If t is a positive integer, is t^3 + 1 an odd number? (1) t is the sma

Question

If t is a positive integer, is t^3 + 1 an odd number?

(1) t is the smallest integer that is divisible by all integers from 21 to 25, inclusive.
(2) 5^t is an odd number.

Saikrishna341 · Answer

I think E is the answer to the above question
Solution:
Statement 1: t is the smallest integer that is divisible by all integers from 21 to 25, inclusive.
 i.e. find the LCM of 21,22,23,24,25 which gives 1062600
 i.e. t3+1 = 1062600, which is an even number 
 therefore statement 1 is sufficient 
Statement 2: 5^t is an odd number
 5^t is always an odd number for any values of t
 therefore we cannot say anything from statement 2
Therefore A is the correct answer in my opinion.

AjitJangale · Answer

t^3 + 1 will be odd when "t" is even.

So we need to find "t" is even?

(1) t is the smallest integer that is divisible by all integers from 21 to 25, inclusive.

We need to find LCM of numbers from 21 to 25. So Factorize all numbers from 21 to 25. We found 2 and 5 are the factors of LCM. Hence we will get number with zero, which is Even. Sufficient to answer question.
Sufficient.

(2) 5^t is an odd number.
5^t always odd for all positive integer value of "t". So "t" may be even or odd.
Insufficient.

IMO Answer is A.

RutuM · Answer

The problem statement asks whether t^3 + 1 is an odd integer.
To determine that, we need to find whether t^3 is odd or even.

Statement 1 -> t is the smallest integer that is divisible by all integers from 21 to 25, inclusive.
In 21 to 25, we have 2 even numbers. As t is LCM of numbers 21 to 25, it has to be even because of its even factors. (No need to calculate the entire LCM)
Thus, from statement 1 we know that t is even and thus t^3 + 1 is odd.
 Statement 1 -> Sufficient

Statement 2 -> 5^t is an odd number.
(Odd integer ^ any integer) results in an odd integer.
Thus, from the given statement, we cannot determine whether t is odd or even.
 Statement 2 -> Insufficient

Answer -> A

If t is a positive integer, is t^3 + 1 an odd number? (1) t is the sma

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GMAT Data Sufficiency (DS) Questions

If t is a positive integer, is t^3 + 1 an odd number? (1) t is the sma

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