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Let P be the product of any three consecutive positive odd integers. T

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Let P be the product of any three consecutive positive odd integers. T  [#permalink]

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New post 18 Jul 2019, 08:41
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A
B
C
D
E

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  75% (hard)

Question Stats:

20% (01:41) correct 80% (01:35) wrong based on 30 sessions

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Let P be the product of any three consecutive positive odd integers. The largest integer dividing all such P is:

(A) 15

(B) 6

(C) 5

(D) 3

(E) 1

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Re: Let P be the product of any three consecutive positive odd integers. T  [#permalink]

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New post 18 Jul 2019, 08:53
Answer should be D?

Since for example 17*19*21 is divisible by 3 and not by 15

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Re: Let P be the product of any three consecutive positive odd integers. T  [#permalink]

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New post 18 Jul 2019, 21:15
Pick up a case like 9x11x13.
They are all-consecutive positive integers. And it is not divisible by 15. Thus, largest divisible option: 3
And: D
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Re: Let P be the product of any three consecutive positive odd integers. T  [#permalink]

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New post 21 Aug 2019, 00:12
Noshad please post OE.
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Re: Let P be the product of any three consecutive positive odd integers. T  [#permalink]

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New post 21 Aug 2019, 01:17
Noshad wrote:
Let P be the product of any three consecutive positive odd integers. The largest integer dividing all such P is:

(A) 15

(B) 6

(C) 5

(D) 3

(E) 1


Given: P is the product of any three consecutive positive odd integers.

Asked: The largest integer dividing all such P is:

Let the 3 consecutive odd integers be a-2, a & a+2 where a is odd

P is the product of any three consecutive positive odd integers = (a-2) * a * (a+2)
One of the 3 numbers will be divisible by 3 since
If a=3k => a is divisible by 3 => p is divisible by 3
If a=3k+1 => a+2 is divisible by 3 => p is divisible by 3
If a=3k+2 => a-2 is divisible by 3 => p is divisible by 3
=> E is OUT

Since all numbers are odd => p is NOT divisible by 2 => B is OUT

Let us consider a case e.g. 7,9,11 non of the numbers is divisible by 5. => A & C are OUT

IMO D
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Re: Let P be the product of any three consecutive positive odd integers. T   [#permalink] 21 Aug 2019, 01:17
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