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a and b are two positive even integers such that a>b. Which of the

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kiran120680
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a and b are two positive even integers such that a>b. Which of the [#permalink] New post   16 May 2019, 00:44
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a and b are two positive even integers such that a > b. Which of the following represents the number of odd integers less than a + 2 and greater than b - 2?

A. (a + 1 − b − 1)/2
B. (a − b − 2)/2
C. (a + 2 − b − 2)/2
D. (a + 2 − b + 2)/2
E. (a − b)/2 + 1­
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D
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Re: a and b are two positive even integers such that a>b. Which of the [#permalink] New post   16 May 2019, 01:03
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Hi Kiran, I'll help:

=> In such questions, the best way to get the answer is to plug in numbers and check,

Let's take a = 8, b = 6 as the question stem says: Then:

a+2 = 10
b-2 = 4,

So the odd numbers in between 4 and 10 are 5,7,9(a total of 3 numbers).

Now plug a=8 and b=6 in the answer choices and see which gives you 3. Option D.

Hope this helps, if you like it, please give a kudos:).
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Re: a and b are two positive even integers such that a>b. Which of the [#permalink] New post   19 May 2019, 20:10
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kiran120680 wrote:
a and b are two positive even integers such that a>b. Which of the following represents the number of odd integers less than a+2 and greater than b-2?


A. a+1−b−1)/2
B. (a−b−2)/2
C. (a+2−b−2)/2
D. (a+2−b+2)/2
E. ((a−b)/2)+1


The largest odd integer in the range of b - 2 to a + 2 (when a and b are even and a > b) is a + 1, and the smallest odd integer is b - 1. Therefore, the number of odd integers in this range is:

[(a + 1) - (b - 1)]/2 + 1 = (a - b + 2)/2 + 2/2 = (a + 2 - b + 2)/2

Answer: D
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Re: a and b are two positive even integers such that a>b. Which of the [#permalink] New post   05 Jun 2020, 09:57
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kiran120680 wrote:
a and b are two positive even integers such that a>b. Which of the following represents the number of odd integers less than a+2 and greater than b-2?


A. a+1−b−1)/2
B. (a−b−2)/2
C. (a+2−b−2)/2
D. (a+2−b+2)/2
E. ((a−b)/2)+1


Given: a and b are two positive even integers such that a>b.
Asked: Which of the following represents the number of odd integers less than a+2 and greater than b-2?

b-2 -> even ; b-1 -> odd -> First term
a+2 -> even ; a+1 -> odd -> Last term
Common difference = 2

Odd integers form an arithmetic progression with common difference 2.
Number of terms = (Last term - First term)/(common difference) + 1

Number of odd integers less than a+2 and greater than b-2 = \(\frac{((a+1) - (b-1))}{2} + 1 = \frac{(a-b+2)}{2} + 1= \frac{(a-b+2+2)}{2} = \frac{(a-b+4)}{2} = \frac{(a+2-b+2)}{2}\)

IMO D
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Re: a and b are two positive even integers such that a>b. Which of the [#permalink] New post   19 Jun 2019, 22:54
if a= 6 & b=4 then
a+2 =8
b-2= 2
odd nos b/w 8& 2 are 3,5 & 7
D will give the answer.
But if I consider a =4 & b=2 then
then a+2 =6
b-2 = 0
odd nos b/w 6 & 0 are 1,3 & 5
A,C & D all will give answer
Am I missing something ?
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Re: a and b are two positive even integers such that a>b. Which of the [#permalink] New post   20 Jun 2019, 09:51
ashminkaul with your solution - even option A gives the answer 3. How do you pick between A and D then?
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Re: a and b are two positive even integers such that a>b. Which of the [#permalink] New post   20 Jun 2019, 09:56
rahul12988 I think the below:
if you take a=4
b=2
then the no of odd numbers between 0 and 6 are 1,3 and 5 which is 3 numbers.
Substitute the values of a=4 and b=2 in each of the options and the solution which gives answer as 3 is D. hence the answer is D

Please correct me if I am wrong
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Re: a and b are two positive even integers such that a>b. Which of the [#permalink] New post   21 Jun 2019, 04:13
No. Option A will give 1
(8-6+1-1)/2=1

Only D will give right answer.
You have already cleared my doubt about (4 & 2)

so Only D will provide solution.
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Re: a and b are two positive even integers such that a>b. Which of the [#permalink] New post   23 Mar 2024, 22:51
kinvestor wrote:
Hi Kiran, I'll help:

=> In such questions, the best way to get the answer is to plug in numbers and check,

Let's take a = 8, b = 6 as the question stem says: Then:

a+2 = 10
b-2 = 4,

So the odd numbers in between 4 and 10 are 5,7,9(a total of 3 numbers).

Now plug a=8 and b=6 in the answer choices and see which gives you 3. Option D.

Hope this helps, if you like it, please give a kudos :).

­But if we take a=6, b= 4 the value is 3 option E . how is E incorrect
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Re: a and b are two positive even integers such that a>b. Which of the [#permalink] New post   24 Mar 2024, 03:39
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rmahe11 wrote:
kinvestor wrote:
Hi Kiran, I'll help:

=> In such questions, the best way to get the answer is to plug in numbers and check,

Let's take a = 8, b = 6 as the question stem says: Then:

a+2 = 10
b-2 = 4,

So the odd numbers in between 4 and 10 are 5,7,9(a total of 3 numbers).

Now plug a=8 and b=6 in the answer choices and see which gives you 3. Option D.

Hope this helps, if you like it, please give a kudos :).

­But if we take a=6, b= 4 the value is 3 option E . how is E incorrect

­
If a = 6 and b = 4, then the number of odd integers between a + 2 = 8 and b - 2 = 2, is three: 3, 5, and 7. Substituting a = 6 and b = 4 into D and E gives:

D. (a + 2 − b + 2)/2 = 3
E. (a − b)/2 + 1­ = 2­

Hope it helps.
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Re: a and b are two positive even integers such that a>b. Which of the [#permalink]
24 Mar 2024, 03:39
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