If a, b and c are positive prime numbers, what is the value of a^3b^3c

Question

If a, b and c are prime numbers, what is the value of  a^3b^3c^3 ?

(1)  a^3bc = 2457

(2)  b = 7

saurabh9gupta · Answer

so we need to check whether any of the three values are positive or negative.
1. 2457 = (3)^3 * 7 * 13

a = 3 but
b and c could be 7 and 13 (or vice versa) OR
b and c could be -7 and -13 (or vice versa)

Not sufficient.

2. Not Sufficient

combine, we know that b and c will be positive (a definitive answer) so C

bebs · Answer

saurabh9gupta  Prime numbers can't be negative so you can't try a negative number. I got the same answer (C) like you though. Fingers crossed for the OA. Cheers!

PS: Looked at the question again and C is a wrong answer. Answer is  A .

BrentGMATPrepNow · Answer

Target question :    What is the value of a³b³c³?

Given : a, b and c are prime numbers

Statement 1 : a³bc = 2457  
2457 = (3)(3)(3)(7)(13) = (3³)(7)(13)
So, we can be certain that a =3
From here there are two possible cases:
 Case a : a = 3, b = 7 and c = 13. In this case, the answer to the target question is  a³b³c³ = 3³7³13³ 
 Case b : a = 3, b = 13 and c = 7. In this case, the answer to the target question is  a³b³c³ = 3³13³7³ 
Notice that, for each case, the answer to the target question is the SAME (i.e., 3³7³13³ = 3³13³7³) 
So, it  must  be the case that  a³b³c³ = 3³7³13³ 
Since we can answer the  target question  with certainty, statement 1 is SUFFICIENT

Statement 2 : b = 7 
Since there's no information about a and c, there's no way to answer the  target question  with certainty.
So, statement 2 is NOT SUFFICIENT

Answer: A

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Sreyoshi007 · Answer

IMO answer should be  A.

Statement 1 :  a^3.b.c=2457 
On  prime factorizing  2457;

2457 = 3^3. 17. 7

So we can write  a^3bc=2457 
 a^3.b.c  =  3^3. 17. 7

From this we can tell  a = 3 and b or c = 17 or 7 
We can find the value of a^3.b^3.c^3, since we don't need to know if b or c is 17 or 7. The answer will remain the same if b = 17 or 7 and same with c.
 Sufficient.

Statement 2: b = 7
Clearly insufficient as we do know know the values of a or c.

If a, b and c are positive prime numbers, what is the value of a^3b^3c

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