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What is the remainder when 24^3*38^5 is divided by 3 ?

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Bunuel
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What is the remainder when 24^3*38^5 is divided by 3 ? [#permalink] New post   11 May 2022, 04:15
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A
B
C
D
E

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35% (medium)

Question Stats:

59% (01:06) correct 41% (01:30) wrong based on 74 sessions
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What is the remainder when \(24^3*38^5\) is divided by 3 ?

A. 0
B. 1
C. 2
D. 3
E. Cannot be calculated
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buitri84
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Re: What is the remainder when 24^3*38^5 is divided by 3 ? [#permalink] New post   19 May 2022, 01:30
Bunuel wrote:
What is the remainder when \(24^3*38^5\) is divided by 3 ?

A. 0
B. 1
C. 2
D. 3
E. Cannot be calculated


The answer should be C (2). The given answer seems wrong.
24 is divisible by 3, so we can ignore it.
38 gives a remainder of 2 when divided by 3.
So we are basically looking at what's the remainder of 2^5 when divided by 3. And that should be 32 mod 3 = 2.
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Bunuel
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What is the remainder when 24^3*38^5 is divided by 3 ? [#permalink] New post   19 May 2022, 01:37
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buitri84 wrote:
Bunuel wrote:
What is the remainder when \(24^3*38^5\) is divided by 3 ?

A. 0
B. 1
C. 2
D. 3
E. Cannot be calculated


The answer should be C (2). The given answer seems wrong.
24 is divisible by 3, so we can ignore it.
38 gives a remainder of 2 when divided by 3.
So we are basically looking at what's the remainder of 2^5 when divided by 3. And that should be 32 mod 3 = 2.


24 itself is a multiple of 3, which means that \(24^3*38^5=(a \ multiple \ of \ 3)(integer) = (a \ multiple \ of \ 3)\). So, the answer is 0 and all those exponents there are just to confuse us.

Hope it helps.
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buitri84
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Re: What is the remainder when 24^3*38^5 is divided by 3 ? [#permalink] New post   20 May 2022, 03:13
Bunuel wrote:
buitri84 wrote:
Bunuel wrote:
What is the remainder when \(24^3*38^5\) is divided by 3 ?

A. 0
B. 1
C. 2
D. 3
E. Cannot be calculated


The answer should be C (2). The given answer seems wrong.
24 is divisible by 3, so we can ignore it.
38 gives a remainder of 2 when divided by 3.
So we are basically looking at what's the remainder of 2^5 when divided by 3. And that should be 32 mod 3 = 2.


24 itself is a multiple of 3, which means that \(24^3*38^5=(a \ multiple \ of \ 3)(integer) = (a \ multiple \ of \ 3)\). So, the answer is 0 and all those exponents there are just to confuse us.

Hope it helps.


Yes you are right. Typical careless move from me. It's a multiplication with a multiple of 3 yet I'm all forcused on the 38. Nice.
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Re: What is the remainder when 24^3*38^5 is divided by 3 ? [#permalink]
20 May 2022, 03:13
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