If x is the number of odd integers between 10 and 51, and y is the number of even integers
between 10 and 51, what is the value of x + y?
(A) 39
(B) 40
(C) 41
(D) 48

C. 41

Step-by-step explanation:

We want to find the number of odd integers from 10 to 51.

The first odd integer from 10 to 51 is 11; the second is 13; the third is 15; and so on until 51. So, our list looks like this:

11, 13, 15, ... , 51

We need to figure out how many numbers there are. Let's add 1 to all of them:

11 + 1, 13 + 1, 15 + 1, ... 51 + 1

12, 14, 16, ... , 52

Now, let's divide by 2:

12/2, 14/2, 16/2, ... 52/2

6, 7, 8, ... , 26

Finally, subtract 5 from them:

6 - 5, 7 - 5, 8 - 5, ... , 26 - 5

1, 2, 3, ... , 21

There are 21 odd integers, so x = 21.

The even integers from 10 to 51 start with 12, 14. They end with 50. So, we have:

12, 14, ... 50

Let's use a similar method as above. Divide by 2:

12/2, 14/2, ... , 50/2

6, 7, ... , 25

Subtract 5:

6 - 5, 7 - 5, ... , 25 - 5

1, 2, 3, ... , 20

There are 20 even integers, so y = 20.

Then, x + y = 21 + 20 = 41.

The answer is thus C.

~ an aesthetics lover

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step-by-step explanation: