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- Question
Find the number which when added to itself 13 times, gives 112.
Options- A. 7
- B. 8
- C. 9
- D. 11
- Correct Answer
- 8
ExplanationLet the number be x. Then, x + 13x = 112 ⟺ 14x = 112 ⟺ x = 8.
Arithmetic Reasoning problems
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- 1. David gets on the elevator at the 11th floor of a building and rides up at the rate of 57 floors per minute. At the same time, Albert gets on an elevator at the 51st floor of the same building and rides down at the rate of 63 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross?
Options- A. 19
- B. 28
- C. 30
- D. 37 Discuss
Correct Answer: 30
Explanation:
- 2. A printer numbers the pages of a book starting with 1 and uses 3189 digits in all. How many pages does the book have?
Options- A. 1000
- B. 1074
- C. 1075
- D. 1080 Discuss
Correct Answer: 1074
Explanation:
No. of digits in 1-digit page nos. = 1x9 = 9.No. of digits in 2-digit page nos. = 2 x 90 = 180.
No. of digits in 3-digit page nos. = 3 x 900 = 2700.
No. of digits in 4-digit page nos. = 3189 - (9 + 180 + 2700) = 3189 - 2889 = 300.
Therefore No. of pages with 4-digit page nos. = (300/4) = 75.
Hence, total number of pages = (999 + 75) = 1074.
- 3. Mr. X, a mathematician, defines a number as 'connected with 6 if it is divisible by 6 or if the sum of its digits is 6, or if 6 is one of the digits of the number. Other numbers are all 'not connected with 6'. As per this definition, the number of integers from 1 to 60 (both inclusive) which are not connected with 6 is
Options- A. 18
- B. 22
- C. 42
- D. 43 Discuss
Correct Answer: 43
Explanation:
Numbers from 1 to 60, which are divisible by 6 are : 6,12,18, 24, 30, 36,42, 48, 54, 60.There are 10 such numbers.
Numbers from 1 to 60, the sum of whose digits is 6 are : 6, 15, 24, 33, 42, 51, 60.
There are 7 such numbers of which 4 are common to the above ones. So, there are 3such uncommon numbers.
Numbers from 1 to 60, which have 6 as one of the digits are 6, 16, 26, 36, 46, 56, 60.
Clearly, there are 4 such uncommon numbers.
So, numbers 'not connected with 6' = 60 - (10 + 3 + 4) = 43.
- 4. A player holds 13 cards of four suits, of which seven are black and six are red. There are twice as many diamonds as spades and twice as many hearts as diamonds. How many clubs does he hold?
Options- A. 4
- B. 5
- C. 6
- D. 7 Discuss
Correct Answer: 6
Explanation:
Clearly, the black cards are either clubs or spades while the red cards are either diamonds or hearts.Let the number of spades be x. Then, number of clubs = (7 - x).
Number of diamonds = 2 x number of spades = 2x;
Number of hearts = 2 x number of diamonds = 4x.
Total number of cards = x + 2x + 4x + 7 - x = 6x + 7.
Therefore 6x + 7 = 13 ⟺ 6x = 6 ⟺ x - 1.
Hence, number of clubs = (7 - x) = 6.
- 5. A placed three sheets with two carbons to get two extra copies of the original. Then he decided to get more carbon copies and folded the paper in such a way that the upper half of the sheets were on top of the lower half. Then he typed. How many carbon copies did he get?
Options- A. 1
- B. 2
- C. 3
- D. 4 Discuss
Correct Answer: 2
Explanation:
Since the number of carbons is 2, only two copies can be obtained.- 6. The taxi charges in a city comprise of a fixed charge, together with the charge of the distance covered. For a journey of 16 km, the charges paid are Rs. 156 and for a journey of 24 km, the charges paid are Rs. 204. What will a person have to pay for travelling a distance of 30 km?
Options- A. Rs. 236
- B. Rs. 240
- C. Rs. 248
- D. Rs. 252 Discuss
Correct Answer: Rs. 240
Explanation:
Let the fixed charge be Rs. x and variable charge be Rs.y per km. Then,x + 16y = 156 ...(i) and
x + 24y = 204 ...(ii)
Solving (i) and (ii), we get: x = 60, y = 6.
Therefore Cost of travelling 30 km = 60 + 30 y = Rs. (60 + 30 x 6) = Rs. 240.
- 7. Nitin's age was equal to square of some number last year and the following year it would be cube of a number. If again Nitin's age has to be equal to the cube of some number, then for how long he will have to wait?
Options- A. 10 years
- B. 38 years
- C. 39 years
- D. 64 years Discuss
Correct Answer: 38 years
Explanation:
Clearly, we have to first find two numbers whose difference is 2 and of which the smaller one is a perfect square and the bigger one a perfect cube.Such numbers are 25 and 27.
Thus, Nitin is now 26 years old. Since the next perfect cube after 27 is 64,
so required time period = (64 - 26) years = 38 years.
- 8. A student got twice as many sums wrong as he got right. If he attempted 48 sums in all, how many did he solve correctly?
Options- A. 12
- B. 16
- C. 18
- D. 24 Discuss
Correct Answer: 16
Explanation:
Suppose the boy got x sums right and 2x sums wrong.Then, x + 2x = 48 ⟺ 3x = 48 ⟺ x = 16.
- 9. In a family, a couple has a son and a daughter. The age of the father is three times that of his daughter and the age of the son is half of that of his mother. The wife is 9 years younger to her husband and the brother is seven years older than his sister. What is the age of the mother?
Options- A. 40 years
- B. 45 years
- C. 50 years
- D. 60 years Discuss
Correct Answer: 60 years
Explanation:
Let the daughter's age be x years.Then, father's age = (3x) years.
Mother's age = (3x - 9) years; Son's age = (x + 7) years.
So, x + 7 = (3x-9)/2 ⟺ 2x + 14 = 3x - 9 ⟺ x = 23.
Therefore Mother's age = (3X - 9) = (69 - 9) years = 60 years.
- 10. On Children's Day, sweets were to be equally distributed among 175 children in a school. Actually on the Children's Day, 35 children were absent and therefore each child got 4 sweets extra. Total how many sweets were available for distribution?
Options- A. 2400
- B. 2480
- C. 2680
- D. 2800 Discuss
Correct Answer: 2800
Explanation:
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