SAT Math: More Listing and Counting Problems

If you’ve read my recent post on Listing and Counting and you’re looking for some more practice on this type of SAT Math problem, here are a few more examples you can try.  The answers appear at the bottom of this post.

1)  Six points are drawn on a circle.  How many triangles can be drawn by connecting any three of these points?

(A)  12
(B)  20
(C)  30
(D)  60
(E)  120

2)  The Theater class consists of four seniors and six juniors.  A group of three of these students is to be selected to attend an acting workshop.  If the group is to be made up of a senior and two juniors, how many different groups could be created?

(A)  12
(B)  18
(C)  24
(D)  30
(E)  60

3)  How many three-digit even numbers can be formed from the digits 2, 3, 4, 5 and 7 if no digit can be repeated?  Not all of the digits will be used to form the number.  For example, one possibility is 542 with the 3 and 7 going unused.

(A)  5
(B)  6
(C)  12
(D)  24
(E)  120

4)  Tyler has forgotten his three-digit access code for an online account.  He does remember, however, that the first two digits are odd and that they are different numbers.  What is the maximum number of codes he would have to try before he enters the correct code?

(A)  20
(B)  120
(C)  200
(D)  400
(E)  900

5)  There are six teams in a lacrosse league.  If each team plays all of the other teams three times, how many total games are played?

(A)  15
(B)  30
(C)  45
(D)  60
(E)  90

If you have questions about these problems, the “Listing and Counting” techniques, or anything else to do with the SAT, leave a comment or send me an email at info@cardinalec.com .

Solutions:
1)  (B)
2)  (E)
3)  (D)
4)  (C)
5)  (C)

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