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.

1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
21	22	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40
41	42	43	44	45	46	47	48	49	50	51	52	53	54	55	56	57	58	59	60
61	62	63	64	65	66	67	68	69	70	71	72	73	74	75	76	77	78	79	80
81	82	83	84	85	86	87	88	89	90	91	92	93	94	95	96	97	98	99	100
101	102	103	104	105	106	107	108	109	110	111	112	113	114	115	116	117	118	119	120
121	122	123	124	125	126	127	128	129	130	131	132	133	134	135	136	137	138	139	140
141	142	143	144	145	146	147	148	149	150	151	152	153	154	155	156	157	158	159	160
161	162	163	164	165	166	167	168	169	170	171	172	173	174	175	176	177	178	179	180
181	182	183	184	185	186	187	188	189	190	191	192	193	194	195	196	197	198	199	200
201	202	203	204	205	206	207	208	209	210	211	212	213	214	215	216	217	218	219	220
221	222	223	224	225	226	227	228	229	230	231	232	233	234	235	236	237	238	239	240
241	242	243	244	245	246	247	248	249	250	251	252	253	254	255	256	257	258	259	260
261	262	263	264	265	266	267	268	269	270	271

Passage Reading Verbal Logic Non Verbal Logic Numerical Logic Data Interpretation Reasoning Analytical Ability Basic Numeracy About Us Contact Privacy Policy Major Tests FAQ

---