If x is odd, does it mean that x-1 is even?

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Shridharvk: Junior | Next Rank: 30 Posts; Posts: 19; Joined: Wed May 26, 2010 2:26 am

by Shridharvk » Mon Jul 19, 2010 2:34 am

If x^3 –x = p, and x is odd, is p divisible by 24?

This is the answer I found in MGMAT book: -

p= (x-1)x(x+1).

If x is odd, then (x-1) and (x+1) must be even. Thus p is divisible by atleast 4. Futher more, (x-1) and (x+1) are consecutive multiples of 2. So either (x-1) or (x+1) must have another 2 and is therefore divisible by 8.

In addition, one of the number is divisible by 3. Therefore p is divisible by 24.

My question is, if x is odd, then x-1 can be zero also. Why is it mentioned that the minimum value of x-1 is 2?

Source: Beat The GMAT — Problem Solving | Mon Jul 19, 2010 2:34 am

gmatmachoman: Legendary Member; Posts: 2326; Joined: Mon Jul 28, 2008 3:54 amFollowed by: 2 members; Thanked: 173 times; GMAT Score:710

by gmatmachoman » Mon Jul 19, 2010 2:45 am

Shridharvk wrote:If x^3 –x = p, and x is odd, is p divisible by 24?

This is the answer I found in MGMAT book: -

p= (x-1)x(x+1).

If x is odd, then (x-1) and (x+1) must be even. Thus p is divisible by atleast 4. Futher more, (x-1) and (x+1) are consecutive multiples of 2. So either (x-1) or (x+1) must have another 2 and is therefore divisible by 8.

In addition, one of the number is divisible by 3. Therefore p is divisible by 24.

My question is, if x is odd, then x-1 can be zero also. Why is it mentioned that the minimum value of x-1 is 2?

(x^3 –x )

x(x^2 -1)

x(X+1)(X-1)

This is certainly divisible by 3.

Since X is odd, lets take X = 3, then x-1 = 2, x+1 = 4

3*2 *4 is divisible by 24. YES

Another example : X= 21

21* 20 * 22 is divisible by 24 YES!!

Ok what if X is even, then we can't say with certainity that p is divisible by 24.

Coming to your query if we take X = 1, then X-1 will be zero and ofcourse zero is divisible by 24.

The question could have been better framed as X notequal to 1 or -1.. Is that fine???

R&D on GMAT algorithm:

https://www.beatthegmat.com/r-d-on-gmat- ... tml#305739

pradeepkaushal9518: Legendary Member; Posts: 1309; Joined: Wed Mar 17, 2010 11:41 pmFollowed by: 5 members; Thanked: 33 times

by pradeepkaushal9518 » Mon Jul 19, 2010 2:48 am

x3-x=p and x is odd

let x= 1,3,5,7

1-1=0 is divisble by 24 yes

3^3-3=24 is divisble by 24 yes

5^3-5=120 is divisble by 24 yes

and so on

if u divide 0 with anything it will be zero and it is not necessary to mention anything extra information.

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