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# If a is a positive integer, then which of the following must be true

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If a is a positive integer, then which of the following must be true  [#permalink]

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28 May 2019, 00:08
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67% (01:03) correct 33% (01:12) wrong based on 87 sessions

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If a is a positive integer, then which of the following must be true of (a − 1)(a)(a + 1)?

I. It is always divisible by 3.
II. It is always divisible by 4.
III. It is non-prime.

A. I only
B. II only
C. III only
D. I and III only
E. I, II and III

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If a is a positive integer, then which of the following must be true  [#permalink]

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Updated on: 28 May 2019, 00:40
Bunuel wrote:
If a is a positive integer, then which of the following must be true of (a − 1)(a)(a + 1)?

I. It is always divisible by 3.
II. It is always divisible by 4.
III. It is non-prime.

A. I only
B. II only
C. III only
D. I and III only
E. I, II and III

we can test the given relation (a − 1)(a)(a + 1) for values of a=1,2,3,4 so on
and see that only option 1 & 3 is valid always
IMO D

Originally posted by Archit3110 on 28 May 2019, 00:23.
Last edited by Archit3110 on 28 May 2019, 00:40, edited 1 time in total.
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Re: If a is a positive integer, then which of the following must be true  [#permalink]

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28 May 2019, 00:37
1
1
Bunuel wrote:
If a is a positive integer, then which of the following must be true of (a − 1)(a)(a + 1)?

I. It is always divisible by 3.
II. It is always divisible by 4.
III. It is non-prime.

A. I only
B. II only
C. III only
D. I and III only
E. I, II and III

IMO D.
I. three consecutive numbers always div. by 3
II. check a=2, not possible.
III. The number will have at least one power of 2 and 3 each, so non prime.
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Re: If a is a positive integer, then which of the following must be true  [#permalink]

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28 May 2019, 00:39
Archit3110 wrote:
Bunuel wrote:
If a is a positive integer, then which of the following must be true of (a − 1)(a)(a + 1)?

I. It is always divisible by 3.
II. It is always divisible by 4.
III. It is non-prime.

A. I only
B. II only
C. III only
D. I and III only
E. I, II and III

we can test the given relation (a − 1)(a)(a + 1) for values of a=1,2,3,4 so on
and see that only option 1 is valid always
IMO A

Archit, (a − 1)(a)(a + 1) is always 3k, shouldn't be a composite number?
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Re: If a is a positive integer, then which of the following must be true  [#permalink]

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28 May 2019, 00:40
LeoN88 wrote:
Archit3110 wrote:
Bunuel wrote:
If a is a positive integer, then which of the following must be true of (a − 1)(a)(a + 1)?

I. It is always divisible by 3.
II. It is always divisible by 4.
III. It is non-prime.

A. I only
B. II only
C. III only
D. I and III only
E. I, II and III

we can test the given relation (a − 1)(a)(a + 1) for values of a=1,2,3,4 so on
and see that only option 1 is valid always
IMO A

Archit, (a − 1)(a)(a + 1) is always 3k, shouldn't be a composite number?

yes, i did an error solving...
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Re: If a is a positive integer, then which of the following must be true  [#permalink]

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28 May 2019, 00:58
Bunuel wrote:
If a is a positive integer, then which of the following must be true of (a − 1)(a)(a + 1)?

I. It is always divisible by 3.
II. It is always divisible by 4.
III. It is non-prime.

A. I only
B. II only
C. III only
D. I and III only
E. I, II and III

In the product of 3 consecutive integers, there will ALWAYS be a multiple of 2 (as multiple of 2 repeats after every 2 integers; 0, 2, 4, . . . ) and a multiple of 3 ALWAYS (as multiple of 3 repeats after every 3 integers; 0, 3, 6, 9, . . . . )

So, if (a − 1)(a)(a + 1) is divisible by 2 and 3; its always divisible by 6

I - YES
II - NO (1*2*3, 2*3*4, 3*4*5, 4*5*6, 5*6*7, . . . . )
III - YES. It will be non-prime as (a − 1)(a)(a + 1) has more than 2 factors always.

IMO Option D
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If a is a positive integer, then which of the following must be true  [#permalink]

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Updated on: 30 May 2019, 16:00
What would happen if a=1 (+ve integer)

Then the wole term would be 0.

Thank you LeoN88!!!

Originally posted by jfranciscocuencag on 30 May 2019, 14:05.
Last edited by jfranciscocuencag on 30 May 2019, 16:00, edited 1 time in total.
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If a is a positive integer, then which of the following must be true  [#permalink]

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30 May 2019, 15:53
1
jfranciscocuencag wrote:
Bunuel LeoN88

What would happen if a=1 (+ve integer)

Then the wole term would be 0.

"which of the following must be true"
In these types of sums try to negate options that becomes false under particular situations/conditions.

Zero is divisible by 3. Infact zero is divisible by any number. jfranciscocuencag
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Re: If a is a positive integer, then which of the following must be true  [#permalink]

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09 Dec 2019, 19:16
In case a = 1 then the product is 0. It is not divisible by 3. Please help
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Re: If a is a positive integer, then which of the following must be true  [#permalink]

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10 Dec 2019, 03:52
Sanket05 wrote:
In case a = 1 then the product is 0. It is not divisible by 3. Please help

You have zero chocolate, you have to divide it among three children. How much will each get. Answer=0.
Re: If a is a positive integer, then which of the following must be true   [#permalink] 10 Dec 2019, 03:52
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