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# The sum of a certain number and its reciprocal is equal to 2.9

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Manager
Status: Quant Expert Q51
Joined: 02 Aug 2014
Posts: 103
The sum of a certain number and its reciprocal is equal to 2.9  [#permalink]

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03 Nov 2016, 12:42
3
8
00:00

Difficulty:

75% (hard)

Question Stats:

58% (02:34) correct 42% (02:39) wrong based on 163 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

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Joined: 28 Jun 2016
Posts: 205
Concentration: Operations, Entrepreneurship
Re: The sum of a certain number and its reciprocal is equal to 2.9  [#permalink]

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03 Nov 2016, 13:11
2
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

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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Manager
Status: Quant Expert Q51
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Posts: 103
Re: The sum of a certain number and its reciprocal is equal to 2.9  [#permalink]

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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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Re: The sum of a certain number and its reciprocal is equal to 2.9  [#permalink]

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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

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Joined: 07 Dec 2014
Posts: 1218
Re: The sum of a certain number and its reciprocal is equal to 2.9  [#permalink]

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03 Nov 2016, 23:14
1
1
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
Manager
Status: Quant Expert Q51
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Posts: 103
Re: The sum of a certain number and its reciprocal is equal to 2.9  [#permalink]

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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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Re: The sum of a certain number and its reciprocal is equal to 2.9  [#permalink]

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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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08 Sep 2017, 05:50
1
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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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]

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06 Feb 2019, 12:13
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Re: The sum of a certain number and its reciprocal is equal to 2.9   [#permalink] 06 Feb 2019, 12:13
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