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# How many integers, N, exist such that x < N < x + 12 where N is a mult

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Math Expert
Joined: 02 Sep 2009
Posts: 53063
How many integers, N, exist such that x < N < x + 12 where N is a mult  [#permalink]

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28 Aug 2018, 04:24
00:00

Difficulty:

75% (hard)

Question Stats:

54% (02:01) correct 46% (02:16) wrong based on 108 sessions

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How many integers, N, exist such that x < N < x + 12 where N is a multiple of 3?

(1) x is odd.

(2) x is not a multiple of 3.

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Director
Joined: 18 Jul 2018
Posts: 676
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Re: How many integers, N, exist such that x < N < x + 12 where N is a mult  [#permalink]

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28 Aug 2018, 04:35
1
From statement 1:

If X is odd.
Let's take X as 1 then 1<N<13.
Number of integers which are multiple of 3 are 3,6,9,12. N = 4.
If X = 3. Then 3<N<15.
Number of integers which are multiple of 3 are 6,9,12. N = 3.
So, insufficient.

From statement 2:

X is not a multiple of 3.
Lets take X as 2.
Then 2<N<14. N = 4.
Lets take X as 5.
Then 5<N<17. N = 4.
Sufficient.

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Intern
Joined: 27 Nov 2017
Posts: 5
How many integers, N, exist such that x < N < x + 12 where N is a mult  [#permalink]

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07 Nov 2018, 23:41
From statement 2:

X is not a multiple of 3.
Why can't we take negative x values
Lets take X as -1
Then -1<N<11. N =3( 3,6,9)
Lets take X as 5.
Then 5<N<17. N = 4.
Which is not sufficient.please let me know where I'm doing wrong.
How many integers, N, exist such that x < N < x + 12 where N is a mult   [#permalink] 07 Nov 2018, 23:41
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