question: If n is an integer, then the least possible value of |8 - 9n| is?
Options:
(A) 0
(B) 1
(C) 2
(D) 3
(E) 11
answer: Stream of consciousness: |8 - 9n| represents the distance between 8 and 9n on the number line. Now, the distance will be minimized when 9n, which is multiple of 9, is closest to 8. Multiple of 9 which is closest to 8 is 9 (for n = 1), so the least distance is 1: |8 - 9| = 1. The answer is (B).
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question: What is the are of an equilateral triangle of side 16 cm?
Options:
(A) 64√5
(B) 64√9
(C) 64√4
(D) 64√3
(E) 64√2
answer: Stream of consciousness: Area of an equilateral triangle = √3/4 S2
If S = 16, Area of triangle = √3/4 * 16 * 16 = 64√3 cm2; The answer is (D).
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question: Find the third proportional to 9 and 12?
Options:
(A) 10
(B) 12
(C) 16
(D) 19
(E) 20
answer: Stream of consciousness: Formula = Third proportional = (b × b)/a
A = 9 and B = 12
(12 × 12)/ 9 = 144/9 = 16 The answer is (C).
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question: Eddy and Freddy start simultaneously from city A and they travel to City B and City C respectively. Eddy takes 3 hours and Freddy takes 4 hours to complete the journey. If the distance between City A and City B is 600 kms and City A and City C is 460 kms. What is the ratio of their average speed of travel? (Eddy: Freddy)
Options:
(A) 8/3
(B) 3/8
(C) 8/5
(D) 5/8
(E) 40/23
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: Distance traveled by Eddy = 600 km
Time taken by Eddy = 3 hours
Average speed of Eddy = 600/3 = 200 km/hour
Distance traveled by Freddy = 460 km
Time taken by Freddy = 4 hours
Average speed of Freddy = 460/4 = 115 km/hour
Ratio of average speed of Eddy to Freddy = 200/115 = 40/23 The answer is (E).
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