manu101

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.

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

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]

Thanks in advance

jamesford

You need to know is that the number of numbers between X and Y inclusive is

Y - X + 1

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.

Your question is a little vague. Could you give a specific problem?

manu101

Sure. Here's a few that I got wrong from practice tests.

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

And y = the sum of all even integers from 2 to 50, inclusive

And z= the sum of alll integers from 1 to 48, inclusive

what is the value of x + y - z?

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?

manu101

Bump..........Before the SAT'ers return!

gcf101

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

2)
31+32+33+...+58+59+60-
-1 - 2 - 3 - ...-28-29-30 =
30+30+30+...+30+30+30 =
30x30

prmdi

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

gcf101

oops... missed "odd" and "even" in 1).
Corrected in Edit.

Thanks, prmdi!