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555-605 Level|   Algebra|   Inequalities|         
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If x is an integer, what is the value of x? (1) 1/5 < 1/(x + 1) < 1/2 Updated on: 23 May 2020, 07:11
Originally posted by jlgdr on 18 Sep 2013, 15:38.
Last edited by Bunuel on 23 May 2020, 07:11, edited 3 times in total.
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If x is an integer, what is the value of x?


(1) \(\frac{1}{5}<\frac{1}{x+1}<\frac{1}{2}\)

(2) \((x-3)(x-4)=0\)


PS21277
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C
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If x is an integer, what is the value of x? (1) 1/5 < 1/(x + 1) < 1/2 18 Sep 2013, 15:48
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If x is an integer, what is the value of x?

(1) \(\frac{1}{5}<\frac{1}{x+1}<\frac{1}{2}\). Since x is an integer, the x+1=4 or x+1=3, from which it follows that x=3 or x=2. Not sufficient.

(2) (x-3)(x-4)=0 --> x=3 or x=4. Not sufficient.

(1)+(2) Common value is x=3. Sufficient.

Answer: C.
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If x is an integer, what is the value of x? (1) 1/5 < 1/(x + 1) < 1/2 30 Oct 2014, 22:35
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If x is an integer, what is the value of x?

(1) \(\frac{1}{5}<\frac{1}{x+1}<\frac{1}{2}\)

(2) \((x-3) (x-4) = 0\)

Source: New Oriental Education and technology group

C.

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.
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If x is an integer, what is the value of x? (1) 1/5 < 1/(x + 1) < 1/2 07 Nov 2014, 05:34
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dmmk
If x is an integer, what is the value of x?

(1) \(\frac{1}{5}<\frac{1}{x+1}<\frac{1}{2}\)

(2) \((x-3) (x-4) = 0\)

Source: New Oriental Education and technology group

C.

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
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If x is an integer, what is the value of x? (1) 1/5 < 1/(x + 1) < 1/2 07 Nov 2014, 06:33
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dmmk
If x is an integer, what is the value of x?

(1) \(\frac{1}{5}<\frac{1}{x+1}<\frac{1}{2}\)

(2) \((x-3) (x-4) = 0\)

Source: New Oriental Education and technology group

C.

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.

Hope it's clear.
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If x is an integer, what is the value of x? (1) 1/5 < 1/(x + 1) < 1/2 08 Oct 2015, 10:08
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Bunuel
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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If x is an integer, what is the value of x? (1) 1/5 < 1/(x + 1) < 1/2 08 Oct 2015, 10:51
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Bunuel
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.


Question : x = ?

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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If x is an integer, what is the value of x? (1) 1/5 < 1/(x + 1) < 1/2 08 Oct 2015, 21:24
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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.

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 .

St 2
(x – 3)(x – 4) = 0
So can x is either 3 or 4


Not sufficient


Together ---- putting the value of x = 3 or 4 from st 2 and putting them in st 1

1/5 < 1/(1 + x) < 1/2
x= 3
0.2 < 0.3 <0.5

x=4
0.2 < 0.25 < 0.5

Hence together not sufficient .

E ans
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If x is an integer, what is the value of x? (1) 1/5 < 1/(x + 1) < 1/2 08 Oct 2015, 22:53
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(1) 1/5 < 1/(1 + x) < 1/2
From this statement, we can say 5>(1+x)>2, so x= 2 or 3....Insufficient

(2) (x – 3)(x – 4) = 0
x=3 or 4...Insufficient.

From both the statements...x=3. Hence, ans 'C'.
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If x is an integer, what is the value of x? (1) 1/5 < 1/(x + 1) < 1/2 09 Oct 2015, 22:25
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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.

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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If x is an integer, what is the value of x? (1) 1/5 < 1/(x + 1) < 1/2 10 Oct 2015, 18:55
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Answer is C.

1. is not sufficient as x can assume multiple values
2. x=3 or x=4. No unique value. Not Sufficient

1. and 2. sufficient. x=3
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If x is an integer, what is the value of x? (1) 1/5 < 1/(x + 1) < 1/2 25 Nov 2020, 12:30
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jlgdr
If x is an integer, what is the value of x?


(1) \(\frac{1}{5}<\frac{1}{x+1}<\frac{1}{2}\)

(2) \((x-3)(x-4)=0\)


PS21277

(1) Since we're told x is an integer, we can have:

\(\frac{1}{5} < \frac{1}{4} < \frac{1}{3} < \frac{1}{2}\)

\(\frac{1}{x+1} = \frac{1}{4}\)

\(x = 3\)

\(\frac{1}{x+1}= \frac{1}{3}\)

\( x = 2\)

INSUFFICIENT.

(2) \((x-3)(x-4) = 0\)

\(x = 3, x = 4\)

INSUFFICIENT.

(1&2) Combined, x must be 3. SUFFICIENT.

Answer is C.
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If x is an integer, what is the value of x? (1) 1/5 < 1/(x + 1) < 1/2 07 Jul 2024, 01:30
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