STUDY GUIDE FOR MATH SECTION OF PSAT / NMSQT
(These are the 20 most missed problems from previous years)
1)
If 5n = k, where n is a positive integer, which of the
following could be the value of k?
(A) 1
2)
(B) 10
(E) 350
(C) 16
(D) 24
(E) 32
(C) n-1
(D) n-3
(E) n+1
If x+ y+ z = 7 and 3x+3y = 12, what is the value of z?
(A) 3
5)
(D) 100
Sarah is 4 years younger than David. If n represents
David’s age now, what will Sarah’s age be in 5 years in
terms of n?
(A) n+9 (B) n+5
4)
(C) 125
Each time Jasmine counted her blocks by either 3’s or 5’s
she had one left over. But when she counted them by 8’s,
she had none left over. What is the least number of blocks
she could have had?
(A) 5
3)
(B) 8
(B) 5
(C) 7
(D) 9
(E) 11
If the area of each face of a cube is 81sq. inches, what is
the total length, in inches, of all the edges of the cube?
(A) 54 (B) 64
(C) 108
(D) 120
(E) 280
6)
Food X%
Tuition 35%
Books 12%
Housing
30%
Total cost of one year of college at Public
University in TN = $9800
According to the graph, what percent of the total cost is
food?
(A) 20% (B) 23% (C) 13%
7)
(B) 6
(C) 8
(D) -20
(E) -32
If (x+ y) 2 - (x- y) 2 = 140 and x and y are positive integers,
which of the following could be a value of x+ y ?
(A) 12
9)
(E) 18%
If |x+6| <12, which of the following could be a value of x?
(A) 4
8)
(D) 33%
(B) 14
(C) 16
(D) 18
(E) 20
In the xy-plane, the line y = ax + 8 is perpendicular to the
line 4x + 5y = 6. What is the value of a ?
(A) -5
(B) – 4/5 (C) 5/4
(D) 6/5
(E) -6/5
10) An empty tank has a capacity of 20 gallons. A pump can
deliver c gallons of gas every d seconds. In terms of c and
d, how many seconds will it take this pump to fill the tank?
(A) 20d/c (B) cd/20 (C) c/(20d)
(D) 20c/d (E) 20cd
11)
On the number line above, the letters represent
consecutive integers. If a + g = 16, what is the value of d?
(A) 5
(B) 6
(C) 7
(D) 8
(E)9
12) Equal numbers of cards that are marked either with a, b, or
c are placed in a box. If one card is drawn at random from
the box, what is the probability that it will be marked either
b or c?
(A) 1/9
(B) 1/3
(C) 1/2
(D) 2/3
(E) 4/9
13) The lengths of two sides of a triangle are 9 and 16,
respectively. What is one possible length of the third side?
14)
20 gorps = 1 shaz
100 dinks = 1 shaz
According to the equations above, how many dinks equal
50 gorps?
15) If ac = 20 and 4abc = 20, what is the value of 3b ?
16) Jennie has 12 large cookies and Max has 20 small cookies.
They will trade one of Jennie’s large cookies for 2 of
Max’s small cookies. After how many trades will Jennie
and Max have an equal number of cookies?
17) Hexagon ABCDEF is a regular polygon. If the measure of
<CAB is x◦ , what is the value of x?
18) If the average (arithmetic mean) of a, b, c, and d is 36,
what is the average of 2a-4b, c+7-a, 4b+d, and b+13?
19)
12, 5, 7, 2, …
In the sequence above, the first term is 12, the second term
is 5, and each term after the second term is the nonnegative
difference between the two previous terms. If the nth term
is the first term of the sequence that is equal to zero, what
is the value of n?
20) If x 6 = 2460 and
x4
y
= 12, what is the value of x 2 y?