Quant - Arithmetic & Numbers

Question 1

What makes a number divisible by 2?

Answer 1

Last digit is 0, 2, 4, 6, or 8.

Question 2

Divisibility rule for 3?

Answer 2

Sum of digits divisible by 3.

Question 3

Divisibility rule for 4?

Answer 3

Last two digits divisible by 4.

Question 4

Divisibility rule for 5?

Answer 4

Ends in 0 or 5.

Question 5

Divisibility rule for 6?

Answer 5

Divisible by both 2 and 3.

Question 6

Divisibility rule for 8?

Answer 6

Last three digits divisible by 8.

Question 7

Divisibility rule for 9?

Answer 7

Sum of digits divisible by 9.

Question 8

Divisibility rule for 10?

Answer 8

Ends in 0.

Question 9

Definition of a prime number?

Answer 9

A number with exactly two positive factors: 1 and itself.

Question 10

Is 1 prime?

Answer 10

No. It has only one factor.

Question 11

Smallest prime number?

Answer 11

2.

Question 12

Only even prime?

Answer 12

2.

Question 13

What is a composite number?

Answer 13

A number with more than two factors.

So:
• Prime number → has exactly two factors (1 and itself)
• Composite number → has more than two factors

Examples:
• 7 → factors are 1 and 7 → only two → ✅ prime
• 8 → factors are 1, 2, 4, 8 → more than two → ✅ composite
• 12 → factors are 1, 2, 3, 4, 6, 12 → composite

So basically:

👉 If a number can be “broken apart” evenly in extra ways besides just 1 and itself, it’s composite.

Question 14

Definition of a factor?

Answer 14

A number that divides another evenly.

Question 15

Definition of a multiple?

Answer 15

A number obtained by multiplying another number.

Question 16

What is the GCF?

Answer 16

Greatest common factor — largest shared factor.

Question 17

What is the LCM?

Answer 17

Least common multiple — smallest shared multiple.

Question 18

Prime factorization means?

Answer 18

Expressing a number as product of primes.

Question 19

If a number is divisible by both 4 and 6, must it be divisible by 12?

Answer 19

Yes (because LCM of 4 and 6 is 12).

Question 20

Even × even = ?

Answer 20

Even.

Question 21

Even × odd = ?

Answer 21

Even.

Question 22

Odd × odd = ?

Answer 22

Odd.

Question 23

Even + even = ?

Answer 23

Even.

Question 24

Odd + odd = ?

Answer 24

Even.

Question 25

Even + odd = ?

Answer 25

Odd.

Question 26

Negative × negative = ?

Answer 26

Positive.

Question 27

Negative × positive = ?

Answer 27

Negative.

Question 28

|x| represents?

Answer 28

Distance from zero.

Question 29

If |x| = 7, possible values?

Answer 29

7 and −7.

Question 30

Square of any real number is?

Answer 30

Nonnegative.

Question 31

Cube of a negative number is?

Answer 31

Negative.

Question 32

If a number has exactly 3 factors, what must it be?

Answer 32

A square of a prime.

Question 33

If a number ends in 0, what must it contain as factors?

Answer 33

2 and 5.

Question 34

What is a reciprocal?

Answer 34

1 divided by the number.

Question 35

Reciprocal of 3/4?

Answer 35

4/3.

Question 36

0 divided by any nonzero number?

Answer 36

0.

Question 37

Division by zero equals?

Answer 37

Undefined.

Question 38

If a > b and b > c, then?

Answer 38

a > c.

Question 39

If a and b are both even, is their sum divisible by 4?

Answer 39

Not necessarily.

Question 40

If a number is divisible by 6, must it be divisible by 3?

Answer 40

Yes.

Question 41

What is a perfect square?

Answer 41

An integer multiplied by itself.

Question 42

What is a perfect cube?

Answer 42

An integer multiplied by itself twice. A perfect cube is: a whole number multiplied by itself three times (number × number × number) So instead of just the definition, here are clean examples: 1³ = 1 × 1 × 1 = 1 2³ = 2 × 2 × 2 = 8 3³ = 3 × 3 × 3 = 27 4³ = 4 × 4 × 4 = 64 5³ = 5 × 5 × 5 = 125 6³ = 6 × 6 × 6 = 216 7³ = 7 × 7 × 7 = 343 8³ = 8 × 8 × 8 = 512 9³ = 9 × 9 × 9 = 729 10³ = 10 × 10 × 10 = 1000 So the perfect cubes in that list are: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000

Question 43

If x² = 25, what are possible x values?

Answer 43

5 and −5.

Question 44

If a number has prime factorization 2³ × 3², how many total factors does it have?

Answer 44

(3+1)(2+1) = 12 factors. Step 1: Add 1 to each exponent • 3 + 1 = 4 • 2 + 1 = 3 Step 2: Multiply 4 × 3 = 12 factors Rule: If a number is p^a \times q^b, total factors = (a + 1)(b + 1)

Question 45

Rule for counting total factors from prime factorization?

Answer 45

Add 1 to each exponent, then multiply.

Question 46

If a number is divisible by 12, must it be divisible by 4?

Answer 46

Yes.

Question 47

If a number is divisible by 12, must it be divisible by 6?

Answer 47

Yes.

Question 48

If a number is divisible by 15, what prime factors must it contain?

Answer 48

3 and 5.

Question 49

What is the units digit of 7²?

Answer 49

9.

Question 50

What is the repeating units digit pattern of 7ⁿ?

Answer 50

7, 9, 3, 1 (repeats every 4 powers).