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 ?
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 ?
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?
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! ?
Let x be 5 !
(5 !)!/ 5! = x!/x
= x (x- 1)!/x
= (x - 1)!
= (5! - 1)!
= (120 - 1)!
Hence none of the above is the answer.
Question 5 :
What is (a2 + 2ab + b2)/(a + b)3 ?
(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 ?
If it takes 3 cats 3 minutes to catch 3 mice, then it will take 3(1) cats 3x minute to catch 3x mice, as long as x is an integer.
3x = 99
x = 33
Since x is an integer, it will take 3(1) = 3 cats.
Question 7 :
The sum of seven consecutive odd integers is 749. What is the largest of the seven integers ?
Let "x" be the odd integer,
then 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
Question 8 :
V = πr2 h 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 ?
"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 ?
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 ?
June month salary of John = $4000
Percentage of salary raised = 4%
New salary in the month July = 4000 + 4% of 4000
= 4000 + 160
John's 1 week salary = 4160/4 = 1040
He works 40 hours per week.
Hourly rate for the month July = 1040/40 = $26
After having gone through the stuff given above, we hope that the students would have understood "PSAT Practice Questions in Math".
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