Integers x and y are each odd, and x > y. Which of the following repre

ScottTargetTestPrep, could you suggest way of solving this faster?

To solve problems requiring us to calculate the number of values in a set, we need to know whether to include or exclude the extreme ends.

For example, say we want to find the number of values between 2 and 9.
1. Number of values between 2 and 9, inclusive (meaning that 2 and 9 are included):
(9-2)+1 = 8 (The numbers are 2,3,4,5,6,7,8,9)
2. Number of values between 2 and 9 (not including 2 and 9):
(9-2)-1 = 6 (The numbers are 3,4,5,6,7,8)
The takeaway is that we add 1 when we want to include the min and max and we subtract 1 when we want to exclude the min and max.

Same concept applies to finding the number of even or odd integers in a set. The key is to set both of your extreme ends as odd if finding the number of odd integers or to set both of your extreme ends as even if finding the number of even integers. In this problem, we know that x and y are both odd, that x is max and y is min, and that we're excluding x and y from the final result so:
\(\frac{x-y}{2}\) - 1 = \(\frac{x-y-2}{2}\)

This sentence to me seems to ask the number of odd integers that fall between X and Y.

let's pick odd integer values for X and Y, whereby odd integer X is greater than odd integer Y a.k.a. X>Y

If X=5 and Y=1 Then the odd integer that falls between 1 and 5 is 3, which is only 1 odd integer.

So we have to find a choice that clearly shows there is only 1 odd integer between 1 and 5, which is 3. and the only choice that does that is choice E

Lets test that accoring to choice E

(X-Y-2)/2= 5-1-2 / 2=

5-1-2=2 and if we divide that 2 by the denominator 2 2/2=1, meaning there is 1 odd integer between 1 and 5, which is 3.


Another example: lets X=7 and Y=1, then the number of odd integers that falls between 1 and 7 is 2, which are 3 and 5.

Again using the methode of choice E, it looks like this:

(7-1-2)/2= 4/2=2, which are the 2 odd integers that fall between 1 and 7, meaning 3 and 5

I hope it is clear.

One need to understand the question stem properly to answer it correctly.

The question is asking the number of odd integer between given odd integer such that X>Z>Y.

So, lets consider X,Y, and Z as 7,3, and 5 and as per question 7>5>3. Here, we have only 1 odd integer between between 7 and 3.

If you use expression in option E, you will get your answer

So option E is correct.

why is option A incorrect?

Use formula for general term of an AP ie a_n=a_1+(n-1)d$

where first term is x+2, nth term is y-2 (as only odd numbers are taken).

Posted from my mobile device