If x is an integer greater than 1 but less than 101, is 1/2*x an integ

Question

If x is an integer greater than 1 but less than 101, is 1/2*x an integer?

(1) x=s^2, where s is a positive integer.
(2) x=t^4, where t is a positive integer.

raarun · Answer

The question basically asks is x even ?

Stmnt 1 > 
x= 2^2 so x i even
x=3^2 so x is not even
So Stmnt 1 is insufficient

Stmnt 2 >
x=2^4 =16 so x is even
x=3^4=81 so x is not even
So Stmnt 2 is insufficient

Stmn 1 + 2 > s^2 = t^4 --> s=t^2
when t = 2 s= 4 so x =16 is even
when t=3 s=9 so x=81 is not even

Ans - E

wintersrhn · Answer

The question can be framed as 1 x = s^2, => s <=10 ,=> s can be 2,3,4,5,6,7,8,9,10 , => x can be 4,9,16,25,36,49,64,81,100 - insuffcient Option 2 -> x = t^4, => t <=3 => , t=2,3 => x = 16 or x = 81, insufficient. 1&2 => x - 16 or 81 => insufficient

chetan2u · Answer

Hi,
you cannot assume taht x is EVEn..
We have to find whether x is EVEN or ODD..
so option 2 gives us two values 16 and 81..
you can rework the solution now..

CrackverbalGMAT · Answer

If x is an integer greater than 1 but less than 101, is 1/2*x an integer?

Its given that  1< x < 101. 
We need to find whether  \frac{1}{2} * x   is an integer or not.

\frac{1}{2} * x   is an integer only if x is even.
If x is odd,  \frac{1}{2} * x   will not be an integer.
Therefore, we can re-frame the question stem as  Is x is even  ?

(1)  x=s^2 , where s is a positive integer.
if S is even integer, then  S^2  will be even but if S is an odd integer ,then  S^2  will be odd.
Since we don't know whether S is even or odd, we cannot confirm whether  S^2  or  x  is even or not. Hence Statement 1 alone is insufficient.

(2)  x=t^4 , where t is a positive integer.

Since 1< x < 101, the only possible values of t are 2 and 3
Case 1: t = 2, x =  2^ 4  = 16 in this case, x is even and 1/2 * x is an integer.

Case 2: t = 3, x =  3^4  = 81 Here, x is odd and 1/2 * x is not an integer.

Since both cases are possible, Statement 2 alone is insufficient.

Even-though if you combining 2 statements, x could be even or odd.

x = t^4 =s^2  
Case 1:   x = 2^4 =4^2 = 16  Here, X is even

Case 2:  x = 3^4 =9^2 = 81 . In this case, X is odd

Option E is the correct answer.

Thanks,
  Clifin J Francis,
GMAT SME

SalahT · Answer

The question has basically asked that x is even or not.
This is an yes / no question
Always odd is sufficient.
Always even is also sufficient.
But Both is not sufficient.
(i) x can be odd of even Because s can be odd or even
Not sufficient
(ii) x can be odd of even Because t can be odd or even
Not sufficient

(i+ii) s and t independent of each other.  s^2=t^4  can be odd or even

Thus, IMO Answer is E.

SalahT · Answer

The question has basically asked that x is even or not.
This is an yes / no question
Always odd is sufficient.
Always even is also sufficient.
But Both is not sufficient.
(i) x can be odd of even Because s can be odd or even
Not sufficient
(ii) x can be odd of even Because t can be odd or even
Not sufficient

(i+ii) s and t independent of each other.  s^2=t^4  can be odd or even

Thus, IMO Answer is E.

bumpbot · Answer

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If x is an integer greater than 1 but less than 101, is 1/2*x an integ

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If x is an integer greater than 1 but less than 101, is 1/2*x an integ

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