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705-805 (Hard)|   Algebra|   Arithmetic|      
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maliyeci
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A author writes in his book : "I was born in year (x^2 + 4x + 4 ) and Updated on: 04 Sep 2016, 04:45
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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C
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75% (hard)

Question Stats:

59% (02:38) correct 41% (02:32) wrong based on 170 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
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C
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Senthil1981
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A author writes in his book : "I was born in year (x^2 + 4x + 4 ) and 28 Aug 2016, 17:53
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maliyeci
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
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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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A author writes in his book : "I was born in year (x^2 + 4x + 4 ) and 28 Aug 2016, 18:38
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Senthil1981
maliyeci
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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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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A author writes in his book : "I was born in year (x^2 + 4x + 4 ) and 28 Aug 2016, 19:19
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Donnie84
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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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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A author writes in his book : "I was born in year (x^2 + 4x + 4 ) and 28 Aug 2016, 19:51
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Senthil1981
Donnie84
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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Interesting technique. Made sense.
+1 to you.
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A author writes in his book : "I was born in year (x^2 + 4x + 4 ) and 03 Sep 2016, 10:39
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Senthil1981
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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.
Show more

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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