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 438th symbol ?

Solution :

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

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

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

Note : The set of symbols ends up with 438th 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 + 5+ 55  =  5a + 1, what is a ?

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

Solution :

55 + 55 + 55 + 5+ 55  =  5a + 1

5 (55) =  5a + 1

5 1 + 5  =  5a + 1

6  =  5a + 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)=  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.

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