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What is the units digit of the product of any five consecutive positiv

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What is the units digit of the product of any five consecutive positiv  [#permalink]

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New post 08 Mar 2019, 02:39
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

97% (00:39) correct 3% (00:35) wrong based on 35 sessions

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[GMAT math practice question]

What is the units digit of the product of any five consecutive positive integers?

A. 0
B. 2
C. 4
D. 6
E. 8

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Re: What is the units digit of the product of any five consecutive positiv  [#permalink]

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New post 08 Mar 2019, 02:49

Solution


To find:
    • The units digit of the product of any five consecutive positive integers

Approach and Working:
If we consider any five consecutive positive integers, then among those five integers
    • 1 multiple of 5 will be always present
    • At least 2 multiples of 2 will be always present.

Now, if we multiply a multiple of 5 with an even number (multiple of 2), then the product will be always a multiple of 10.
    • Therefore, the units digit of the product = 0

Hence, the correct answer is option A.

Answer: A

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What is the units digit of the product of any five consecutive positiv  [#permalink]

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New post 08 Mar 2019, 21:38
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Re: What is the units digit of the product of any five consecutive positiv  [#permalink]

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New post 10 Mar 2019, 18:22
=>

Since one of the five consecutive integers must be a multiple of \(5\) and one must an even number, their product is a multiple of \(10\).
Thus, the units digits of the product is \(0\).

Therefore, the answer is A.
Answer: A

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Re: What is the units digit of the product of any five consecutive positiv  [#permalink]

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New post 11 Mar 2019, 08:12
MathRevolution wrote:
[GMAT math practice question]

What is the units digit of the product of any five consecutive positive integers?

A. 0
B. 2
C. 4
D. 6
E. 8


Since we know that the product of 5 consecutive integers will always have prime factors of 2 and 5, the units digit of that product will always end in a zero.

Alternate solution:

Since the product of any five consecutive positive integers is divisible by 5! = 120, then the units digit of the product must be 0.

Answer: A
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Re: What is the units digit of the product of any five consecutive positiv   [#permalink] 11 Mar 2019, 08:12
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