Welcome to College Confidential!

The leading college-bound community on the web

Sign Up For Free

Join for FREE, and start talking with other members, weighing in on community polls, and more.

Also, by registering and logging in you'll see fewer ads and pesky welcome messages (like this one!)

As a CC member, you can:

Help Naviance, a relative of College Confidential, fine-tune a design. You could receive a $10 gift card to Amazon. Start here: https://ethn.io/67193

SAT math problem

Snake24Snake24 Posts: 23Registered User New Member
If you haven't taken CB SAT online Test #3 dont do this probem.
Wouldn’t want to ruin it for u.

Is there a way to do this problem quickly!
Any help appreciated.

Online Test #3 sec 9, Q 16
If (s) denotes the sum of the integers from 1 to 30 inclusive, and (t) denotes the sum of the integers from 31 to 60 inclusive, what is the value of (t - s)?
(A) 30
(B) 31
(C) 180
(D) 450
(E) 900
Post edited by Snake24 on

Replies to: SAT math problem

  • eng_dudeeng_dude Posts: 412. Member
    1+30 =31

    Sum is 15X31


    Sum is 15x91

    See the pattern here??

    Difference is (15x91) - (15x31)
    simplifies to 15*60 = 900

    pretty simple algorithm --> sum of terms = number of terms/2*(1st term +nth term)
  • MartinMartin Posts: 470Registered User Member

    the sum of (s) is 60+59+58+57+56....
    the sum of (t) is 30+29+28+27+26....

    BUT note that the difference of every couple is 30s (60-30, 59-29, 58-28, 57-27, etc)

    so u have 30 digits every of which is 30 => 30x30=900

    is 900 the answer ?
  • evil_asian_dictatorevil_asian_dictator Posts: 2,306- Senior Member
    Below is a very useful formula to remember when doing math problem solving at any level.

    sum of terms from 1 to n inclusive=n(n+1)/2...Remember, this algorithm only works when you are STARTING summing from 1 and continue to a certain number n without skipping.

    For, this SAT problem...
    Sum from 1-30:30(30+1)/2=465(s)
    Sum from 1-60:60(60+1)/2=1,830...
    1,830-465=1,365-sum from 31-60(t);
  • s snacks snack Posts: 1,050Registered User Senior Member
    I did it differently...and I think my way is easier.
    Line up the numbers...start with only the first and last of each series.

    You'll notice that each number from t is 30 greater than the corresponding term from s. So for any term number x: T(x)-S(x)=30
    And since there are 30 terms...the answer is 30x30=900
  • obsessedAndreobsessedAndre Posts: 240Registered User Junior Member
  • MartinMartin Posts: 470Registered User Member
    s snack, my way is the same :)
  • s snacks snack Posts: 1,050Registered User Senior Member
    ^Sorry about that...I just read the one were they used that formula...but I'm glad someone else can do these problems with logic like I do rather than relying on silly little formulas.
  • eng_dudeeng_dude Posts: 412. Member
    Yeah, the method I used didn't directly depend on any formula. I was just demonstrating the reasoning I used to find the answer quickly without having to remember any silly formula...Your method is more efficient though.
  • s snacks snack Posts: 1,050Registered User Senior Member
    ^ Sorry for being so vague, I was only referring to the evil asian dictator's post.
  • MarkSWMarkSW Posts: 87Registered User Junior Member
    well...i actually thought of evil asian dictator's SAT answer first. i got that formula from calculus and i remember having to do equations using someting like that. except sigma "i" is replaced by n(n+1)/2 and sigma "i^2" is n(n+1)(2n+1)/6... so basically its not that hard to use a formula you have learned or seen before. also the pattern is also a very useful way to do this. sometimes i get mixed up with them for some reason =/.
Sign In or Register to comment.