 Aptitude Tests 4 Me

Basic Numeracy/Quantitative Aptitude

Detailed Solution

39. d: The correct answer was 3/10.
I will use the first letters of the colors as variables representing the number of pencils of a certain color. Since you are 2.3 times more likely to draw a green pencil than a blue one, there are 2.3 times more green pencils than blue ones. Since there is a 4% chance of drawing a yellow pencil, there are 2 yellow pencils.
The following equations are true:
B + R + Y + G = 50
B = G/(2.3)
R = G - 8
Y = 2
We can replace the B and R with equal variables in terms of G.
G/(2.3) + G - 8 + 2 + G = 50
Simplified, we get:
G/(2.3) + G + G = 56
Multiply both sides by 2.3 and we get:
G + (2.3)G + (2.3)G = 128.8
Simplified again, we get:
(5.6)G = 128.8
G = 23
Since there are 8 more green pencils than red ones, this means there are 15 red pencils. The odds of drawing a red pencil are 15/50 or 3/10.

40. a: The correct answer was 33/221.
First I'll figure out the odds that you won't draw an ace. Since there are 4 aces, the odds of not drawing an ace are 48/52 or 12/13. The odds of the second card not being an ace are 47/51. Multiply 47/51 by 12/13 and you get 564/663 or 188/221. Since 188/221 are the odds you won't get an ace, the odds you will get at least 1 ace are 33/221.

41. c: The correct answer was 3/8.
There are two possible results of flipping a coin, and 4 coin flips, so the number of possible flip results is 2 to the 4th power or 16. The possible combinations of ways to get two heads and two tails, are: HHTT, HTHT, HTTH, THHT, THTH, and TTHH. Since there are 6 results that are two heads and two tails, the probability of getting that result is 6/16 or 3/8.

42. b: The correct answer was 2/9.
The product of the two numbers rolled will be from 1 to 36. The square numbers between them are 1, 4, 9, 16, 25, and 36. 1-1, 1-4, 4-1, 2-2, 3-3, 4-4, 5-5, and 6-6 are the 8 results you can get that will give you two numbers that will multiply to a square number. There are 36 possible results from rolling two dice, so the odds are 8/36 or 2/9.

43. Solution. Clearly, the more workers there are, the less time will be required. This is an example
of inverse variation, so multiply. The job takes:
(15 workers) i(24 days) = 360 worker-days.v Then (40 workers) i(d days) = 360 worker-days.
40d = 360; d = 9.
This job will take 9 days.

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