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Re: According to the results of a survey by Lake Enthusiast Magazine, 25% [#permalink]
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(B U C) = (B) + (C) + B ⋂ C

=> 46 = 25 + 30 - B ⋂ C

=> B ⋂ C = 25 + 30 - 46 = 9

=> Only canoe: 30 - 9 = 21

Percent of those subscribers who own a canoe does not own a boat: \(\frac{21}{30} * 100= 70%\)

Answer E
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Re: According to the results of a survey by Lake Enthusiast Magazine, 25% [#permalink]
why would take the percentage out of 30 and not 100
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Re: According to the results of a survey by Lake Enthusiast Magazine, 25% [#permalink]
Is there a way to do this problem using the 2 set matrix?
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Re: According to the results of a survey by Lake Enthusiast Magazine, 25% [#permalink]
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Total - Neither = Boat + Canoe - Both

=> 46 = 25 + 30 - Both

=> Both = 55 - 46 = 9

=> Only Canoe : 30 - 9 = 21

=> Percent of those subscribers who own a canoe does not own a boat: \(\frac{21}{30} * 100 = 70%\)

Answer E
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Re: According to the results of a survey by Lake Enthusiast Magazine, 25% [#permalink]
why at the end we took % from 30 not 100.
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Re: According to the results of a survey by Lake Enthusiast Magazine, 25% [#permalink]
Bunuel wrote:
According to the results of a survey by Lake Enthusiast Magazine, 25% of subscribers own a boat, and 30% of subscribers own a canoe. If 46% of subscribers own either a boat or a canoe, then what percent of those subscribers who own a canoe do not own a boat?

A. 9%

B. 16%

C. 21%

D. 64%

E. 70%


total no of people who own a canoe and boat together = 55

Total no of people who own either a boat or canoe = 46

No of people who have a canoe and boat = 9

% for a person who has a canoe but no boat = 30-9 / 30*100 = 70

THerefore IMO E
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Re: According to the results of a survey by Lake Enthusiast Magazine, 25% [#permalink]
I think the approach is not clear. Answer should be 21%. Based on 2 matrix approach percent of people who has canoe but not boat should come from total which is 100 and not 30. please suggest why it is taken from total canoe and not grand total figure (100)
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Re: According to the results of a survey by Lake Enthusiast Magazine, 25% [#permalink]
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Bunuel wrote:
According to the results of a survey by Lake Enthusiast Magazine, 25% of subscribers own a boat, and 30% of subscribers own a canoe. If 46% of subscribers own either a boat or a canoe, then what percent of those subscribers who own a canoe do not own a boat?

A. 9%

B. 16%

C. 21%

D. 64%

E. 70%


Let's assume 100 subscribers.

46 = 25 + 30 - Both
Both = 9

Out of 30 people who own a canoe, 9 own a boat too while 21 own only a canoe.
So 21 of 30 canoe owners do not own a boat i.e. 21/30 * 100 = 70% canoe owners do not own a boat.

Answer (E)
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Re: According to the results of a survey by Lake Enthusiast Magazine, 25% [#permalink]
KarishmaB wrote:
Bunuel wrote:
According to the results of a survey by Lake Enthusiast Magazine, 25% of subscribers own a boat, and 30% of subscribers own a canoe. If 46% of subscribers own either a boat or a canoe, then what percent of those subscribers who own a canoe do not own a boat?

A. 9%

B. 16%

C. 21%

D. 64%

E. 70%


Let's assume 100 subscribers.

46 = 25 + 30 - Both
Both = 9

Out of 30 people who own a canoe, 9 own a boat too while 21 own only a canoe.
So 21 of 30 canoe owners do not own a boat i.e. 21/30 * 100 = 70% canoe owners do not own a boat.

Answer (E)


The problem I have is with the wording "own either a boat or a canoe". I take this as if you either either a boat or canoe you are in this group, and you are not in this group if you own both a boat and canoe.

But if we draw a venn diagram, and use the formula you have stated, the statement above is not correct. Because you would have to minus 2 lots of "Both" to get that definition of either. As Canoe plus Boat includes two lots of "both"
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Re: According to the results of a survey by Lake Enthusiast Magazine, 25% [#permalink]
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