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How many cats, c, does Eleanor own?

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Joined: 02 Sep 2009
Posts: 46051
How many cats, c, does Eleanor own? [#permalink]

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New post 08 Feb 2017, 01:42
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

68% (00:56) correct 32% (00:59) wrong based on 55 sessions

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Senior Manager
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Joined: 19 Apr 2016
Posts: 275
Location: India
GMAT 1: 570 Q48 V22
GMAT 2: 640 Q49 V28
GPA: 3.5
WE: Web Development (Computer Software)
Re: How many cats, c, does Eleanor own? [#permalink]

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New post 08 Feb 2017, 02:56
Bunuel wrote:
How many cats, c, does Eleanor own?

(1) c^2 = 5c + 14

(2) 3c^2 = 22c - 7


St I \(c^2 = 5c + 14\)
On solving the equation we have c = 7 or c =-2 Since #cats cant be negative, c has to be 7 --------Sufficient.

St II \(3c^2 = 22c - 7\)
On solving the equation we have c = 7 or c =1/3 Since #cats cant be fractional, c has to be 7 --------Sufficient.

Hence Option D is correct.
Hit Kudos if you liked it 8-)
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Re: How many cats, c, does Eleanor own? [#permalink]

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New post 08 Feb 2017, 14:51
Statement 1

c^2 = 5c + 14
=> c^2 - 5c - 14 = 0
=> c^2 - 7c + 2c -14 =0
=> c (c-7) +2 (c-7) = 0
=> (c+2) (c-7) = 0
Therefore,C = 7, Statement 1 is sufficient

Statement 2

3c^2 = 22c - 7
=> 3c^2 - 22c + 7 = 0
=> 3c^2 - 21c - c + 7 = 0
=> 3c(c-7) -1(c-7)=0
=>(3c-1)(c-7)
Therefore, C=7. Statement 2 is sufficient.

Answer is D.
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Re: How many cats, c, does Eleanor own? [#permalink]

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New post 09 Feb 2017, 04:41
How many cats, c, does Eleanor own?

Number of cats is POSITIVE number.

(1) c^2 = 5c + 14

c^2- 5c - 14= 0........implies there are tow factors: one is positive and other is negative. Accept positive number only . No need to factor out.

Sufficient

(2) 3c^2 = 22c - 7

3c^2 -22c + 7= 0........implies there are tow factors: one is positive and other is negative. Accept positive number only . No need to factor out.

Sufficient

Answer: D
Re: How many cats, c, does Eleanor own?   [#permalink] 09 Feb 2017, 04:41
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How many cats, c, does Eleanor own?

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