**PSAT Math Practice Quiz :**

Here we are going to see some sample 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 Practice Quiz

**Question 11 :**

[(1/2)-(3/4)] ÷ (1/2) =

**Solution :**

= [(1/2)-(3/4)] ÷ (1/2)

= [(2 - 3)/4] ÷ (1/2)

= (-1/4) ÷ (1/2)

= (-1/4) ⋅ (2/1)

= -1/2

Hence the answer is -1/2.

**Question 12 :**

Line q intersects the parallel lines p and l. What is y^{3}/3 ?

**Solution :**

The lines p and l are parallel lines and q is a transversal. So, corresponding angle are equal.

y = x^{2}

y^{3}/3 = (x^{2})^{3}/3

= x^{6}/3

Hence the value y^{3}/3 is x^{6}/3.

**Question 13 :**

Given the arithmetic sequence x, y, 30, z, f find x + y + z + f ?

**Solution :**

In a arithmetic sequence, the common difference is d.

x = 30 - 2d

y = 30 - d

z = 30 + d

f = 30 + 2d

x + y + z + f = 30 - 2f + 30 - d + 30 + d + 30 + 2d

= 120

Hence the answer is 120.

**Question 14 :**

If (-1)^{2} = 1, then the value (-1) ^{2023} is

**Solution :**

(-1) ^{2023 }= (-1)^{2022 }⋅ (-1)

= ((-1)^{2})^{1011 }⋅ (-1)

= 1^{1011 }⋅ (-1)

= 1^{1011 }⋅ (-1) = -1

Hence the answer is -1.

**Question 15 :**

Caroline has two times as many marbles as Jake. Jake has 12 less than 7 times as many marbles James has. James has 14 marbles. How many marbles dies Caroline have ?

**Solution :**

Number of marbles with James = 14

Number of marbles with Jake = 7(14) - 12

= 98 - 12

= 86

Number of marbles with Caroline = 2 (86)

= 172

Hence Caroline has 172 marbles.

**Question 16 :**

John is trying to escape a ditch. Every time he jumps 10 meters, he falls back 5 meters right after. The ditch is 19 meters long. What is the minimum number of jumps he needs to make to escape ?

**Solution :**

At the first jump, he reaches 10 meters, but he falls back 5 meters. Now, John crossed 5 m.

At the second jump, he reaches from 5m to 15 m, but he falls back 5 m. So, he will be at 10 m.

At the third jump, he reaches from 10m to 20 m, but he falls back 5 m. So, he will be at 15 m

20 m is away from 19, so 3 jumps are required to escape.

**Question 17 :**

What is the largest number of digits the product of 3 digit and 2 digit number has ?

**Solution :**

The product of 3 digit and 2 digit number will be 4 digit or 5 digit number.

Since we need the largest number of digits, the answer is 5 digits.

**Question 18 :**

If Fn = 2 F_{n-1} + 3 F_{n-2}, then what is F_{3} if F_{1 } = F_{2} = 1 ?

**Solution :**

n = 3

F_{3} = 2 F_{3-1} + 3 F_{3-2}

F_{3} = 2 F_{2} + 3 F_{1}

F_{3} = 2 (1) + 3 (1)

F_{3} = 2 + 3 = 5

**Question 19 :**

Sam walks 3 m to the west, then 4m south, then 4 m North. How far is he from his original location?

**Solution :**

So he will be at 3 m distance from the starting point.

**Question 20 :**

If a = 3 and b = 5, what is the value of 9a/(b-a) ?

**Solution :**

9a / (b - a) = 9(3)/(5-3)

= 27/2

Hence the answer is 27/2.

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