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Math Expert V
Joined: 02 Sep 2009
Posts: 59756
How many odd numbers are there between m and n?  [#permalink]

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Difficulty:   75% (hard)

Question Stats: 24% (02:04) correct 76% (01:16) wrong based on 33 sessions

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Competition Mode Question

How many odd numbers are there between m and n?

(1) m – n = 9
(2) m is a positive integer.

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Senior Manager  P
Joined: 01 Mar 2019
Posts: 345
Location: India
Concentration: Strategy, Social Entrepreneurship
Schools: Ross '22, ISB '20, NUS '20
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Re: How many odd numbers are there between m and n?  [#permalink]

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1
(1) m – n = 9
If m=9.5,n=0.5
1,3,5,7,9....Total 5
If m=9,n=0
1,3,5,7.....Total 4.....So not sufficient

(2) m is a positive integer.... Clearly insufficient

ComBining both we can get 4 odd numbers....

OA:C

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GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 5492
Location: India
Concentration: Sustainability, Marketing
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WE: Marketing (Energy and Utilities)
Re: How many odd numbers are there between m and n?  [#permalink]

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1
How many odd numbers are there between m and n?

(1) m – n = 9
(2) m is a positive integer.

#1
m-n=9
-1-(-10) or 5-(-4)
insufficient
#2
m is a positive integer.
no relation of n
insufficeint
from 1 &2
we can say
the set will be +ve always as m>n and m-n=9 also the count of odd integers will be 4 always
IMO C
Senior Manager  P
Joined: 25 Jul 2018
Posts: 403
Re: How many odd numbers are there between m and n?  [#permalink]

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1
How many odd numbers are there between m and n?

(Statement1): m—n= 9
—> 0.5.......9.5 —> 1,3,5,7,9 —five odd numbers
—> 1.5......10.5 —> 3,5,7,9 —four odd numbers

Insufficient

(Statement2): m is a positive integer
No info about what n is
Insufficient

Taken together 1&2,
—> 1......10
—> 2......11

No matter m and n in the 1....10 range or in the 2.....11 range, both of the ranges have the same number of odd numbers.

Sufficient

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Director  P
Joined: 24 Nov 2016
Posts: 977
Location: United States
Re: How many odd numbers are there between m and n?  [#permalink]

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2
Quote:
How many odd numbers are there between m and n?

(1) m – n = 9
(2) m is a positive integer.

(1) m – n = 9 insufic.

$$(m,n)=(10,1)…m-n=9…odds:(9-3/2)+1=4…[3,5,7,9]$$
$$(m,n)=(9.5,0.5)…m-n=9…odds:(9-1/2)+1=5…[1,3,5,7,9]$$

(2) m is a positive integer insufic.

(1 & 2) sufic.

$$(m,n)=(10,1)…m-n=9…odds:(9-3/2)+1=4$$

Director  P
Joined: 18 May 2019
Posts: 559
Re: How many odd numbers are there between m and n?  [#permalink]

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We are to determine the number of odd numbers between m and n.

1. m-n=9
Sufficient. This is because irrespective of the chosen numbers, m and n, as long as they satisfy the condition in statement 1, there will be 4 odd numbers.
For example, let m=10 and n=1, m-n=9, the odd numbers between m and n are: 3,5,7, and 9.
when m=5 and n=-4, m-n=9, odd numbers between -4 and 5 are: -3, -1, 1, and 3.

Statement 2: m>0
merely knowing that m is positive is not enough to determine how many odd numbers exist between m and n. For example, let m=10 and n=1, then there will be 4 odd numbers between m and n.
If m=7 and n=2, then there will be 2 odd numbers between m and n.
Statement 2 is therefore not sufficient.

Manager  G
Joined: 17 Mar 2019
Posts: 109
Re: How many odd numbers are there between m and n?  [#permalink]

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How many odd numbers are there between m and n?

(1) m – n = 9
(2) m is a positive

IMO A

Statement 1: m-n=9

eg: 10-1=9. 5 odd numbers are between 10 to 1

eg: -4-(-13)=9. we still have 5 odd numbers.

Statement 2: m is positive and non conclusive to determine

Manager  G
Joined: 17 Jan 2019
Posts: 127
Re: How many odd numbers are there between m and n?  [#permalink]

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1
How many odd numbers are there between m and n?

(1) m – n = 9

if m=10 n=1
10-1=9
3,5,7,9 --4 odds no.

if m= -1 n =-10
-1-(-10)=9
1,3,5,7,9 --5 odds no.

insufficient

(2) m is a positive integer.
alone say nothing
insufficient

Together,
we know there's 4
therefore, C
VP  D
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Concentration: Entrepreneurship, Marketing
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Re: How many odd numbers are there between m and n?  [#permalink]

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1
How many odd numbers are there between m and n?

(1) m – n = 9 --> m = n + 9
We do not know whether m is an integer or fraction --> Insufficient

(2) m is a positive integer.
Does not talk about 'n' --> Insufficient

Combining (1) & (2),
m = n + 9

Case 1: n is even integer (Assume n = 2), m = 11
--> Number of odd integers between 2 & 11 = 4

Case 2: n is an odd integer (Assume n = 3), m = 12
--> Number of odd integers between 3 & 12 = 4

--> Sufficient

IMO Option C Re: How many odd numbers are there between m and n?   [#permalink] 24 Oct 2019, 21:59
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