## Arithmetic Reasoning Questions and Answers Part-6

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 ?
a) 19
b) 28
c) 30
d) 37

Explanation:

2. I have a few sweets to be distributed. If I keep 2, 3 or 4 in a pack, I am left with one sweet. If I keep 5 in a pack, I am left with none. What is the minimum number of sweets I have to pack and distribute ?
a) 25
b) 37
c) 54
d) 65

Explanation: Clearly, the required number would be such that it leaves a remainder of 1 when divided by 2, 3 or 4 and no remainder when divided by 5. Such a number is 25.

3. If a clock takes seven seconds to strike seven, how long will it take to strike ten ?
a) 7 seconds
b) 9 seconds
c) 10 seconds
d) None of these

Explanation:

4. In a group of cows and hens, the number of legs are 14 more than twice the number of heads. The number of cows is
a) 5
b) 7
c) 10
d) 12

Explanation: Let the number of cows be x and the number of hens be y.
Then, 4x + 2y = 2 (x + y) + 14 ⇔ 4x + 2y = 2x + 2y + 14 ⇔ 2x = 14 ⇔ x = 7.

5. A father tells his son, "I was of your present age when you were born". If the father is 36 now, how old was the boy five years back ?
a) 13
b) 15
c) 17
d) 20

Explanation: Let the father's age be x and the son's age be y.
Then, x - y = y or x = 2y,
Now, x = 36. So, 2y = 36 or y = 18.
Therefore Son's present age = 18 years.
So, son's age 5 years ago = 13 years.

6. A pineapple costs Rs. 7 each. A watermelon costs Rs. 5 each. X spends Rs. 38 on these fruits. The number of pineapples purchased is
a) 2
b) 3
c) 4

Explanation:

7. A woman says, "If you reverse my own age, the figures represent my husband's age. He is, of course, senior to me and the difference between our ages is one-eleventh of their sum." The woman's age is
a) 23 years
b) 34 years
c) 45 years
d) None of these

Explanation: Let x and y be the ten's and unit's digits respectively of the numeral denoting the woman's age.
Then, woman's age = (10X + y) years; husband's age = (10y + x) years.
Therefore (10y + x)- (10X + y) = (1/11) (10y + x + 10x + y)
⇔ (9y-9x) = (1/11)(11y + 11x) = (x + y) ⇔ 10x = 8y ⇔ x = (4/5)y
Clearly, y should be a single-digit multiple of 5, which is 5.
So, x = 4, y = 5.
Hence, woman's age = 10x + y = 45 years.

8. A girl counted in the following way on the fingers of her left hand : She started by calling the thumb 1, the index finger 2, middle finger 3, ring finger 4, little finger 5 and then reversed direction calling the ring finger 6, middle finger 7 and so on. She counted upto 1994. She ended counting on which finger ?
a) Thumb
b) Index finger
c) Middle finger
d) Ring finger

Explanation: Clearly, while counting, the numbers associated to the thumb will be : 1, 9,17, 25,.....
i.e. numbers of the form (8n + 1).
Since 1994 = 249 x 8 + 2, so 1993 shall correspond to the thumb and 1994 to the index finger.

9. 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 ?
a) 45
b) 60
c) 75
d) 90