A Simple Math IQ Quiz

1. How much is 1/4 of the sum of 260 and 64?

16

65

81

324

To find 1/4 of the sum of 260 and 64, we first need to calculate the sum which is 324. Then, we divide this sum by 4 to find the 1/4 value. Therefore, 1/4 of 324 is 81.

Explanation

To find 1/4 of the sum of 260 and 64, we first need to calculate the sum which is 324. Then, we divide this sum by 4 to find the 1/4 value. Therefore, 1/4 of 324 is 81.

2. What's the width of a cube whose height is 10 inches?

10 Inches

100 Inches

5 Inches

20 Inches

The width of a cube is equal to its height, so if the height of the cube is 10 inches, then the width would also be 10 inches.

Explanation

The width of a cube is equal to its height, so if the height of the cube is 10 inches, then the width would also be 10 inches.

3. In how many different ways can the cars of a three-car train be arranged?

6

10

30

20

To calculate the number of different ways the cars of a three-car train can be arranged, you can use the concept of permutations. In this case, you want to arrange three distinct cars, so you would use a permutation of 3 objects taken 3 at a time.

The formula for permutations is:

[P(n, r) = frac{n!}{(n - r)!}]

where:

- (P(n, r)) is the number of permutations of (n) objects taken (r) at a time.

- (n!) is the factorial of (n), which is the product of all positive integers from 1 to (n).

- ((n - r)!) is the factorial of (n - r).

For your three-car train, you have three cars, so (n = 3), and you want to arrange all three, so (r = 3).

Using the permutation formula:

[P(3, 3) = frac{3!}{(3 - 3)!} = frac{3!}{0!} = frac{6}{1} = 6]

There are 6 different ways to arrange the cars of the three-car train.

Explanation

To calculate the number of different ways the cars of a three-car train can be arranged, you can use the concept of permutations. In this case, you want to arrange three distinct cars, so you would use a permutation of 3 objects taken 3 at a time.

The formula for permutations is:

[P(n, r) = frac{n!}{(n - r)!}]

where:

- (P(n, r)) is the number of permutations of (n) objects taken (r) at a time.

- (n!) is the factorial of (n), which is the product of all positive integers from 1 to (n).

- ((n - r)!) is the factorial of (n - r).

For your three-car train, you have three cars, so (n = 3), and you want to arrange all three, so (r = 3).

Using the permutation formula:

[P(3, 3) = frac{3!}{(3 - 3)!} = frac{3!}{0!} = frac{6}{1} = 6]

There are 6 different ways to arrange the cars of the three-car train.

4. Which of the examples below shows the "Multiplicative Inverse"?

2 x (1/2) = 1

2 + 0 = 2

2 x 0 = 0

2 + (-2) = 0

The example 2 x (1/2) = 1 shows the "Multiplicative Inverse" because when a number is multiplied by its multiplicative inverse, the result is always 1. In this case, 2 is multiplied by the multiplicative inverse of 2, which is 1/2, resulting in 1.

Explanation

The example 2 x (1/2) = 1 shows the "Multiplicative Inverse" because when a number is multiplied by its multiplicative inverse, the result is always 1. In this case, 2 is multiplied by the multiplicative inverse of 2, which is 1/2, resulting in 1.

5. How would you write 4^3 (4 to the 3rd power) without an exponent?

64

12

43

16

To write 4^3 without an exponent, we need to multiply 4 by itself three times. This can be written as 4 × 4 × 4, which equals 64.

Explanation

To write 4^3 without an exponent, we need to multiply 4 by itself three times. This can be written as 4 × 4 × 4, which equals 64.

6. Which number is evenly divisible by 7?

674

672

673

671

672 is evenly divisible by 7 because it can be divided by 7 without leaving a remainder.

Explanation

672 is evenly divisible by 7 because it can be divided by 7 without leaving a remainder.

7. What is 2/3 of 192?

118

138

128

108

To find 2/3 of 192, we can multiply 192 by 2 and then divide the result by 3. This gives us (192 * 2) / 3 = 384 / 3 = 128. Therefore, the correct answer is 128.

Explanation

To find 2/3 of 192, we can multiply 192 by 2 and then divide the result by 3. This gives us (192 * 2) / 3 = 384 / 3 = 128. Therefore, the correct answer is 128.

8. If a = 1.9 and b = 0.6, what is a/b (round to 2 decimal places)?

2.5

3.17

1.3

0.32

To find the value of a/b, we divide the value of a (1.9) by the value of b (0.6). Dividing 1.9 by 0.6 gives us approximately 3.17 when rounded to 2 decimal places. Therefore, the correct answer is 3.17.

Explanation

To find the value of a/b, we divide the value of a (1.9) by the value of b (0.6). Dividing 1.9 by 0.6 gives us approximately 3.17 when rounded to 2 decimal places. Therefore, the correct answer is 3.17.

9. How many feet are in 2/3 of a mile?

8,520 Feet

5,280 Feet

3,520 Feet

1,760 Feet

There are 5,280 feet in a mile. To find 2/3 of a mile, we can multiply 5,280 by 2 and then divide by 3. This gives us 3,520 feet, which is the correct answer.

Explanation

There are 5,280 feet in a mile. To find 2/3 of a mile, we can multiply 5,280 by 2 and then divide by 3. This gives us 3,520 feet, which is the correct answer.

10. What is the prime factorization of 100?

10 x 10

2 x 2 x 5 x 5

2 x 2 x 25

2 x 5

The prime factorization of 100 is 2 x 2 x 5 x 5 because it can be expressed as a product of prime numbers. The number 100 can be divided by 2, resulting in 50. Then, 50 can be divided by 2 again, resulting in 25. Finally, 25 can be divided by 5, resulting in 5. Therefore, the prime factorization of 100 is 2 x 2 x 5 x 5.

Explanation

The prime factorization of 100 is 2 x 2 x 5 x 5 because it can be expressed as a product of prime numbers. The number 100 can be divided by 2, resulting in 50. Then, 50 can be divided by 2 again, resulting in 25. Finally, 25 can be divided by 5, resulting in 5. Therefore, the prime factorization of 100 is 2 x 2 x 5 x 5.