If x is a positive integer, is x^2 + 1 an odd number?

Question

(1) x is the smallest integer that is divisible by all integers from 11 to 15, inclusive.
(2) 3^x is an odd number.

Fdambro294 · Answer

Rule: an Integer Exponent will have no effect on the Even/Odd Nature of the underlying Base

If X = Odd ———> then (X)^2 = Odd * Odd = Odd

Statement 1: if X is Divisible by Even Numbers such as 12 and 14, then X itself will be Even

As stated above, (X)^2 will retain the Even nature of X

Thus (X)^2 + 1 = Even + Odd = Odd
Stmt 1 Sufficient

Statement 2: (3)^x Power = Odd

As the rule states above, the (+) Positive Integer Exponent X will have no effect on the Even/Odd Nature of the Result, regardless of whether X is Even or Odd

Since we can not tell whether X is Even or Odd (both will result in 3 raised to the +Pos. Integer X power = Odd)

We can NOT answer definitively whether (X)^2 + 1 = Even or Odd

Statement 2 NOT Sufficient

-A-

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IanStewart · Answer

Statement 1 tells us the exact value of x (or tells us how to find it at least), and of course we can answer any question about x if we know what x equals. Statement 2 is always true if x is a positive integer, so it doesn't tell us anything and can't possibly be sufficient.

So it really doesn't matter what the question even asks here. As long as it's asking something about x alone (and not about some other letter like y too), then the answer to this question is automatically A.

To answer Mahi14's question above: Statement 1 (which needs to say "smallest positive integer" to be correct) says that x is the Least Common Multiple of 11, 12, 13, 14 and 15. If you know how to find LCMs, you could work out that x = (2^2)(3)(5)(7)(11)(13), but fortunately we don't need to actually compute x here, since it's a DS question.

chetan2u · Answer

So  x\geq{1} 
Thus the answer will depend on x. If x is odd, x^2+1 is even, otherwise odd.

(1) x is the smallest integer that is divisible by all integers from 11 to 15, inclusive.
x is divisible by 11, 12, 13, 14, 15.
Since x is divisible by EVEN numbers, x is even.
Suff

(2) 3^x is an odd number.
x could be odd or even, as 3^x will always be odd.
Insuff

A

exc4libur · Answer

x>=1
x2+1=odd?
x2+odd=odd, when x=even

(1) sufic
x/{11,12...15}=integer
x=even

(2) insufic
3^x=odd, then x = {odd or even}

(A)

TestPrepUnlimited · Answer

Is  x^2 + 1  odd?
Is  x^2  even?
Is  x  even?

Statement 1: 
"The smallest integer" reveals there is only one such value for x, since there is only one value for x this is automatically sufficient.

Statement 2: 
No matter how high you raise the power of 3,  3^x  is always going to odd, so this doesn't tell us anything about x. Insufficient.

Ans: A

winterschool · Answer

If x is a positive integer, is x^2 + 1 an odd number?

(1) x is the smallest integer that is divisible by all integers from 11 to 15, inclusive.
(2) 3^x is an odd number.

Statement 1:

x = 3*4*5**7*11*13

x^2 + 1, identifiable

Sufficient

Statement 2:

for any positive value of x , 3^x = odd

Notsufficient

Answer A

GCMEMBER · Answer

If x is a positive integer, is x^2 + 1 an odd number?

x^2 + 1 will be an odd number only when x is even.

(1) x is the smallest integer that is divisible by all integers from 11 to 15, inclusive.
Therefore, x is even.
Sufficient.

(2) 3^x is an odd number.
Therefore, x can be 1, 2, 3 etc.

So x can be even or odd.

Not sufficient.

Option A

If x is a positive integer, is x^2 + 1 an odd number?

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GMAT Data Sufficiency (DS) Questions

If x is a positive integer, is x^2 + 1 an odd number?

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