BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

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

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 19
Joined: Wed May 26, 2010 2:26 am

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

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?
Top
Source: — Problem Solving |
Legendary Member
Posts: 2326
Joined: Mon Jul 28, 2008 3:54 am
Thanked: 173 times
Followed by:2 members
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???
Top
User avatar
Legendary Member
Posts: 1309
Joined: Wed Mar 17, 2010 11:41 pm
Thanked: 33 times
Followed by:5 members

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.
Top
Post new topic Post Reply
• Page 1 of 1