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

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Math Expert
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If a, b and c are positive prime numbers, what is the value of a^3b^3c  [#permalink]

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25 Sep 2018, 05:34
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If a, b and c are prime numbers, what is the value of $$a^3b^3c^3$$?

(1) $$a^3bc = 2457$$

(2) $$b = 7$$

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Re: If a, b and c are positive prime numbers, what is the value of a^3b^3c  [#permalink]

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25 Sep 2018, 07:21
Bunuel wrote:
If a, b and c are prime numbers, what is the value of $$a^3b^3c^3$$?

(1) $$a^3bc = 2457$$

(2) $$b = 7$$

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

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Updated on: 25 Sep 2018, 09:48
1
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.

saurabh9gupta wrote:
Bunuel wrote:
If a, b and c are prime numbers, what is the value of $$a^3b^3c^3$$?

(1) $$a^3bc = 2457$$

(2) $$b = 7$$

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

Originally posted by funsogu on 25 Sep 2018, 08:09.
Last edited by funsogu on 25 Sep 2018, 09:48, edited 1 time in total.
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Re: If a, b and c are positive prime numbers, what is the value of a^3b^3c  [#permalink]

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25 Sep 2018, 09:31
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Top Contributor
Bunuel wrote:
If a, b and c are prime numbers, what is the value of $$a^3b^3c^3$$?

(1) $$a^3bc = 2457$$

(2) $$b = 7$$

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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Re: If a, b and c are positive prime numbers, what is the value of a^3b^3c  [#permalink]

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25 Sep 2018, 09:58
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.
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Re: If a, b and c are positive prime numbers, what is the value of a^3b^3c &nbs [#permalink] 25 Sep 2018, 09:58
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# If a, b and c are positive prime numbers, what is the value of a^3b^3c

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