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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.
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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
    2+29=31
    3+28=31
    ....
    15+16=31

    Sum is 15X31

    31+60=91
    32+59=91
    33+58=91
    ....
    45+46=91

    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
    well,

    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);
    (t-s)=(1,365-465)=900
  • 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.
    1.....30
    31...60

    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 =/.
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