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

Question

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

kinvestor · Answer

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:).

ScottTargetTestPrep · Answer

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:

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

Answer: D

rahul12988 · Answer

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 ?

hiralk126 · Answer

ashminkaul  with your solution - even option A gives the answer 3. How do you pick between A and D then?

hiralk126 · Answer

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

rahul12988 · Answer

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.

Kinshook · Answer

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

rmahe11 · Answer

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

Bunuel · Answer

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.

bumpbot · Answer

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