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

Question

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 red roses. Did more than half the customers buy exactly two varieties of rose?

(1) Of the 80 customers the florist had, only those people buying red roses also bought exactly one other type of rose.
(2) Of the 80 customers the florist had, half of the people who bought red roses bought exactly one other type of rose.

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omairdilawer27 · Answer

Can anyone tell me that why its can`t D. Because second statement is also sufficient as half of total is 40. Now, when 24+12 < 40 also 12 + 12 <40. Then why statement 2 is not sufficient

meetnikhil · Answer

Second statement does not have word 'only'. so we don't about rest of customers. IMO that is the reason.
Even I missed that.

Sejal16 · Answer

Bunuel  can u help here ? 
Option B - Even if the other customer (yellow & orange flower ones) bought exactly one another rose, still the no. is less than 40. 24/2 +24 = 36 <40, sufficient.
Since it is given that 1/2 customers who bought red bought another rose, it will be safe to consider that another half do not fall in this category ?

jasmeet447 · Answer

Statement 1 seems to indicate that ALL of the people buying red roses bought exactly one other type of rose. Total = 48(number of customers buying roses). Sufficient.
Statement 2 indicates that only HALF of the people buying red roses bought exactly one other type of rose. We don't know about the people buying yellow or orange roses and about the relationship between the numbers. Total = 12 + 12 = 24. Not Sufficient.

TarunKumar1234 · Answer

Stat1: if Total customers= 80, then roses = 80*60% = 48, then Red roses = 48* 50% = 24,
Now, People got Red (24 nos.) and Yellow (24 nos.). now,24 people have 1 choice either buy Yellow(24) or Orange (24) roses. It means, Customers having two types of Roses = 24 nos. < 40. So, less than half of the customers buy two types of roses. Sufficient.

Stat2: if Total customers= 80, then roses = 80*60% = 48, then Red roses = 48* 50% = 24.
Now, People got Red (24 nos.) and given, half of the people who bought red roses bought exactly one other type of rose. It means, half, 12 nos. have Yellow & Red roses. But, the first half of the customers having Red roses can buy 3 types of roses (Red, yellow and Orange) or one type Red roses only. Till now, 24 or 12 customers got 2 types (Red and Yellow) of roses.
Rest, 24 people can get Yellow or Orange or both.

So, customers bought two types of rose = 12 or 12+24=36 or 24 or 24+24= 48, now, we are not Sure, if more or less than half of the customers (40) buy two types of roses. Insufficient.

So, I think A.

Fdambro294 · Answer

Bunuel

As statement 2 and the question stem is written, is it not the case that we get a definite no answer?

Did more than half of the customers buy exactly two varieties?

Since only 60% actually bought roses, we have 60%(80) = 48 people who bought roses

And we know that of these 48 people who bought roses, half bought red roses: 24

S2: half of the people who bought red roses bought exactly one other type of rose:

So of the 24 red rose purchasers 
12 = exactly two varieties 
12 = more than two varieties (or just red alone)

Even if the remaining 24 other people who bought roses bought exactly two varieties (yellow and Orange) that gives us:

(12 + 24) = 36 people who bought exactly two varieties

Still short of (1/2) of 80 total customers

Am I missing something? Thank you for your help.

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SCismynightmare · Answer

The maximum that we can get is 36 roses through statement 2, and because the question is asking for those who bought EXACTLY two varieties of roses, we are able to reach at an answer through statement 2 as well. Please help, as the official answer is A.

Posted from my mobile device

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

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