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# What is the value of s?

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Intern
Joined: 24 Aug 2017
Posts: 8
What is the value of s?  [#permalink]

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11 Oct 2017, 21:01
00:00

Difficulty:

35% (medium)

Question Stats:

73% (01:41) correct 27% (01:31) wrong based on 49 sessions

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What is the value of s?

1) $$\frac{1}{s} = \frac{1}{(s+25)} + \frac{1}{(s+1)}$$
2) -1/5 is not a reciprocal of s
Math Expert
Joined: 02 Aug 2009
Posts: 7035
Re: What is the value of s?  [#permalink]

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12 Oct 2017, 00:24
1
khalid228 wrote:
What is the value of s?

1) $$\frac{1}{s} = \frac{1}{(s+25)} + \frac{1}{(s+1)}$$
2) -1/5 is not a reciprocal of s

Let's see the statements
1) $$\frac{1}{s} = \frac{1}{(s+25)} + \frac{1}{(s+1)}$$
$$\frac{1}{s+25}+\frac{1}{s+1}-\frac{1}{s}=0........\frac{s^2+s+s^2+25s-(s^2+26s+25)}{s(s+1)(s+25)}=0.........$$
For the fraction to be 0, numerator has to be 0..
So $$s^2-25=0$$ or s=5 or s=-5
Two values possible..
Insufficient

2) -1/5 is not a reciprocal of s
s can be any value except-5
Insufficient

Combined..
Only value possible is s as 5
Sufficient

C
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Intern
Joined: 24 Aug 2017
Posts: 8
What is the value of s?  [#permalink]

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12 Oct 2017, 00:39
chetan2u I understand the concept and ideal behind it now, but could you explain to me how you went from the first equation to the second?

$$\frac{1}{s+25}+\frac{1}{s+1}-\frac{1}{s}=0............. \frac{s^2+s+s^2+25s-(s^2+26s+25)}{s(s+1)(s+25)}=0$$
Math Expert
Joined: 02 Aug 2009
Posts: 7035
What is the value of s?  [#permalink]

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12 Oct 2017, 19:18
khalid228 wrote:
chetan2u I understand the concept and ideal behind it now, but could you explain to me how you went from the first equation to the second?

$$\frac{1}{s+25}+\frac{1}{s+1}-\frac{1}{s}=0............. \frac{s^2+s+s^2+25s-(s^2+26s+25)}{s(s+1)(s+25)}=0$$

Hi..

We are actually getting all terms in equivalent form by getting the denominator same for all fractions
First take LCM of the denominator and then simplify the term by adding all fractions.

$$\frac{1}{s+25}+\frac{1}{s+1}-\frac{1}{s}=\frac{1*(s+1)*s+(s+25)*s-(s+1)(s+25)}{(s+1)(s+25)(s)}=0............. \frac{s^2+s+s^2+25s-(s^2+26s+25)}{s(s+1)(s+25)}=0$$[/quote]
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Director
Joined: 17 Dec 2012
Posts: 629
Location: India
Re: What is the value of s?  [#permalink]

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14 Oct 2017, 20:57
The second statement is a giveaway. It suggests we get two values from statement 1. Solving the first statement is also straightforward. We get 2 values for s. With statements 1 and 2, the question can be answered.

Hence C.
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Srinivasan Vaidyaraman
Sravna Holistic Solutions
http://www.sravnatestprep.com

Holistic and Systematic Approach

Re: What is the value of s? &nbs [#permalink] 14 Oct 2017, 20:57
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