PSAT Practice Questions in Math :
Here we are going to see some sample questions for PSAT exams. For each and every questions, you will have solutions with step by step explanation.
Question 1 :
If x and y are integers, which is always even ?
(A) (x + y)/2 (B) 2(x + y)/x (C) x - y
(D) 2(x + y) (E) x2 + y2
Solution :
Since x and y are integers, the sum of those integers will be odd or even. The multiple of 2 will not be odd. So the answer is 2 (x + y).
Question 2 :
What is the probability that a point chosen will be in the shaded region ?
(A) y2/x2 (B) (x + y)2/y2 (C) x2/(y2-x2)
(D) (y2-x2)/y2 (E) π
Solution :
Sample space = n(S) = πy2
Let "a" be the event that a point chosen in a shaded region.
Area of shaded region = πy2 - πx2
n(A) = π(y2 - x2)
P(A) = n (A) / n (S)
= π(y2 - x2)/πy2
= (y2 - x2)/y2
Let us look into the next example on "PSAT Practice Questions in Math".
Question 3 :
If q = x + y and x = y + z, what is z in terms of y and q?
(A) q - 2x (B) q - 2y (C) 2x - q (D) 2y + q (E) 2q + x
Solution :
q = x + y -----(1)
x = y + z ------(2)
z = x - y
From the first equation, let us find the value of x in terms of y and q
x = q - y
z = (q - y) - y
z = q - y - y
z = q - 2y
Question 4 :
What is (5 !)!/ 5! ?
(A) 1 (B) 5 (C) 120 (D) 720 (E) None of these
Solution :
Let x be 5 !
(5 !)!/ 5! = x!/x
= x (x- 1)!/x
= (x - 1)!
= (5! - 1)!
= (120 - 1)!
= 119!
Hence none of the above is the answer.
Question 5 :
What is (a2 + 2ab + b2)/(a + b)3 ?
(A) a + b (B) a2 + b2 (C) 1/(a + b)
(D) 1/(a+ b)2 (E) (a + b)2
Solution :
(a2 + 2ab + b2)/(a + b)3
= (a + b)2/(a + b)3
= 1/(a + b)
Question 6 :
It takes 3 cats 3 minutes to catch 3 mice. How many cats are needed to catch 99 mice in 99 minutes ?
(A) 3 (B) 6 (C) 11 (D) 33 (E) 99
Solution :
Given : It takes 3 cats 3 minutes to catch 3 mice.
That is,
3 cats -----> 3 minutes -----> 3 mice
Let us assume,
3 cats = 1 man
Then, we have
1 man -----> 3 minutes -----> 3 mice
Based on the above statement, we can consider the following situations also.
1 man -----> 1 minute -----> 1 mouse
1 man -----> 5 minutes -----> 5 mice
1 man -----> 10 minutes -----> 10 mice
In this way, we can have
1 man -----> 99 minutes -----> 99 mice
But, we know that,
1 man = 3 cats
Then, we have
3 cats -----> 99 minutes -----> 99 mice
Therefore, 3 cats are needed to catch 99 mice in 99 minutes.
Question 7 :
The sum of seven consecutive odd integers is 749. What is the largest of the seven integers ?
(A) 99 (B) 103 (C) 11 (D) 113 (E) 115
Solution :
Let x be the odd integer.
6 consecutive odd integers will be (x+2), (x+4), (x+6), (x+8), (x+10) and (x+12).
Sum of seven consecutive integers = 749
x + x+2 + x+4 + x+6 + x+8 + x+10 + x+12 = 749
7x + 42 = 749
7x = 749 - 42
7x = 707
x = 707/7 ==> 101
Largest number of seven consecutive odd numbers
= x + 12
= 101 + 12
= 113
Question 8 :
V = πr2h Using the formula, if r is doubled and h is divided by 2, what is the ratio of the original volume to the new volume ?
(A) 1 : 4 (B) 1 : 2 (C) 1 : 1 (D) 2 : 1 (E) 4 : 1
Solution :
r is doubled means r = 2r
h is divided by 2 means h = h/2
New volume :
V1 = π(2r)2 (h/2)
V1 = π(4r2) (h/2)
V1 = 2πr2 h
Ratio of the original volume to the new volume :
= V : V1
= πr2 h : 2πr2 h
= 1 : 2
Hence the required ratio is 1 : 2.
Question 9 :
A yellow cab has the base fare of $3.50 per ride plus $0.20 for each 1/4 of mile ridden. If a yellow cab costs $ 22.50, how many miles long was the ride ?
(A) 23.75 miles (B) 42.5 miles (C) 47.5 miles
(D) 95 miles (E) 112.5 miles
Solution :
Let "x" be the number of miles ridden
To find the (1/4)th miles of x miles, we have to multiply 4 by x.
So, there are 4x (1/4)th miles in x miles.
To understand this, let us consider the following example in the picture given below.
Cost of yellow cab = $22.50
3.50 + 0.20 (4x) = 22.50
0.80x = 22.50 - 3.50
0.80x = 19
(80x/100) = 19
x = 19(100)/80
x = 23.75 miles
Hence he traveled 23.75 miles.
Question 10 :
John works 40 hours a week, and his monthly salary in June was $4000. In the month July, John got 4% raise on his monthly salary. In the month of July, what was John's hourly rate ?
(A) $25 (B) $26 (C) $40 (D) $100 (E) $104
Solution :
June month salary of John = $4000
Percentage of salary raised = 4%
New salary in the month July = 4000 + 4% of 4000
= 4000 + 160
= 4160
John's 1 week salary = 4160/4 = 1040
He works 40 hours per week.
Hourly rate for the month July = 1040/40 = $26
PSAT MATH ONLINE WORKSHEETS
PSAT online practice test math - Paper 1
PSAT online practice test math - Paper 2
PSAT online practice test math - Paper 3
PSAT online practice test math - Paper 4
PSAT online practice test math - Paper 5
PSAT online practice test math - Paper 6
PSAT online practice test math - Paper 7
PSAT online practice test math - Paper 8
PSAT online practice test math - Paper 9
PSAT online practice test math - Paper 10
PSAT online practice test math - Paper 11
After having gone through the stuff given above, we hope that the students would have understood, how to solve PSAT math problems.
Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.
You can also visit our following web pages on different stuff in math.
WORD PROBLEMS
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
Word problems on compound interest
Word problems on types of angles
Complementary and supplementary angles word problems
Trigonometry word problems
Markup and markdown word problems
Word problems on mixed fractrions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Word problems on sets and venn diagrams
Pythagorean theorem word problems
Percent of a number word problems
Word problems on constant speed
Word problems on average speed
Word problems on sum of the angles of a triangle is 180 degree
OTHER TOPICS
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions with holes
Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits