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The sum of a certain number and its reciprocal is equal to 2,9.

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The sum of a certain number and its reciprocal is equal to 2,9. [#permalink]

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59% (02:23) correct 41% (06:02) wrong based on 123 sessions

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The sum of a certain number and its reciprocal is equal to 2,9. What is the absolute value of the difference of this number and its reciprocal ?

A. 2,2 B. 1,2 C. 0,3 D. 0,4 E. 2,1
[Reveal] Spoiler: OA

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Re: The sum of a certain number and its reciprocal is equal to 2,9. [#permalink]

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New post 03 Nov 2016, 13:11
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ReussirleGMAT wrote:
The sum of a certain number and its reciprocal is equal to 2,9. What is the absolute value of the difference of this number and its reciprocal ?

A. 2,2 B. 1,2 C. 0,3 D. 0,4 E. 2,1


x + 1/x = 2.9

x-1/x = y


Add two equations

2x = 2.9 + y

So when 2.9 and correct answer choice are added, the final digit should be even

So eliminate A, B and D

Substitute y=0.3

x=1.6

1.6+1/1.6 is not equal to 2.9


Substitute y = 2.1

So x=2.5


2.5+1/2.5 =2.9

E


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Re: The sum of a certain number and its reciprocal is equal to 2,9. [#permalink]

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New post 03 Nov 2016, 13:33
Nice method acegmat123

There is another way to solve this problem, could you find it?

Anis
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The sum of a certain number and its reciprocal is equal to 2,9. [#permalink]

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New post 03 Nov 2016, 19:20
x+1/x = 2.9. We need to find x-1/x.

We know that \((x+1/x)^2-4\) = \((x-1/x)^2\) \* using relation \((a+b)^2\) = \(a^2+b^2+2ab\) and \((a-b)^2\) = \(a^2+b^2-2ab\) \*

Therefore 8.41-4 =\((x-1/x)^2\) and,

abs(x-1/x) =\sqrt{(4.41)} i.e. 2.1

Answer choice E

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Re: The sum of a certain number and its reciprocal is equal to 2,9. [#permalink]

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New post 03 Nov 2016, 23:14
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ReussirleGMAT wrote:
The sum of a certain number and its reciprocal is equal to 2,9. What is the absolute value of the difference of this number and its reciprocal ?

A. 2,2 B. 1,2 C. 0,3 D. 0,4 E. 2,1



x+1/x=2.9
x^2-2.9x+1=0
10x^2-29x+10=0
(5x-2)(2x-5)=0
5x=2
x=2/5=.4
1/.4-.4=2.1
E

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Re: The sum of a certain number and its reciprocal is equal to 2,9. [#permalink]

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New post 03 Nov 2016, 23:45
Nice Method seneca04 but it is not the best way, please check how gracie did it.
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The sum of a certain number and its reciprocal is equal to 2,9. [#permalink]

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New post 08 Sep 2017, 05:33
a+1/a = 2.9
\(a^2\)-2.9a+1=0
10\(a^2\)-29a+10=0
(5a-2) ( a-5) =0
a cant be 5 as sum is less
a=2/5

so 1/a-a => 5/2-2/5 =21/10 =2.1 = option E
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Re: The sum of a certain number and its reciprocal is equal to 2,9. [#permalink]

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New post 08 Sep 2017, 05:50
ANOTHER METHOD

(a+1/a)^2 = a^2 +1/a^2 +2
2.9^2 = y+2 where y= a^2+1/a^2

(a-1/a)^2 = a^2 + 1/a^2 -2
z^2 = y-2 WHERE z= a-1/a

z^2 - 2.9^2 = -4
z^2 = 2.9^2-4
z^2 = 8.41-4
Z^2 = 4.41
Z= 2.1 OPTION E
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Re: The sum of a certain number and its reciprocal is equal to 2,9. [#permalink]

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New post 08 Sep 2017, 05:52
AnisMURR wrote:
Nice Method seneca04 but it is not the best way, please check how gracie did it.



check my method, How i did it apart from gracie 'S method.
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Re: The sum of a certain number and its reciprocal is equal to 2,9.   [#permalink] 08 Sep 2017, 05:52
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The sum of a certain number and its reciprocal is equal to 2,9.

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