question: How many two-digit numbers satisfy this property.: The last digit (unit's digit) of the square of the two-digit number is 7 ?
Options:
(A) 3
(B) 1
(C) 4
(D) 0
(E) 2
answer: Stream of consciousness: A number ending with 7 can never be a perfect square. The answer is (D).
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question: A car has a 20-gallon fuel to travel 500 miles.At this rate, how many gallons of fuel are needed for a 1000 mile car ?
Options:
(A) 10
(B) 30
(C) 20
(D) 40
(E) 50
answer: Stream of consciousness: Number of gallons of fuel per mile = 500 /20 = 25 gallons per mile
Number of gallons of fuel for a 1000 mile car = 1000/25 = 40 The answer is (D).
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question: A train 650 m long is running at a speed of 81 km/hr. In what time will it pass a bridge 340 m long?
Options:
(A) 42
(B) 43
(C) 44
(D) 45
(E) 46
answer: Stream of consciousness: Speed = 81 * 5/18 = 45/2 m/sec
Total distance covered = 650 + 340 = 990 m
Required time = 990 * 2/45 = 44 se The answer is (C).
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question: A password of a computer consists of five digits 1 through 6. What is the probability that all digits are divisible by 3 ?
Options:
(A) 1/3
(B) 1/6
(C) 1/27
(D) 1/243
(E) 1/486
answer:

Show your work and conclude with the exact phrasing "Therefore, the final answer is [answer]." where [answer] is just the final number or expression that solves the problem.
user
Stream of consciousness: For each digit there are six possibilities. Two of them (3 and 6) are divisible by three, so there is a one in three chance for each digit, and since the digits are independent of each other, overall probability is 1 / 3^5 or The answer is (D).
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