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

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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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a and b are two positive even integers such that a>b. Which of the  [#permalink]

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New post 16 May 2019, 01:03
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]

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New post 19 May 2019, 20:10
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]

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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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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]

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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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a and b are two positive even integers such that a>b. Which of the  [#permalink]

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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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a and b are two positive even integers such that a>b. Which of the   [#permalink] 21 Jun 2019, 04:13
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