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# How many odd numbers are there between the integers n and m?

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How many odd numbers are there between the integers n and m?  [#permalink]

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22 Dec 2016, 02:33
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65% (hard)

Question Stats:

55% (01:42) correct 45% (01:26) wrong based on 82 sessions

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How many odd numbers are there between the integers n and m?

(1) n – m = 100
(2) n + m is even

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Re: How many odd numbers are there between the integers n and m?  [#permalink]

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22 Dec 2016, 11:11
1) is sufficient,as it provides range for calculation. Taking any 100 integers into account , extremes inclusive will have 50 Odd nos. Eg 100 -0= 100, will have 50 Odd Integers

2) Insufficient as it doesn't provide any range for calculation.

Omkar Kamat
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Re: How many odd numbers are there between the integers n and m?  [#permalink]

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22 Dec 2016, 23:28
Omkar.kamat wrote:
1) is sufficient,as it provides range for calculation. Taking any 100 integers into account , extremes inclusive will have 50 Odd nos. Eg 100 -0= 100, will have 50 Odd Integers

2) Insufficient as it doesn't provide any range for calculation.

Omkar Kamat
When The Going Gets Tough, The Tough Gets Going !!

Should be E.

1. As 100 can be either 121-21 = 51 odd integers , or 122-22 = 49 odd integers
2. Insufficient as it can 231-221 = 6 odd integers or 230-220 = 5 odd integers

Combination insufficent
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Re: How many odd numbers are there between the integers n and m?  [#permalink]

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22 Dec 2016, 23:34
Bunuel wrote:
How many odd numbers are there between the integers n and m?

(1) n – m = 100
(2) n + m is even

IMO : E

n,m both should be odd or even.

when we combine , if say both is odd for ex 119 and 19
if say both are even ex 118 and 18

in first case definitely we will have large number of odd numbers than second one.

so even after combine we didnt get any answer
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Re: How many odd numbers are there between the integers n and m?  [#permalink]

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23 Dec 2016, 00:58
Bunuel wrote:
How many odd numbers are there between the integers n and m?

(1) n – m = 100
(2) n + m is even

(1) n – m = 100

We can start with odd and end with odd (199 – 99) or we can start with even and end with even (198 – 98). In two cases we’ll have:

$$\frac{100}{2} + 1$$ odd numbers and $$\frac{100}{2} – 1$$ even numbers or vice versa. Insufficient.

(2) n + m is even

This is generalization of the previous case.

$$odd + odd = even$$ and $$even + even = even$$

Our set can start and end either with even or with odd. Again insufficient.

Combining both two will not give us additional information about first and last elements in our set. Insufficient.

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Re: How many odd numbers are there between the integers n and m?  [#permalink]

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23 Dec 2016, 01:25
hershkoch wrote:
Omkar.kamat wrote:
1) is sufficient,as it provides range for calculation. Taking any 100 integers into account , extremes inclusive will have 50 Odd nos. Eg 100 -0= 100, will have 50 Odd Integers

2) Insufficient as it doesn't provide any range for calculation.

Omkar Kamat
When The Going Gets Tough, The Tough Gets Going !!

Should be E.

1. As 100 can be either 121-21 = 51 odd integers , or 122-22 = 49 odd integers
2. Insufficient as it can 231-221 = 6 odd integers or 230-220 = 5 odd integers

Combination insufficent

Hi,

I used the following formula

No of Odds/ Evens in a Range= (highest -lowest)/2 +1. For both the ranges you mentioned returns value as 51.

Omkar Kamat
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Re: How many odd numbers are there between the integers n and m?  [#permalink]

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23 Dec 2016, 01:51
Omkar.kamat wrote:
hershkoch wrote:
Omkar.kamat wrote:
1) is sufficient,as it provides range for calculation. Taking any 100 integers into account , extremes inclusive will have 50 Odd nos. Eg 100 -0= 100, will have 50 Odd Integers

2) Insufficient as it doesn't provide any range for calculation.

Omkar Kamat
When The Going Gets Tough, The Tough Gets Going !!

Should be E.

1. As 100 can be either 121-21 = 51 odd integers , or 122-22 = 49 odd integers
2. Insufficient as it can 231-221 = 6 odd integers or 230-220 = 5 odd integers

Combination insufficent

Hi,

I used the following formula

No of Odds/ Evens in a Range= (highest -lowest)/2 +1. For both the ranges you mentioned returns value as 51.

Omkar Kamat
When The Going Gets Tough, The Tough Gets Going !!

If your set starts with odd and ends with odd you'll be counting the # of odd integers, but if your set starts with even and ends with even than you'll be counting the number of even elements.

$$\frac{199 - 99}{2} + 1 = 51$$ odd number. Number of even = $$100 - 51 = 49$$

$$\frac{198 - 98}{2} + 1 = 51$$ even numbers. # of odd = $$100 - 51 = 49$$

So we can get number of odd integers either 51 or 49. Insufficient.
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Re: How many odd numbers are there between the integers n and m?  [#permalink]

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24 Dec 2016, 11:38
E

1) n and m could be 51 and 151, or 50 and 150. Each option gives a different number of odd numbers. INSUFFICIENT

2) INSUFFICIENT

1) and 2) give no new information. E.g. 51 + 151 is even but so is 50 + 150. INSUFFICIENT
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Re: How many odd numbers are there between the integers n and m?  [#permalink]

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24 Dec 2016, 11:52
Original statement says n and m are 'integers'
Question= howmany odds btw m and n

1) n-m=100
Endless possibilities (-1,-101), (105,5).... NOT SUFFICIENT

2)n+m=even
Endless possibilities (-2,2), (2022,5400000)... NOT SUFFICIENT

1) & 2)
Still not clear as we can't get a certain value for n+m to use a^2-b^2 formula

Hence E

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How many odd numbers are there between the integers n and m?  [#permalink]

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14 Jul 2017, 01:06
Hi @Bunnuel !

Can odd numbers be negative (for example: is -3 an odd number?) ?

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Re: How many odd numbers are there between the integers n and m?  [#permalink]

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14 Jul 2017, 01:13
leanhdung wrote:
Hi @Bunnuel !

Can odd numbers be negative (for example: is -3 an odd number?) ?

Yes.

An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder. So, ..., -4, -2, 0, 2, 4, ... are all even integers.

An odd number is an integer that is not evenly divisible by 2. So, ..., -3, -1, 1, 3, 5, ... are all odd integers.
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Re: How many odd numbers are there between the integers n and m?   [#permalink] 14 Jul 2017, 01:13
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