4.5 bl 111 Answer ExplanationsPS03831
91.For each^ trip,^ a taxicab^ company^ charges^ $^4.^25 for
the first mile and $2.65 for each add巾onal mile or
fraction thereof. If the total charge for a certain trip
was $62.55, how many miles at most was the trip?
(Al^21
(Bl^22
(C) 23
(D)^24
(El 25II. n is necessarily a multiple of 5 since the
value of n is either 5, 10, or 20.
III. n is a factor of 20 since 20 = qn for some
positive integer q.
Th e correct answer 1s D.
PS12759- What is the thousandths digit in the decimal equivalent
of
53
5 000.
，Arithmetic
Subtracting the charge for the first mile leaves a
charge of $62.55 -$4.25 = $58.30 for the miles
after the first mile. Divide this amount by $2.65
to find the number of miles to which $58.30
corresponds: 58.30 = 22 miles. Therefore, the
2.65
total number of miles is at most 1 (the first mile)
added to 22 (the number of miles after the first
mile), which equals 23.Th e correct answer 1s C.
PSl2857
92. When 24 is divided by the positive integer n, the
remainder is 4. Which of the following statements
about n must be true?
I. n 1s even.
II. n is a multiple of 5.
Ill. n is a factor of 20.
(A) Ill only
(B) I and II only
(C) I and Ill only
(D) II and Ill only
(El I, II, and IllArithmetic
Since the remainder is 4 when 24 is divided by
the positive integer n and the remainder must be
less than the divisor, it follows that 24 = qn + 4 for
some positive integer q and 4 < n, or qn = 20 and
n > 4. It follows that n = 5, or n = 10, or n = 20
since these are the only factors of 20 that exceed 4.I. n is not necessarily even. For example, n
could be 5.Ol356,l�'
,I'
，i'＇，ABCDE
＇，
．．
，＇，＇Arithmetic \l.11,"'(^53) = (^106) = 0.0106 and the thousandths
5,000 10,000
digit is 0.
Th e correct answer 1s A.
PS00986
94. The average (arithmetic mean) of the positive integers
x, y, and z is 3. If x < y < z, what is the greatest
possible value of z?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Algebra
x+y+z
It is given that = 3, or x + y + z = 9,
or z = 9 + (-x -y). lt follows that the greatest
possible (^) value of z occurs when (^) -x -y = -( x + y)
has the greatest possible value, which occurs
when x + y has the least possible value. Because
x and y are different positive integers, the least
possible value of x + y occurs when x = 1 and
y = 2. Therefore, the greatest possible value of z
is 9 - 1 - 2 = 6.
1h e correct answer 1s B.