If a and b are positive integers and X = 2^a * 3^b, what is the value

Question

If a and b are positive integers and X = 2^a * 3^b, what is the value of X?

(1) a and b are consecutive prime numbers
(2) a = 2

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8.toastcrunch · Answer

(1) a and b are consecutive prime numbers.
a and b must have distinct values from among 2 and 3- being the only pair of consecutive positive prime numbers; but we don't know the individual values of a and b,Hence, statement (1) alone is insufficient

(2) a = 2.
If a = 2, However, we don't have enough information about the value of b. Without knowing the value of b, we cannot determine the value of X. Hence, statement (2) alone is insufficient to determine the value of X.

By combining both the statement we get a= 2 and b=3,sufficient
Answer is

zhanbo · Answer

Consecutive prime numbers refer to a sequence of prime numbers that are next to each other with no other prime numbers between them.

(1) Only
Evidently insufficient

(2) Only
b is unknown. Insufficient.

(1)(2) Together
So a =2, and b = 3
Sufficient

The answer is thus  (C)

fdfd97 · Answer

Statement 1- a and b must have distinct values from among 2 and 3- being the only pair of consecutive positive prime numbers; but we don't know the individual values of a and b- Insufficient

Statement 2- a=2, we don't know the value of b- Insufficient

Combining the 2 Statements- If a=2, b must be 3, so we can solve 2^2 * 3^3- Sufficient- Option C.

Archit3110 · Answer

find value of X
X = 2^a * 3^b

#1
a and b are consecutive prime numbers
2,3 ; 3,5 ; 5,7 so on
value of X will differ ; insufficient
#2
a is 2
insufficient as b is not known
from 1 &2
x = 2^2* 3^3 ; 108

sanchitb23 · Answer

Given: a and b are +ive Integers And  X = 2^a * 3^b 
Question: Value of X?

Statement 1 : a and b are consecutive prime numbers
We know the only Consecutive Prime Numbers are 2 and 3, So we know a and b can have values 2 and 3, but which variable will have what value from both is not clear,  Hence, Statement 1 is not Sufficient

Statement 2 : a = 2
While it directly gives us value of a, we do not know value of b,  Hence, Statement 2 is not Sufficient
 
Statement 1 and 2: 
From 1, we know values can be 2 and 3, but which is which is not clear.
From 2, we know a=2
Combining both, a=2 and b=3,  Hence Together, it is sufficient
 
 Answer is C

If a and b are positive integers and X = 2^a * 3^b, what is the value

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