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# A florist found that 60% of his customers on Valentine's Day bought

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Math Expert
Joined: 02 Sep 2009
Posts: 52231
A florist found that 60% of his customers on Valentine's Day bought  [#permalink]

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27 Mar 2017, 03:43
00:00

Difficulty:

75% (hard)

Question Stats:

57% (02:23) correct 43% (02:32) wrong based on 46 sessions

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A florist found that 60% of his customers on Valentine's Day bought roses. People had the option that day of buying red roses, yellow roses or orange roses and half of all the people who bought roses bought only red roses. How many people bought all three varieties?

(1) Of the 100 customers the florist had, 12 people bought only yellow and orange roses together.
(2) Of the 100 customers the florist had, no one bought only red roses and one other type of rose.

_________________
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Joined: 21 Mar 2016
Posts: 523
Re: A florist found that 60% of his customers on Valentine's Day bought  [#permalink]

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27 Mar 2017, 06:51
stat 1: nothing is told about the number of orange and yellow roses bought by the people, only thing that can be deduced is that people who bought both orange and yellow roses = 12,, not suff

stat 2 : total number who bought red rose = 60
those who bought only red = 60/2 = 30
as per stat 2 , nobody bought only red and one other type ,,,implies 30 bought all three..

ans B
Senior Manager
Joined: 21 Aug 2016
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Location: India
GPA: 3.9
WE: Information Technology (Computer Software)
A florist found that 60% of his customers on Valentine's Day bought  [#permalink]

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28 Mar 2017, 11:21
60 % of the customers bought roses on Valentine's day.

no of the customers who bought roses on VAlentine's day=60

no of the people who bought only red roses are 30

that means the number of people who bought all three kinds of rose will be less than or equal to 30.

Statement 1: no of the people who bought only yellow and orange roses together =12
no of the people who bought all three types of rose will be less than or equal to 18(30-12)

case one : when x bought only yellow roses and 18-x bought only orange roses, no of people who bought all three types of roses=0

case two
: when 18 bought all three kinds of roses, no of people who bought all three types of roses=18

not sufficient

statement 2: number of the customers who bought only red and one other type of roses=0

case one : when x bought only yellow roses and 30-x bought only orange roses, no of people who bought all three types of roses=0

case two: when 30 bought all three kinds of roses, no of people who bought all three types of roses=30

not sufficient
Taking both together also does not help, so the correct answer is E

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A florist found that 60% of his customers on Valentine's Day bought &nbs [#permalink] 28 Mar 2017, 11:21
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