PSAT MATH WORD PROBLEMS

Question 1 :

The distinct prime factors of 232 are

(A)  2, 2, 2, 29  (B)  116, 2  (C)  2, 29 

(D)  2, 2, 58  (E)  2, 58 

Solution :

Hence the distinct prime factors are 2 and 29.

Question 2 :

If the pattern continues, what will be the 438^th symbol ?

Solution :

By grouping the symbols, every group consists of 6 different symbols.

To find the symbol at the 438^th place, let us divide 438 by 6.

Since 438 is divisible by 6, the symbol at the 6^th place is the answer.

Note : The set of symbols ends up with 438^th position.

Question 3 :

Find the value of t. 

t/32  =  x/p

(A)  32p/x (B)  xp/32  (C)  32/px  (D)  32x/p  (E)  32px

Solution :

t/32  =  x/p

Multiply by 32 on both sides, we get

t  =  32x/p

Question 4 :

What is the largest integer greater than 52/3 ?

(A)  16   (B)  17  (C)  18  (D)  19  (E)  20

Solution :

By dividing 52/3, we get 17.33333

The largest integer greater than 52/3 is 18.

Question 5 :

If 5⁵ + 5⁵ + 5⁵ + 5⁵ + 5⁵  =  5^{a + 1}, what is a ?

(A)  3  (B)  4  (C)  5  (D)  6  (E)  7

Solution :

5⁵ + 5⁵ + 5⁵ + 5⁵ + 5⁵  =  5^{a + 1}

5 (5⁵) =  5^{a + 1}

5 ^{1 + 5}  =  5^{a + 1}

5 ⁶  =  5^{a + 1}

Since the bases are equal, the power are also equal.

a + 1  =  6

a  =  5

Question 6 :

If (x + y)²  =  x² + y², then what condition must be true ?

(A)  x  =  y  =  0  (B)  x + y  =  0  (C)  2x  =  0

(D)  2y  =  0  (E)  xy  =  0

Solution :

Formula for (x + y)²  =  x² + y² + 2xy

To make the right hand side as x² + y², we have to apply xy = 0.

Question 7 :

What is the maximum number of points that two distinct circles intersect at ?.

(A)  1  (B)  2  (C)  3  (D)  4  (E) Undefined

Solution :

Two circles will intersect maximum at 2 points.

Question 8 :

A cumulative product of a set {a, b, c, ............} is the sequence a, ab, abc,.............. What is the mean of the terms in cumulative product of {1, 2, 3, 0} ?

(A)  0  (B)  2  (C)  2.25  (D)  3.5  (E)  6

Solution :

The sequence formed by the cumulative product

1, 2, 6, 0.

The mean of the sequence  =  (1 + 2 + 6 + 0)/4

  =  9/4

  =  2.25

Question 9 :

How many integers are in the set of non positive, non negative  integers?

(A)  0  (B)  1  (C)  2  (D)  3  (E)  Undefined

Solution :

The only non negative and non positive integer is 0. Hence the answer is 1.

Question 10 :

How many chords are in the circle below ?

(A)  0  (B)  1  (C)  2  (D)  3  (E)  7

Solution :

The chord must touch the circle at two points. The only segment that does this is the diameter.

Hence there is only one chord, that is diameter.

Question 11 :

In an experiment, a student uses the thermometer that can read temperatures from -94° F to 172° F. The student also converts measurements from  °F to kelvins (K) and degree Rankine (°R) using the following approximate formulas.

T_K = (5x/9) + 255

where x is the temperature in °F and T_k is the temperature in K.

T_R = x + 460

where x is the temperature in °F and T_R is the temperature R.

If the temperature was recorded as 500°R, which of the following is closest to the reading of the thermometer ?

(A)  40°F      (B)  120°F      (C)  710°F     (D)  960°F

Solution :

T_R = x + 460

T_R = 500

500 = x + 460

x = 500 - 460

x = 40

Since 40°F falls within the thermometer's measurable range of -94°F to 172°F, this is the exact reading.

Question 12 :

If  √[17 + (x - y)³] = 9, what is the value of (x - y)³

(A)  4      (B)  9      (C)  16     (D)  25

Solution :

√[17 + (x - y)³] = 9

Squaring on both sides,

[17 + (x - y)³] = 9²

17 + (x - y)³ = 81

(x - y)³ = 81 - 17

(x - y)³ = 64

(x - y)³ = 4³

Then the value of x - y is 4.

(x - y)² = 4²

= 16

So, option C is correct.

Question 13 :

The boiling point of water at sea level is 212 degree Fahrenheit (°F). For every 550 feet above sea level, the boiling point of water is lowered by about 1°F. Which of the following equations can be used to find the boiling point B water, x feet above sea level ?

(A)  B = 550 + (x/212)      (B)  B = 550 - (x/212)

(C)  B = 212 + (x/550)      (D)  B = 212 - (x/550)

Solution :

The initial temperature of water is 212 degrees °F

For every 550 it is lowered by 1°F

So, option D is correct.

Question 14 :

In the xy-plane, the graph of the quadratic function g intersects the x-axis at x = 5 and x = 9. Which of the following could be an equation of g ?

A) g(x) = (x - 5)(x - 9)     B) g(x) = (x + 5)(x + 9)

C) g(x) = (x - 7)² + 4     D) g(x) = (x + 7)² - 4

Solution :

x = 5 and x = 9

Converting into factored form, we get

g(x) = (x - 5)(x - 9)

So, option A is correct.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.