question: Find the remainder when 6^23 is divided by 5 ?
Options:
(A) 3
(B) 2
(C) 1
(D) 0
(E) 4
answer: Stream of consciousness: 6^23 = 6^(4*5+3) = 6^(20) * 6^3 last 3 digits = 216
216/5 remainder = 1 The answer is (C).

q: If the personal income tax rate is lowered from 38% to 30%, what is the differential savings for a tax payer having an annual income before tax to the tune of $36500?
Options:
(A) $1825
(B) $5000
(C) $3150
(D) $7000
(E) $10000
a: Stream of consciousness: Saving = (38-33)% of 36500 = 1825. The answer is (A).

question: What is the units digit of the expression 14^719^4?
Options:
(A) 0
(B) 3
(C) 4
(D) 6
(E) 8
answer: Stream of consciousness: I think answer on this one should be E too. Since we know that 14^7>19^4, as Will said one should always check if the number is positiv The answer is (E).

q: Find the value of y from (12)^3 x 6^4 432 = y?
Options:
(A) 4567
(B) 3435
(C) 5667
(D) 4567
(E) 5184
a: Stream of consciousness: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62 The answer is (E).

question: Alice, Benjamin, and Carol each try independently to win a carnival game. If their individual probabilities for success are 1/5, 3/8, and 3/7, respectively, what is the probability that exactly two of the three players will win but one will lose?
Options:
(A) 63/280
(B) 1/280
(C) 3/56
(D) 3/35
(E) 7/40
answer: Stream of consciousness: P = P(A wins, B wins, C loses) + P(A wins, B loses, C wins) + P(A loses, B wins, C wins) = 1/5*3/8*4/7 + 1/5*5/8*3/7 + 4/5*3/8*3/7 = 63/280. The answer is (A).

question: A shipment of 8 TV sets contains 4 black and white sets and 4 color sets. If 2 TV sets are to be chosen at random from this shipment, what is the probability that at least 1 of the 2 sets chosen will be a black and white set?
Options:
(A) 1/7
(B) 11/14
(C) 5/14
(D) 11/28
(E) 13/28
answer:
Stream of consciousness: 4/8 * 3/7 = 12/56
1-(12/56) = 44/56 = 11/14 The answer is (B).