How many Integers??

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by mayonnai5e » Mon Oct 15, 2007 4:29 pm
It's quite simple once you learn the technique. The basic idea is to break it down into intervals. What is the smallest interval between two numbers that will match the criteria? The first number would be 324,713. The second number would be 324,813. So the smallest interval is 100.

1) Find the lowest and highest numbers that match the criteria in the range: 324,713 and 458,513

2) Subtract lowest from highest then divide by the interval:
(458,513 - 324,713)/100 = 1338

3) Add 1 to the result: 1339

The basic formula is one that you will need again and again:

The number of integers given a particular range: B - A + 1 where B is the high integer and A is the low integer

The formula used above is a variation of this formula:

(B - A) / (interval size) + 1

Memorize both. You will see it again. And again. And again.

* I have seen other people that just divide the number by the interval straight out without determining the low and high value, but I feel this could lead to a situation where you're not quite sure of the accuracy (e.g. answer choices contain both 1339 and 1338 and a rounding error can influence the result). Finding the low and high value takes only a few extra seconds, but is guaranteed to be accurate.
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by mayonnai5e » Tue Oct 16, 2007 2:58 am
Peter wrote:
mayonnai5e wrote: 2) Subtract lowest from highest then divide by the interval:
(458,513 - 324,713)/100 = 1338
Thanks ...
Now, why did you divide by 100 in step (2)...?
Because there will be 1 number per 100 that matches the criteria stated above. This is also referred to as the common difference in the arithmetic progression formual stated above:

L = F + (n -1) * D

last term = first term + (#terms - 1) * common difference between each term.

I never made this connection before, but the formula I cited above is actually just the AP formula rearranged:

L = F + (n-1) *D
L - F = (n-1) * D
(L - F)/d = n-1
[(L- F)/d] + 1 = n