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In a survey of 500 students regarding pet ownership of cats and dogs,

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In a survey of 500 students regarding pet ownership of cats and dogs,  [#permalink]

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New post 20 Mar 2018, 00:23
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A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

93% (01:10) correct 7% (01:34) wrong based on 47 sessions

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In a survey of 500 students regarding pet ownership of cats and dogs, c students own at least one cat, d students own at least one dog, and b students own at least one dog and at least one cat. How many students own neither a cat nor a dog?

(A) 500 - c - d + b
(B) 500 - c - d - b
(C) 500 - c + d
(D) 500 - c - d
(E) 500 - b

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Re: In a survey of 500 students regarding pet ownership of cats and dogs,  [#permalink]

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New post 20 Mar 2018, 00:26
Bunuel wrote:
In a survey of 500 students regarding pet ownership of cats and dogs, c students own at least one cat, d students own at least one dog, and b students own at least one dog and at least one cat. How many students own neither a cat nor a dog?

(A) 500 - c - d + b
(B) 500 - c - d - b
(C) 500 - c + d
(D) 500 - c - d
(E) 500 - b


19. Overlapping Sets



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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

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Re: In a survey of 500 students regarding pet ownership of cats and dogs,  [#permalink]

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New post 20 Mar 2018, 00:54
Bunuel wrote:
In a survey of 500 students regarding pet ownership of cats and dogs, c students own at least one cat, d students own at least one dog, and b students own at least one dog and at least one cat. How many students own neither a cat nor a dog?

(A) 500 - c - d + b
(B) 500 - c - d - b
(C) 500 - c + d
(D) 500 - c - d
(E) 500 - b


Using overlapping 2-set formula:

A+B-both+neither=Total we get->

c (Cats) + d (Dogs) - b (Both) + x (neither) = 500
x = 500 - c - d + b.

Hence Option A.

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Re: In a survey of 500 students regarding pet ownership of cats and dogs,  [#permalink]

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New post 21 Mar 2018, 15:17
Bunuel wrote:
In a survey of 500 students regarding pet ownership of cats and dogs, c students own at least one cat, d students own at least one dog, and b students own at least one dog and at least one cat. How many students own neither a cat nor a dog?

(A) 500 - c - d + b
(B) 500 - c - d - b
(C) 500 - c + d
(D) 500 - c - d
(E) 500 - b


We can create the equation:

Total = own a dog + own a cat - both + neither

500 = d + c - b + neither

500 - d - c + b = neither

Answer: A
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Re: In a survey of 500 students regarding pet ownership of cats and dogs, &nbs [#permalink] 21 Mar 2018, 15:17
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