GRE-Math-Questions-to-Know-by-Test-Day-2nd-Edition_pag178

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96. (A) The fundamental counting principle states that for a sequence of k tasks, if a first task 
can be done in any one of n1 different ways, and for each of these ways, a subsequent task 
can be done in any one of n2 different ways, and for each of these ways, a following task can 
be done in any one of n3 different ways, and so on to the kth task, which can be done in any 
one of nk different ways, then the total number of different ways the sequence of k tasks can 
be done is × × × ×n n n nk1 2 3 . Applying this principle to four tasks, the number of possible 
lunches that can be selected is the product of the number of ways to select a salad, the 
number of ways to select an entrée, the number of ways to select a beverage, and the number 
of ways to select a dessert. Hence, Quantity A is × × ×4 2 3 5 = 120. Quantity A is greater.
97. (C) For both Quantity A and Quantity B, there are five positions to fill: first, second, 
third, fourth, and fifth. The number of arrangements of the five people (or the five letters) is 
the product of the number of ways to fill each position. There are 5 people (or letters) from 
which to choose to fill the first position. Following that selection, there are 4 people (or 
letters) from which to choose to fill the second position. Following that selection, there are 
3 people (or letters) from which to choose to fill the third position. Following that selection, 
there are 2 people (or letters) from which to choose to fill the fourth position. Following 
that selection, there is 1 person (or letter) to fill the fifth position. Therefore, Quantity A = 
Quantity B = × × × ×5 4 3 2 1 = 120. The two quantities are equal. Select (C).
98. (B) In a three-digit number, there are three positions to fill: hundreds place, tens place, 
and units place. Quantity A is × ×5 4 3 = 60 (because digits may not repeat). Quantity B is 
× ×5 5 5 = 125 (because repetitions are allowed). Quantity B is greater.
99. (C) Use the combination formula to determine Quantity A and Quantity B. A combination 
is a selection from a set of objects without regard to order; that is, different arrangements of 
the same objects are considered to be the same selection. The number of combinations of r 
objects from n distinct objects, denoted Cn r or n
r
 is 
−
n
n r r
!
( )! !
. Note: The symbol “!” is 
read “factorial”; n! is the product of all positive integers less than or equal to n (except 0! = 1). 
The order in which committee members are selected is immaterial. Quantity A is:
C5 2 = 
−
5!
(5 2)!2!
 = 5!
(3)!2!
. Quantity B is C5 3 = 
−
5!
(5 3)!3!
 = 5!
(2)!3!
 
 The two quantities are equal. Select (C).
100. (B) Quantity A is:
graduate
graduate
number of vowels in
number of letters in
 = 4
8
 = 1
2
 
 Quantity B is:
a d graduate
graduate
number of letters other than or in
number of letters in
 = 5
8
 
 Quantity B is greater. Tip: A shortcut for this question is to recognize that the prob-
abilities will have the same denominator, so you need to compare only the numerators of 
the two quantities.
06_McCune_Answer.indd 169 2/21/22 4:45 PM