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# A author writes in his book : "I was born in year (x^2 + 4x + 4 ) and

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A author writes in his book : "I was born in year (x^2 + 4x + 4 ) and  [#permalink]

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Updated on: 04 Sep 2016, 04:45
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Difficulty:

65% (hard)

Question Stats:

62% (02:39) correct 38% (02:31) wrong based on 115 sessions

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A author writes in his book : "I was born in year (x^2 + 4x + 4 ) and I was (x+2) in year k". What is the value of k?

(1) k is less than 1850
(2) k is more than 1800

Originally posted by maliyeci on 28 Aug 2016, 12:48.
Last edited by Bunuel on 04 Sep 2016, 04:45, edited 1 time in total.
RENAMED THE TOPIC.
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Re: A author writes in his book : "I was born in year (x^2 + 4x + 4 ) and  [#permalink]

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28 Aug 2016, 17:53
1
maliyeci wrote:
A author writes in his book : "I was born in year (x^2 + 4x + 4 ) and I was (x+2) in year k". What is the value of k?
1-k is less than 1850
2-k is more than 1800

The stem can be written in algebraic form as $$k - (x + 2) ^2 = (x+2) and reduced to k = (x+2)(x+3)$$

Consider 1) $$X$$can have multiple values for $$K$$ when $$K$$ is below 1850 ($$x$$ can be from 0 to 40 ), Not sufficient . Eliminate A and D

Consider 2) Same as 1) $$X$$ can have multiple values. Eliminate B

Consider 1) and 2) Only one value of $$X$$ holds true for $$K$$ between 1850 to 1800. Answer is C
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Re: A author writes in his book : "I was born in year (x^2 + 4x + 4 ) and  [#permalink]

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28 Aug 2016, 18:38
Senthil1981 wrote:
maliyeci wrote:
A author writes in his book : "I was born in year (x^2 + 4x + 4 ) and I was (x+2) in year k". What is the value of k?
1-k is less than 1850
2-k is more than 1800

The stem can be written in algebraic form as $$k - (x + 2) ^2 = (x+2) and reduced to k = (x+2)(x+3)$$

Consider 1) $$X$$can have multiple values for $$K$$ when $$K$$ is below 1850 ($$x$$ can be from 0 to 40 ), Not sufficient . Eliminate A and D

Consider 2) Same as 1) $$X$$ can have multiple values. Eliminate B

Consider 1) and 2) Only one value of $$X$$ holds true for $$K$$ between 1850 to 1800. Answer is C

Hi Senthil1981,

I got up to k = (x+2)(x+3) but then picked E.

How have you concluded that only one value of x between 1800 and 1850 satisfies the equation?
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Re: A author writes in his book : "I was born in year (x^2 + 4x + 4 ) and  [#permalink]

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28 Aug 2016, 19:19
1
Donnie84 wrote:
Hi Senthil1981,

I got up to k = (x+2)(x+3) but then picked E.

How have you concluded that only one value of x between 1800 and 1850 satisfies the equation?

Hi Donnie84, We know $$40^2 = 1600$$, so i picked 42 and 43 and applied in the equation and (x+2) = 42 satisfied the condition.
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Re: A author writes in his book : "I was born in year (x^2 + 4x + 4 ) and  [#permalink]

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28 Aug 2016, 19:51
Senthil1981 wrote:
Donnie84 wrote:
Hi Senthil1981,

I got up to k = (x+2)(x+3) but then picked E.

How have you concluded that only one value of x between 1800 and 1850 satisfies the equation?

Hi Donnie84, We know $$40^2 = 1600$$, so i picked 42 and 43 and applied in the equation and (x+2) = 42 satisfied the condition.

+1 to you.
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Re: A author writes in his book : "I was born in year (x^2 + 4x + 4 ) and  [#permalink]

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03 Sep 2016, 10:39
1
Donnie84 wrote:
Senthil1981 wrote:
Donnie84 wrote:
Hi Senthil1981,

I got up to k = (x+2)(x+3) but then picked E.

How have you concluded that only one value of x between 1800 and 1850 satisfies the equation?

Hi Donnie84, We know $$40^2 = 1600$$, so i picked 42 and 43 and applied in the equation and (x+2) = 42 satisfied the condition.

+1 to you.

Yes, if we got k = (x+2)(x+3) , we know that k is a product of tow consecutive integers. So, only 42*43 will be such a product that would be > 1800 but less than 1850. Hence, C.
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Re: A author writes in his book : "I was born in year (x^2 + 4x + 4 ) and  [#permalink]

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27 Dec 2018, 19:22
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Re: A author writes in his book : "I was born in year (x^2 + 4x + 4 ) and   [#permalink] 27 Dec 2018, 19:22
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