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# Given that x is a positive integer such that x ≥ 75, which of the foll

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Manager
Joined: 23 Dec 2011
Posts: 54
Given that x is a positive integer such that x ≥ 75, which of the foll  [#permalink]

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31 Jul 2019, 20:54
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Difficulty:

35% (medium)

Question Stats:

66% (01:20) correct 34% (01:39) wrong based on 38 sessions

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Q = x^3 − x

Given that x is a positive integer such that x ≥ 75, which of the following is the remainder when Q is divided by 6?

A. 0
B. 1
C. 3
D. 5
E. Cannot be determined by the information provided
Intern
Joined: 27 Aug 2018
Posts: 49
Location: India
Concentration: Operations, Healthcare
Schools: ISB '21
WE: Operations (Health Care)
Re: Given that x is a positive integer such that x ≥ 75, which of the foll  [#permalink]

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31 Jul 2019, 21:20
1
anupam87 wrote:
Q = x^3 − x

Given that x is a positive integer such that x ≥ 75, which of the following is the remainder when Q is divided by 6?

A. 0
B. 1
C. 3
D. 5
E. Cannot be determined by the information provided

Q = $$x^3$$ - x
Q = x($$x^2$$-1)
Q = x(x+1)(x-1)

Now we know x ≥ 75 and to be divided by 6 a.k.a (2x3)

Rephrasing the question, when

$$\frac{x(x+1)(x-1)}{(2x3)}$$ What is the remainder?

From the above equation it can be clearly seen that the NUM is three consecutive integers. And when any three consecutive integers are multiplied together, they are completely divisible by 2 an 3, thus leaving no remainder.

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Joined: 31 Oct 2013
Posts: 1429
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: Given that x is a positive integer such that x ≥ 75, which of the foll  [#permalink]

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03 Aug 2019, 03:36
1
anupam87 wrote:
Q = x^3 − x

Given that x is a positive integer such that x ≥ 75, which of the following is the remainder when Q is divided by 6?

A. 0
B. 1
C. 3
D. 5
E. Cannot be determined by the information provided

$$Q = x^3 - x$$

$$x(x^2 - 1)$$

x(x + 1) ( x - 1)

3 consecutive integer is always divisible by 6 or 3!.

Re: Given that x is a positive integer such that x ≥ 75, which of the foll   [#permalink] 03 Aug 2019, 03:36
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