Help Needed on This Type of Problem

<p>Hey guys. I'm trying to learn the concepts/strategies for the topics that usually make up the 3-4 wrong I get on the SAT Math sections.</p>

<p>One of the major types is those that ask how many numbers between X and Y inclusive satisfy ______________ [a certain condition]</p>

<p>What is the general approach that you guys use to answer those questions. Are there any neat strategies to get the answer in a more time-efficient way? I usually always take the most time on these types of problems,and I usually just end up trying to do it the long way [which i end up messing up somehow as well, lol]</p>

<p>Thanks in advance :)</p>

<p>You need to know is that the number of numbers between X and Y inclusive is</p>

<p>Y - X + 1</p>

<p>It’s easy to know that the number of numbers between 1 and 999 is 999. But if you had something like 56 to 789, you might be tempted to just do 789 - 56 = 733, but there are actually 734 numbers. </p>

<p>Your question is a little vague. Could you give a specific problem?</p>

<p>Sure. Here’s a few that I got wrong from practice tests.</p>

<p>1) If x = the sum of all odd integers from 1 to 49, inclusive</p>

<p>And y = the sum of all even integers from 2 to 50, inclusive</p>

<p>And z= the sum of alll integers from 1 to 48, inclusive</p>

<p>what is the value of x + y - z?</p>

<p>2) If s denotes the sum of the integers 1 to 30 inclusive, and t denotes the sum of the integers from 31 to 60 inclusive, what is the value of t-s?</p>

<p>Bump…Before the SAT’ers return! :(</p>

<p>1)
1+3+5…+47+49+
+2+4+…+48+50-
-1-2-3-…-48 =
1+2+3+…+48+49+50-
-1-2-3-…-48 =
49 + 50</p>

<p>2)
31+32+33+…+58+59+60-
-1 - 2 - 3 - …-28-29-30 =
30+30+30+…+30+30+30 =
30x30</p>

<p>1) 99
all odd # up to 49 + all even # up to 50 = all # up to 50.
all # up to 50 - all # up to 48 = 49+50 = 99</p>

<p>oops… missed “odd” and “even” in 1).
Corrected in Edit.</p>

<p>Thanks, prmdi!</p>