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.

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