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Snake24
Registered User Posts: **23** New Member

If you haven't taken CB SAT online Test #3 dont do this probem.

Wouldnt 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

Wouldnt 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

412Member2+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)

470Memberthe 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 ?

2,306Senior Membersum 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

1,050Senior MemberLine 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

240Junior Member470Member1,050Senior Member412Member1,050Senior Member87Junior Member