**PSAT Math Word Problems :**

Here we are going to see some practice questions for PSAT exams. For each and every questions, you will have solutions with step by step explanation.

Each question paper will contain set of 20 questions.

PSAT Math Word Problems

**Question 11 :**

The distinct prime factors of 232 are

**Solution :**

Hence the distinct prime factors are 2, 2, 2 and 29.

**Question 12 :**

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 13 :**

Find the value of t.

t/32 = x/p

**Solution :**

t/32 = x/p

Multiply by 32 on both sides, we get

t = 32x/p

**Question 14 :**

What is the largest integer greater than 52/3 ?

**Solution :**

By dividing 52/3, we get 17.33333

The largest integer greater than 52/3 is 18.

**Question 15 :**

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

**Solution :**

5^{5} + 5^{5} + 5^{5} + 5^{5 }+ 5^{5 }= 5^{a + 1}

5 (5^{5}) = 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 16 :**

If (x + y)^{2} = x^{2} + y^{2}, then what condition must be true?

**Solution :**

Formula for (x + y)^{2 }= x^{2} + y^{2} + 2xy

In order to make the right hand side as x^{2} + y^{2}, we have to the value of xy as 0.

**Question 17 :**

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

**Solution :**

Two circles will intersect maximum at 2 points.

**Question 18 :**

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} ?

**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 19 :**

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

**Solution :**

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

**Question 20 :**

How many chords are in the circle below ?

**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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