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**preview**shows half of the first page. to view the full**2 pages of the document.**Math 101 Practice Final Exam #2

1. Determine the third entry of the progression with ﬁrst entry 12 and second

entry 9 if the progression is...

(a) an arithmetic progression. (b) a geometric progression.

2. Determine the last digit of the number 912345?

3. If a meal consisting of steak, salad and potatoes costs $30 where the steak

costs $5 more than the potatoes and the potatoes cost twice as much as the

salad, then how much did each part of the meal cost?

4. Convert the number 20123into base-10.

5. Convert the number 364510 into Roman numerals.

6. Evaluate: (a)11010012+ 1011102; (b) 7658−5678; (c) 5A16 ×3116

7. Find all xsatisfying the following equations.

(a) 5x+ 4 = 6 mod 8

(b) 2x2= 4 mod 9

(c) 4x2= 0 mod 11

(d) x2+ 2x+ 1 = 0 mod 8

8. December 1, 2013 is a Sunday.

(a) What day of the week is December 1, 2153?

(b) What day of the week is December 1, 1953?

9. Find all Nbetween 0 and 1200 satisfying:

N≡2 mod 11

N≡3 mod 13

N≡4 mod 15

10. (a) Find the prime factorization of 8250 and 7700.

(b) How many divisors does 8250 have (i.e., what is d(8250))?

(c) What is gcd(8250,7700) and lcm(8250,7700)? You do not need to sim-

plify the prime factorization.

11. Use the Euclidean Algorithm, to calculate gcd(3964,5428).

12. If 2 chickens can lay 4 eggs in 6 days, then how many eggs will 8 chicken lay

in 12 days.

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