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1) 1/5 < 1/(x+1) < 1/2 or 2 < (x+1) < 5 or 1 < x < 4 x = 2 or 3 insufficient.

2) (x-3)(x-4) = 0 x=3 or 4 insufficient.

(1)+(2) --> x = 3 sufficient.

1/5 < 1/(x+1) < 1/2 or 2 < (x+1) < 5

How do you get this? Could you please explain

From 1/5 < 1/(x+1) we know that x+1 must be positive so, we can cross-multiply to get x+1 < 5. The same way from 1/(x+1) < 1/2 we get 2 < x+1. Therefore 2 < x+1 < 5.

Re: If x is an integer, what is the value of x? [#permalink]

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08 Oct 2015, 10:08

Bunuel wrote:

If x is an integer, what is the value of x?

(1) 1/5 < 1/(1 + x) < 1/2 (2) (x – 3)(x – 4) = 0

Kudos for a correct solution.

(1) from this expression we can say x must be +ve -> 5>1+x>2 4>x>1 NOT Sufficient as x could be 2 or 3 (2) x=3 or 4 Not Sufficient (1+2) X=3 Answer (C)
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Share some Kudos, if my posts help you. Thank you !

Statement 1: 1/5 < 1/(1 + x) < 1/2 i.e. 1+x = 3 or 4 i.e. x = 2 or 3 NOT SUFFICIENT

Statement 2: (x – 3)(x – 4) = 0 i.e. x = 3 or x = 4 NOT SUFFICIENT

Combining the two statements x = 3 is the only common solution

Answer: Option C
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Hi Bunuel , If i am wrong at st 1 using the inequality .please correct me and show the correct approach for this kind of inequality .

St (1) 1/5 < 1/(1 + x) < 1/2

As x integer -- it can be positive and negative .

so we cant cross multiple and solve the the above st .

not sufficient .

The Highlighted statement is Incorrect because x can't be Negative for 1/5 < 1/(1 + x) < 1/2 to be true

for the above mentioned Inequation to be true

(x+1) must lie between 2 and 5

i.e. 2 < (x+1) < 5 i.e. 2-1 < (x) < 5-1 i.e. 1 < (x) < 4

I hope this helps!
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