Math Puzzles and Problems

Find the missing number.

• 22

• 25

• 0

• 24

Answer explanation

In the top triangle, 4 + 6 + 12 = 22

In the second row, the second triangle has a sum of three numbers; 8 + 3 + 11 = 22

Thus, the missing number in the puzzle is:

7 + 5 + 13 = 25

What is the missing number?

• 9

• 3

• 4

• 6

Answer explanation

The numbers in the second row (from the bottom) are the difference of the corresponding two numbers in the bottom row.

That means, 6 = 8 – 2

1 = 3 – 2

7 – 3 =? 

Similarly,

6 – 1 = 5, ? – 1 = 3

And

5 – 3 = 1

From the above, we can say that the missing value is equal to 4.

Find the odd one out.

740, 185, 37, 407, 1369, 111, 78

• 185

• 111

• 37

• 78

Answer explanation

All the other numbers are divisible by 37 except 78.

Rationalise.

• 
• 
• 0

Simplify (√5-√2)(√5+√2)

• 21

• 0

• 3

Answer explanation

Using the identity, (a+b) (a-b) = a² - b²

(√5-√2)(√5+√2) = (√5²-√2²) = 5-2 = 3

Find the value of m, if x + 4 is a factor of the polynomial x² + 3x + m.

• -4

• 4

• 0

Answer explanation

Let p(x) = x² + 3x + mSince (x + 4) or (x – (-4)} is a factor of p(x).∴ p(-4) = 0⇒ (-4)² + 3(-4) + m = 0⇒ 16 – 12 + m = 0⇒ m = -4

Find the remainder when x³+ x² + x + 1 is divided by x – 12 using remainder theorem.

• 0

Answer explanation

Let p(x) = x³+ x² + x + 1 and q(x) = x – 12Here, p(x) is divided by q(x)∴ By using remainder theorem, we have.

If 3x + 2y = 12 and xy = 6, find the value of 27x³ + 8y³

• 0

• 432

• -432

• None of these

Answer explanation

We have 3x + 2y = 12 on cubing both sides, we have⇒ (3x + 2y)³ = 12³

(3x)³ +(2y)³ + 3 × 3x × 2y(3x + 2y) = √728

27x³+ 8y³ + 18xy(3x + 2y) = √728

27x³+ 8y³ + 18 × 6 × 12 = √728

27x³+ 8y³ + 1296 = √728

27x³+ 8y³ = √728 – 1296

27x³+ 8y³ = 432

Factorise 64a³ – 27b³ – 144a²b + 108ab².

• (40 + 3b) (4a + 3b) (4a+3b)

• 0

• (40 – 3b) (4a – 3b) (4a – 3b)

Answer explanation

Simplify the following.

• x+1

• x-1

• 0

• x+2

Answer explanation