GRE-Math-Questions-to-Know-by-Test-Day-2nd-Edition_pag249

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8 outcomes. The probability is 3
8
. (E) There are 3 prime or even numbers out of 8 numbers. 
The probability is 3
8
.
471. (A), (B), (D) To have an average of 85 on four exams, the total number of points must 
be 85 4 340⋅ = . (A) Student A’s three-exam total is 79 80 81 240+ + = . An average of 85 is 
possible if this student scores (340 240) 100− = on the fourth exam. (B) Student B’s three-
exam total is 65 80 180 245+ + = . An average of 85 is possible if this student scores at least 
(340 245) 95− = on the fourth exam. (C) Student C ’s three-exam total is 75 80 80 235+ + = . 
An average of 85 is not possible because this student needs a score of at least (340 235) 105− = 
on the fourth exam. (D) Student D’s three-exam total is 90 80 76 246+ + = . An average of 85 
is possible if this student scores at least (340 246) 94− = on the fourth exam. (E) Student E ’s 
three-exam total is 60 99 75 234+ + = . An average of 85 is not possible because this student 
needs a score of at least (340 234) 106− = on the fourth exam.
472. (B), (C), (E) The mean = sum of data values
number of data values
; after the data are put in order (from 
least to greatest or greatest to least), the median is the middle value (for an odd number of 
data values) or the average of the two middle values (for an even number of data values); 
the mode is the data value (or values) that occurs most often. By inspection select (E) 
and eliminate (D), which has no mode. Eliminate (A) because the mean is 2 and the mode 
is 1. (B) mean = 8 5 1 9 2 5
6
30
6
5+ + + + + = = ; median = 5 5
2
5+ = ; mode = 5. (C) mean = 
6 9 2 10 3 6
6
36
6
6− − − − − − = − = − ; median = 6 6
2
6− − = − ; mode = 6− .
473. (A), (E) By inspection, select (A) and (E). The standard deviation is 0 for the data 
in each of these choices. None of the data sets in the other answer choices have 0 standard 
deviation.
474. (B) Choice (B) has two modes, 1 and 5. The data sets in the other answer choices have 
only one mode.
475. (A), (B), (F) According to the figure, scores that are more than 2 standard deviations 
below the mean or scores that are more than 2 standard deviations above the mean will 
occur less than 2% of the time. Thus, a score that is less than 138 2(5) 128− = or a score that 
is greater than 138 2(5) 148+ = will occur less than 2% of the time. Select (A), (B), (F).
476. (B), (C), (D) One standard deviation above the mean is 100 1(15) 115+ = . One stan-
dard deviation below the mean is 100 1(15) 85− = . Thus, scores that satisfy the inequality 
85 score 115≤ ≤ are within one standard deviation of the mean. Select (B), (C), and (D).
477. (C), (D), (E) The first quartile is the 25th percentile, the score below which lie 
25% of the data values. Using the figure, estimate that the 25th percentile lies a little to the 
right of one standard deviation below the mean. One standard deviation below the mean 
is 118 1(9.5) 108.5− = , which (as the figure shows) is the 14th percentile. Select (C), (D), 
and (E) because these scores are less than 108.5, so they fall below the 14th percentile, and 
07_McCune_Answer.indd 240 2/21/22 4:39 PM