Short Questions
Q1. Think of a number, double it, add 8, divide by 2, subtract the original number.
Solution:
Let the number = x
Step 1: Double it → 2x
Step 2: Add 8 → 2x + 8
Step 3: Divide by 2 → (2x + 8) ÷ 2 = x + 4
Step 4: Subtract original number → (x + 4) − x = 4
Final Answer: 4
Q2. Find the top of pyramid if bottom numbers are 7 and 9.
Solution:
Step 1: Add bottom numbers
Top = 7 + 9 = 16
Final Answer: 16
Q3. Find top-left number if sum of 2×2 grid is 44.
Solution:
Formula:
Sum = 4a + 16
Step 1: 4a + 16 = 44
Step 2: Subtract 16 → 4a = 28
Step 3: Divide by 4 → a = 7
Final Answer: 7
Q4. Reverse 73 and subtract.
Solution:
Step 1: Reverse → 37
Step 2: Subtract → 73 − 37 = 36
Step 3: Check divisibility → 36 ÷ 9 = 4
Final Answer: 36 (divisible by 9)
Q5. Largest product using digits 2, 4, 9.
Solution:
Step 1: Largest digit as multiplier → 9
Step 2: Arrange remaining digits → 42
Step 3: Multiply → 42 × 9 = 378
Final Answer: 378
Q6. Find a if a = 15 + c and c = 5.
Solution:
Step 1: Substitute value → a = 15 + 5
Step 2: Add → a = 20
Final Answer: 20
Q7. Find sum of grid: 8, 9, 15, 16.
Solution:
Step 1: Add numbers
8 + 9 = 17
17 + 15 = 32
32 + 16 = 48
Final Answer: 48
Q8. Find difference of 41 and its reverse.
Solution:
Step 1: Reverse → 14
Step 2: Subtract → 41 − 14 = 27
Final Answer: 27
Q9. Find top of pyramid with bottom row: 1, 3, 5.
Solution:
Step 1: Add first pair → 1 + 3 = 4
Step 2: Add second pair → 3 + 5 = 8
Step 3: Add results → 4 + 8 = 12
Final Answer: 12
Q10. Solve: 2c + 30 = 70
Solution:
Step 1: Subtract 30 → 2c = 40
Step 2: Divide by 2 → c = 20
Final Answer: 20
Long Questions
Q1. Number Trick Proof
Think of a number, multiply by 4, add 12, divide by 4, subtract original number.
Solution:
Let number = x
Step 1: Multiply → 4x
Step 2: Add 12 → 4x + 12
Step 3: Divide by 4 → (4x + 12) ÷ 4 = x + 3
Step 4: Subtract x → (x + 3) − x = 3
Final Answer: Always 3
Q2. Calendar Grid, Sum = 60, find numbers.
Solution:
Step 1: Formula → 4a + 16 = 60
Step 2: Subtract 16 → 4a = 44
Step 3: Divide → a = 11
Step 4: Find numbers:
a = 11
a + 1 = 12
a + 7 = 18
a + 8 = 19
Final Answer: 11, 12, 18, 19
Q3. Pyramid Problem, Top = 70, bottom = 10, c, 20
Solution:
Step 1: a = 10 + c
Step 2: b = c + 20
Step 3: a + b = 70
Step 4: Substitute
(10 + c) + (c + 20) = 70
10 + c + c + 20 = 70
30 + 2c = 70
Step 5: Solve
2c = 40
c = 20
Step 6: Find others
a = 10 + 20 = 30
b = 20 + 20 = 40
Final Answer: c = 20, a = 30, b = 40
Q4. Divisibility Proof Show sum of number and reverse is divisible by 11.
Solution:
Step 1: Let number = 10a + b
Step 2: Reverse = 10b + a
Step 3: Add
(10a + b) + (10b + a)
Step 4: Simplify
= 10a + b + 10b + a
= 11a + 11b
Step 5: Factor
= 11(a + b)
So divisible by 11
Final Answer: Always divisible by 11
Q5. Age Problem Mother is 4 times daughter. After 5 years, mother is 3 times daughter.
Solution:
Step 1: Let daughter = x
Mother = 4x
Step 2: After 5 years
Mother = 4x + 5
Daughter = x + 5
Step 3: Form equation
4x + 5 = 3(x + 5)
Step 4: Solve
4x + 5 = 3x + 15
4x − 3x = 15 − 5
x = 10
Final Answer: Daughter = 10 years
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