# PSAT MATH QUESTIONS

Question 1 :

If x*  =  7/x, what is the value of 14 (14*) ?

Solution :

Given : x*  =  7/x.

Then, we have

14(14*)  =  14(7/14)

14(14*)  =  14(1/2)

14(14*)  =  7

Question 2 :

What is the least common multiple of 4, 16, 25, and 30 ?

Solution :

least common multiple  =  2 ⋅ 2 ⋅ 5 ⋅ 4 ⋅ 5 ⋅ 3

=  1200

Question 3 :

How many positive integers are between -7/3 and 5/2 ?

Solution :

The decimal form of -7/3  =  -2.33

Decimal form of 5/2  =  2.5

Between -7/3 and 5/2, we have

-2, -1, 0, 1, 2

Integers are 1 and 2.

Hence there are 2 positive integers between -7/3 and 2/5.

Question 4 :

The perimeter of the rectangle is 80 inches. If the width is 18 inches, what is the area of the rectangle ?

Solution :

Perimeter of rectangle  =  80 inches

2 (l + w)  =  80

l + w  =  40

width  =  18 inches

l + 18  =  40

l  =  40 - 18  =  22 inches

Area of the rectangle is

=  l ⋅ w

=  22 ⋅ 18

=  396 square inches.

Question 5 :

7|-x - 3|  =  b, if x = -3, what is b ?

Solution :

7|-x - 3|  =  b

Substitute -3 for x.

7|-(-3) - 3|  =  b

7|3 - 3|  =  b

7|0|  =  b

0  =  b

So, the value of b is 0.

Question 6 :

1 + 2 + 3 + 4 + 5 + ............. + 100  =

Solution :

To find the sum of first n natural numbers, we have a formula

Sn  =  n(n + 1)/2

S100  =  100(100 + 1)/2

=  50 (101)

=  5050

Question 7 :

After a 10% increase, a population was 55. What was the population before the increase ?

Solution :

Let "x" be the population before the increase.

x + 10% of x  =  55

x + 10x/100  =  55

x + x/10  =  55

(10x + x) /10  =  55

11x/10  =  55

x  =  55 (10/11)

x  =  50

Question 8 :

The length of a rectangular solid is 10. The width, w and the height h follow the relationship, w3h =  27. What is the volume of the rectangular solid ?

Solution :

w3h =  27

(wh)3  =  27

(wh)3  =  3==> wh  =  3

Length of rectangular solid  =  10

Volume of rectangular solid  =  lwh

=  10 (3)

=  30

Question 9 :

AC has a length of 10 and r, the radius is 7. What is x ?

Solution :

Hence the value of x is 7.

Question 10 :

Find the value of x in the diagram shown above.

Solution :

In a right triangle, the square of hypotenuse side is equal to the sum of squares of other two sides.

(12√3) =  x2 + 10

144(3)  =  x2 + 100

x2  =  432 - 100  =  332

x  =  332

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