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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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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
[Reveal] Spoiler: OA

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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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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New post 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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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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New post 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.


Interesting technique. Made sense.
+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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New post 03 Sep 2016, 10:39
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.


Interesting technique. Made sense.
+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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Re: A author writes in his book : "I was born in year (x^2 + 4x + 4 ) and   [#permalink] 22 Dec 2017, 12:53
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