If x is an integer, what is the value of x? (1) 1/5

Question

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

Bunuel · Answer

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.

thefibonacci · Answer

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.

anupamadw · Answer

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

How do you get this? Could you please explain

Bunuel · Answer

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.

BrainLab · Answer

(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)

GMATinsight · Answer

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

TheKingInTheNorth · Answer

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

asethi · Answer

(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'.

GMATinsight · Answer

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!

longfellow · Answer

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

Basshead · Answer

(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.

Christiantrib · Answer

why is the second one not enough? you get 3 or 4, but you know it cannot be 4 as 1/(4+1) =1/5 so it goes against the initial inequality and has to be 3. Is there something I have overlooked?

Bunuel · Answer

You are using info from (1) to evaluate (2).

If x is an integer, what is the value of x? (1) 1/5 < 1/(x + 1) < 1/2

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GMAT Data Sufficiency (DS) Questions

If x is an integer, what is the value of x? (1) 1/5 < 1/(x + 1) < 1/2

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