cited good service, 7 cit [#permalink] New post   13 Sep 2021, 02:28
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80% (01:07) correct 20% (01:49) wrong based on 41 sessions
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Of 41 reviews of a particular restaurant, 20 cited good service, 7 cited the quality of the desserts, and 20 cited neither good service nor the quality of the desserts. How many of the reviews cited good service and the quality of the desserts?

A. 20

B. 13

C. 9

D. 7

E. 6
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E
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DashingNightmare2
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Re: Of 41 reviews of a particular restaurant, 20 cited good service, 7 cit [#permalink] New post   13 Sep 2021, 15:27
Bunuel wrote:
Of 41 reviews of a particular restaurant, 20 cited good service, 7 cited the quality of the desserts, and 20 cited neither good service nor the quality of the desserts. How many of the reviews cited good service and the quality of the desserts?

A. 20

B. 13

C. 9

D. 7

E. 6


Let I denote good service or quality of desert
II denote both good service and quality of desert

I+ II + 20 = 41
Also, I +2*II =27

Solving we get I =15. II =6
Hence IMO E
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rishabh195
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Re: Of 41 reviews of a particular restaurant, 20 cited good service, 7 cit [#permalink] New post   13 Sep 2021, 16:58
DashingNightmare2 wrote:
Bunuel wrote:
Of 41 reviews of a particular restaurant, 20 cited good service, 7 cited the quality of the desserts, and 20 cited neither good service nor the quality of the desserts. How many of the reviews cited good service and the quality of the desserts?

A. 20

B. 13

C. 9

D. 7

E. 6


Let I denote good service or quality of desert
II denote both good service and quality of desert

I+ II + 20 = 41
Also, I +2*II =27

Solving we get I =15. II =6
Hence IMO E


Hi DashingNightmare2

Can you please elaborate a bit. I am not able to understand from here "Also, I + 2*II = 27" how did you arrive here and why did you took 2*II = 27. Kindly reply.

Thanks
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DashingNightmare2
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Joined: 30 May 2021
Posts: 103
Own Kudos [?]: 79 [0]
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Concentration: Marketing, Technology
Schools: ISB '23 (A)
GMAT 1: 750 Q50 V41
GPA: 2.96
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Of 41 reviews of a particular restaurant, 20 cited good service, 7 cit [#permalink] New post   13 Sep 2021, 23:33
rishabh195 wrote:
DashingNightmare2 wrote:
Bunuel wrote:
Of 41 reviews of a particular restaurant, 20 cited good service, 7 cited the quality of the desserts, and 20 cited neither good service nor the quality of the desserts. How many of the reviews cited good service and the quality of the desserts?

A. 20

B. 13

C. 9

D. 7

E. 6


Let I denote good service or quality of desert
II denote both good service and quality of desert

I+ II + 20 = 41
Also, I +2*II =27

Solving we get I =15. II =6
Hence IMO E


Hi DashingNightmare2

Can you please elaborate a bit. I am not able to understand from here "Also, I + 2*II = 27" how did you arrive here and why did you took 2*II = 27. Kindly reply.

Thanks



Hi rishabh195

Lets try to understand from the venn diagram which I attached below
Good service = A+C =20
quality of the desserts =B+C =7
If we add both above equations. A+B+2*C =27

Also from the question we know that
out of 41 reviews, 20 liked none => 21 viewers liked either one or both service and quality of dessert
or, in simple terms, A+B+C+none =41
=> A+B+C =21

Solving above 2 equation we get C =6,
good service and the quality of the desserts is represented by C

Hence E

In my previous answer, I mentioned A and B as I, and C as II
Because A and B denote that the user has liked only 1 of the 2 things,
whereas II represent C, that is user has liked both

Hope it helps, Thank you :blushing:
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venn2.png
venn2.png [ 19.35 KiB | Viewed 901 times ]

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Of 41 reviews of a particular restaurant, 20 cited good service, 7 cit [#permalink]
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