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- Question
If you write down all the numbers from 1 to 100, then how many times do you write 3?
Options- A. 11
- B. 18
- C. 20
- D. 21
- Correct Answer
- 20
ExplanationClearly, from 1 to 100, there are ten numbers with 3 as the unit's digit- 3, 13, 23, 33, 43, 53, 63, 73, 83, 93; and ten numbers with 3 as the ten's digit - 30, 31, 32, 33, 34, 35, 36, 37, 38, 39.So, required number = 10 + 10 = 20.
Arithmetic Reasoning problems
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- 1. Ayush was born two years after his father's marriage. His mother is five years younger than his father but 20 years older than Ayush who is 10 years old. At what age did the father get married?
Options- A. 23 years
- B. 25 years
- C. 33 years
- D. 35 years Discuss
Correct Answer: 23 years
Explanation:
Ayush's present age = 10 years.His mother's present age = (10 + 20) years = 30 years.
Ayush's father's present age = (30 + 5) years = 35 years.
Ayush's father's age at the time of Ayush's birth = (35 - 10) years = 25 years.
Therefore Ayush's father's age at the time of marriage = (25 - 2) years = 23 years.
- 2. Mac has £ 3 more than Ken, but then Ken wins on the horses and trebles his money, so that he now has £ 2 more than the original amount of money that the two boys had between them. How much money did Mac and Ken have between them before Ken's win?
Options- A. £ 9
- B. £ 11
- C. £ 13
- D. £ 15 Discuss
Correct Answer: £ 13
Explanation:
Let money with Ken = x. Then, money with Mac = x + £ 3.Now, 3x = (x + x + £ 3) + £ 2 ⟺ x = £ 5.
Therefore Total money with Mac and Ken = 2x + £ 3 = £ 13.
- 3. A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has?
Options- A. 45
- B. 60
- C. 75
- D. 90 Discuss
Correct Answer: 90
Explanation:
Let number of notes of each denomination be x.Then, x + 5x + 10x = 480 ⟺ 16x = 480 ⟺ x = 30.
Hence, total number of notes = 3x = 90.
- 4. If 100 cats kill 100 mice in 100 days, then 4 cats would kill 4 mice in how many days?
Options- A. 1 day
- B. 4 days
- C. 40 days
- D. 100 days Discuss
Correct Answer: 100 days
Explanation:
- 5. Two bus tickets from city A to B and three tickets from city A to C cost Rs. 77 but three tickets from city A to B and two tickets from city A to C cost Rs. 73. What are the fares for cities B and C from A?
Options- A. Rs. 4, Rs. 23
- B. Rs. 13, Rs. 17
- C. Rs. 15, Rs. 14
- D. Rs. 17, Rs. 13 Discuss
Correct Answer: Rs. 13, Rs. 17
Explanation:
Let Rs. x be the fare of city B from city A and Rs. y be the fare of city C from city A.Then, 2x + 3y = 77 ...(i) and
3x + 2y = 73 ...(ii)
Multiplying (i) by 3 and (ii) by 2 and subtracting, we get: 5y = 85 or y = 17.
Putting y = 17 in (i), we get: x = 13.
- 6. In three coloured boxes - Red, Green and Blue, 108 balls are placed. There are twice as many balls in the green and red boxes combined as there are in the blue box and twice as many in the blue box as there are in the red box. How many balls are there in the green box?
Options- A. 18
- B. 36
- C. 45
- D. None of these Discuss
Correct Answer: None of these
Explanation:
Let R, G and B represent the number of balls in red, green and blue boxes respectively.Then, .
R + G + B = 108 ...(i),
G + R = 2B ...(ii)
B = 2R ...(iii)
From (ii) and (iii), we have G + R = 2x 2R = 4R or G = 3R.
Putting G = 3R and B = 2R in (i), we get:
R + 3R + 2R = 108 ⟺ 6R = 108 ⟺ R = 18.
Therefore Number of balls in green box = G = 3R = (3 x 18) = 54.
- 7. A motorist knows four different routes from Bristol to Birmingham. From Birmingham to Sheffield he knows three different routes and from Sheffield to Carlisle he knows two different routes. How many routes does he know from Bristol to Carlisle?
Options- A. 4
- B. 8
- C. 12
- D. 24 Discuss
Correct Answer: 24
Explanation:
Total number of routes from Bristol to Carlisle = (4 x 3 x 2) = 24.- 8. A is 3 years older to B and 3 years younger to C, while B and D are twins. How many years older is C to D?
Options- A. 2
- B. 3
- C. 6
- D. 12 Discuss
Correct Answer: 6
Explanation:
Since B and D are twins, so B = D.Now, A = B + 3 and A = C - 3.
Thus, B + 3 = C - 3 ⟺ D + 3 = C-3 ⟺ C - D = 6.
- 9. There are deer and peacocks in a zoo. By counting heads they are 80. The number of their legs is 200. How many peacocks are there?
Options- A. 20
- B. 30
- C. 50
- D. 60 Discuss
Correct Answer: 60
Explanation:
Let x and y be the number of deer and peacocks in the zoo respectively. Then,x + y = 80 ...(i) and
4x + 2y = 200 or 2x + y = 100 ...(ii)
Solving (i) and (ii), we get) x = 20, y = 60.
- 10. A, B, C, D and E play a game of cards. A says to B, "If you give me 3 cards, you will have as many as I have at this moment while if D takes 5 cards from you, he will have as many as E has." A and C together have twice as many cards as E has. B and D together also have the same number of cards as A and C taken together. If together they have 150 cards, how many cards has C got?
Options- A. 28
- B. 29
- C. 31
- D. 35 Discuss
Correct Answer: 28
Explanation:
Clearly, we have :A = B - 3 ...(i)
D + 5 = E ...(ii)
A+C = 2E ...(iii)
B + D = A+C = 2E ...(iv)
A+B + C + D + E=150 ...(v)
From (iii), (iv) and (v), we get: 5E = 150 or E = 30.
Putting E = 30 in (ii), we get: D = 25.
Putting E = 30 and D = 25 in (iv), we get: B = 35.
Putting B = 35 in (i), we get: A = 32.
Putting A = 32 and E = 30 in (iii), we get: C = 28.
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