Manhattan Number Prop.DS question not understood

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coolanujdel: Junior | Next Rank: 30 Posts; Posts: 15; Joined: Thu Aug 26, 2010 11:58 pm

by coolanujdel » Thu Jun 06, 2013 2:23 am

Hi,

Can some one please explain the concept behind this question as I have not understood.

If X>1 what is the value of X?
1) x unique factors of x.
Reason for unique factors and only 1 and 2 number cosidered and not 3 or 4 for some reason in explaination.Kindly answer as I have just preparing.

ANuj

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Source: Beat The GMAT — Data Sufficiency | Thu Jun 06, 2013 2:23 am

Atekihcan: Master | Next Rank: 500 Posts; Posts: 149; Joined: Wed May 01, 2013 10:37 pmFollowed by: 9 members; Thanked: 54 times

by Atekihcan » Thu Jun 06, 2013 4:20 am

1 has exactly 1 factor : 1
But it is already mentioned that X > 1
So, X cannot be equal to 1.

Now, 2 has exactly 2 factors : 1 and 2
So, X can be equal to 2.

Now, for any integer X greater than 2, the number of unique factors of X must be less than X.

Why so?
Because any X greater than 2 will not be divisible by (X - 1)

Why so?
Because X and (X - 1) are consecutive integers.
So, one of them will be odd and the other one will be even.
So, (X - 1) cannot divide X.

So, only possible value of X is 2.

Hope that helps.

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coolanujdel: Junior | Next Rank: 30 Posts; Posts: 15; Joined: Thu Aug 26, 2010 11:58 pm

by coolanujdel » Thu Jun 06, 2013 7:37 am

Not understood.
Now, for any integer X greater than 2, the number of unique factors of X must be less than X.
This above statement is understood by me by the fact that factors cant be greater than the number.

Why so?
Because any X greater than 2 will not be divisible by (X - 1)? Why this statement has come?
This X-1 is if purely notation for consecutive integer then why not X+1 and as a fact any number which is consecutive can not be divisible by its immediate before number. Right?

Why so?
Because X and (X - 1) are consecutive integers.
So, one of them will be odd and the other one will be even.
So, (X - 1) cannot divide X. Why this statement?

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mkdureja: Senior | Next Rank: 100 Posts; Posts: 38; Joined: Fri Jan 04, 2013 12:55 am; Thanked: 11 times

by mkdureja » Thu Jun 06, 2013 7:48 am

For any positive integer x to have x unique factors means that it must be a multiple of every integer from 1 to x.
So, x must be a factor of x-1, which can't be true for any x > 2.
So, x = 2 is the only solution.

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coolanujdel: Junior | Next Rank: 30 Posts; Posts: 15; Joined: Thu Aug 26, 2010 11:58 pm

by coolanujdel » Thu Jun 06, 2013 8:17 pm

I got your point!!!thanks for the info.!!!you must be a expert in maths...have you taken gmat, if yes kindly tell me which book to refer after manhattan gmat maths.
One more thing is why not X+1 is talked about?

Anuj

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