question:Of the 50 electronics components that a factory must
manufacture, 70 percent would be most e ciently manufactured
by Machine A and the remaining 30 percent would be most
e ciently manufactured by Machine B, though either machine
could manufacture any of the 50 components. If 36 percent of
the components were manufactured by Machine A and the
remainder were manufactured by Machine B, what is the
highest possible number of components that were
manufactured by the machine that would manufacture them
the most efficiently?
Options:
(A) 30
(B) 31
(C) 32
(D) 33
(E) 34
answer:(D)
Stream of consciousness:# components A and B could manufacture efficiently:
A: 50*70% = 35
B: 50*30% = 15
# components A and B effectively manufacture:
A: 50*36% = 18
B: 50*64% = 32
Max. # components efficiently manufactured:
18 (from A) and 15 (from B) = 33

question:The number N is 5,3H7, where H represents the ten's digit. If N is divisible by 9, what is the value of H?
Options:
(A) 4
(B) 3
(C) 5
(D) 8
(E) 2
answer:(B)
Stream of consciousness:If the number is divisible by 9, it must also be divisible by 3. Only 3 yields such a number.

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 2/7, respectively, what is the probability that exactly two of the three players will win but one will lose?
Options:
(A) 3/140
(B) 1/28
(C) 3/56
(D) 3/35
(E) 7/40
answer:
(E)
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*5/7 + 1/5*5/8*2/7 + 4/5*3/8*2/7 = 7/40.