Problems on Numbers— Concepts, Formulas & Shortcuts
- A two-digit number with tens digit a and units digit b is 10a + b; reversing it gives 10b + a.
- Reversing a two-digit number changes it by 9(b − a) — always a multiple of 9.
- Consecutive integers: x, x + 1, x + 2; consecutive odd or even: x, x + 2, x + 4.
- "Sum is s and difference is d" ⇒ the numbers are (s + d)/2 and (s − d)/2.
- "A exceeds B by k" means A − B = k; "A is k times B" means A = kB.
- Check the answer against BOTH conditions in the question, not just the one you used.
Problems on Numbers Practice Questions with Answers
Attempt each question first, then open the explanation. All 19 questions below are free to read and require no signup.
Q1.The sum of two numbers is 25 and their difference is 5. The numbers are:
Easy- A12 and 13
- B15 and 10
- C18 and 7
- D20 and 5
Problems on Numbers question 1 of 19+Show Answer & Explanation
Answer: B. 15 and 10
Explanation: Numbers are (25 + 5)/2 = 15 and (25 − 5)/2 = 10.
Q2.A number leaves a remainder 3 when divided by 5. The remainder when its square is divided by 5 is:
Moderate- A1
- B2
- C3
- D4
Problems on Numbers question 2 of 19+Show Answer & Explanation
Answer: D. 4
Explanation: The number ≡ 3 (mod 5), so its square ≡ 9 ≡ 4 (mod 5).
Q3.The sum of a number and its reciprocal is 17/4. The number is:
Difficult- A2
- B3
- C4
- D5
Problems on Numbers question 3 of 19+Show Answer & Explanation
Answer: C. 4
Explanation: x + 1/x = 17/4 → 4x² − 17x + 4 = 0 → (4x − 1)(x − 4) = 0 → x = 4 (or ¼).
Q4.The sum of three consecutive odd numbers is 51. The largest of them is:
Easy- A17
- B19
- C21
- D23
Problems on Numbers question 4 of 19+Show Answer & Explanation
Answer: B. 19
Explanation: x + (x + 2) + (x + 4) = 51 → 3x = 45 → x = 15, so the numbers are 15, 17, 19.
Q5.The sum of the digits of a two-digit number is 9. Reversing the digits increases the number by 27. The number is:
Difficult- A27
- B36
- C45
- D54
Problems on Numbers question 5 of 19+Show Answer & Explanation
Answer: B. 36
Explanation: 9(b − a) = 27 → b − a = 3, and a + b = 9 → a = 3, b = 6, so the number is 36.
Q6.If one-third of a number exceeds its one-fourth by 5, the number is:
Moderate- A45
- B50
- C60
- D75
Problems on Numbers question 6 of 19+Show Answer & Explanation
Answer: C. 60
Explanation: x/3 − x/4 = 5 → x/12 = 5 → x = 60.
Q7.The sum of two numbers is 40 and their difference is 8. The larger number is:
Easy- A20
- B22
- C24
- D26
Problems on Numbers question 7 of 19+Show Answer & Explanation
Answer: C. 24
Explanation: Larger = (40 + 8)/2 = 24.
Q8.Three consecutive even numbers add up to 66. The smallest is:
Easy- A18
- B20
- C22
- D24
Problems on Numbers question 8 of 19+Show Answer & Explanation
Answer: B. 20
Explanation: x + (x + 2) + (x + 4) = 66 → 3x = 60 → x = 20.
Q9.If twice a number decreased by 5 equals 27, the number is:
Easy- A11
- B14
- C16
- D18
Problems on Numbers question 9 of 19+Show Answer & Explanation
Answer: C. 16
Explanation: 2x − 5 = 27 → 2x = 32 → x = 16.
Q10.The digits of a two-digit number differ by 3 and their sum is 11. The number (with the larger digit in the tens place) is:
Moderate- A47
- B56
- C65
- D74
Problems on Numbers question 10 of 19+Show Answer & Explanation
Answer: D. 74
Explanation: a + b = 11 and a − b = 3 → a = 7, b = 4, so the number is 74.
Q11.One-fifth of a number is 12 more than one-seventh of it. The number is:
Difficult- A140
- B175
- C210
- D245
Problems on Numbers question 11 of 19+Show Answer & Explanation
Answer: C. 210
Explanation: x/5 − x/7 = 12 → 2x/35 = 12 → x = 210.
Q12.The product of two consecutive positive integers is 132. The smaller integer is:
Moderate- A10
- B11
- C12
- D13
Problems on Numbers question 12 of 19+Show Answer & Explanation
Answer: B. 11
Explanation: 11 × 12 = 132, so the smaller integer is 11.
Q13.If a number is increased by 20 it becomes three times itself. The number is:
Easy- A8
- B10
- C12
- D15
Problems on Numbers question 13 of 19+Show Answer & Explanation
Answer: B. 10
Explanation: x + 20 = 3x → 2x = 20 → x = 10.
Q14.The sum of two numbers is 30 and one is twice the other. The smaller number is:
Easy- A8
- B10
- C12
- D15
Problems on Numbers question 14 of 19+Show Answer & Explanation
Answer: B. 10
Explanation: x + 2x = 30 → x = 10.
Q15.If 5 is added to a number, the result is 23. The number is:
Easy- A16
- B17
- C18
- D19
Problems on Numbers question 15 of 19+Show Answer & Explanation
Answer: C. 18
Explanation: x + 5 = 23 → x = 18.
Q16.The sum of three consecutive integers is 42. The middle one is:
Easy- A12
- B13
- C14
- D15
Problems on Numbers question 16 of 19+Show Answer & Explanation
Answer: C. 14
Explanation: The middle integer is the average: 42/3 = 14.
Q17.One-fourth of a number is 15 less than one-third of it. The number is:
Moderate- A120
- B150
- C180
- D200
Problems on Numbers question 17 of 19+Show Answer & Explanation
Answer: C. 180
Explanation: x/3 − x/4 = 15 → x/12 = 15 → x = 180.
Q18.The difference between a two-digit number and the number formed by reversing its digits is 36. The difference between the digits is:
Difficult- A2
- B3
- C4
- D6
Problems on Numbers question 18 of 19+Show Answer & Explanation
Answer: C. 4
Explanation: The difference is always 9(a − b), so 9(a − b) = 36 → a − b = 4.
Q19.Three times a number decreased by 7 equals 26. The number is:
Easy- A9
- B10
- C11
- D12
Problems on Numbers question 19 of 19+Show Answer & Explanation
Answer: C. 11
Explanation: 3x − 7 = 26 → 3x = 33 → x = 11.
Problems on Numbers — Frequently Asked Questions
How do I represent a two-digit number in an equation?+
As 10a + b, where a is the tens digit and b the units digit. Writing it as "ab" and treating it as a product is the most common mistake in this topic.
Why is the change on reversing digits always a multiple of 9?+
Because (10b + a) − (10a + b) = 9(b − a). This instantly narrows down the possible digit differences in exam questions.
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