Arithmetic Reasoning - General Inteligence & Reasoning MCQ Questions and Answers

61

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

A) 18 B) 22 C) 42 D) 43 E) None of these

Discuss

Answer & Solution

Answer: Option D

Solution:

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.

62

Find the number which when added to itself 13 times, gives 112.

A) 7 B) 8 C) 9 D) 11 E) None of these

Discuss

Answer & Solution

Answer: Option B

Solution:

Let the number be x. Then, x + 13x = 112 ⇔ 14x = 112 ⇔ x = 8.

63

Aruna cut a cake into two halves and cuts one half into smaller pieces of equal size. Each of the small pieces is twenty grams in weight. If she has seven pieces of the cake in all with her, how heavy was the original cake ?

A) 120 grams B) 140 grams C) 240 grams D) 280 grams E) None of these

Discuss

Answer & Solution

Answer: Option C

Solution:

The seven pieces consist of 6 smaller equal pieces and one half cake piece.
Weight of each small piece = 20 g.
So, total weight of the cake = [2 x (20 x6)]g= 240 g.

64

A total of 324 coins of 20 paise and 25 paise make a sum of Rs. 71. The number of 25-paise coins is

A) 120 B) 124 C) 144 D) 200

Discuss

Answer & Solution

Answer: Option B

Solution:

Let the number of 20-paise coins be x. Then, number of 25-paise coins = (324 - x).
Therefore 0.20 x x + 0.25 (324 - x) = 71 ⇔ 20x + 25 (324 - x) = 7100
⇔ 5x= 1000 ⇔ x = 200. Hence, number of 25-paise coins = (324 - x) - 124.

65

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 ?

A) 4 B) 5 C) 6 D) 7

Discuss

Answer & Solution

Answer: Option C

Solution:

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.

66

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?

A) Rs. 236 B) Rs. 240 C) Rs. 248 D) Rs. 252

Discuss

Answer & Solution

Answer: Option B

Solution:

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.

67

If readymade shirts need alterations 2 out of 3 in sleeves, 3 out of 4 in collar and 4 out of 5 in the body, how many alterations will be required for 60 shirts ?

A) 88 B) 123 C) 133 D) 143

Discuss

Answer & Solution

Answer: Option C

Solution:

68

At the end of a business conference the ten people present all shake hands with each other once. How many handshakes will there be altogether ?

A) 20 B) 45 C) 55 D) 90

Discuss

Answer & Solution

Answer: Option B

Solution:

Clearly, total number of handshakes = (9+ 8 + 7 + 6 + 5 + 4 + 3 + 2+1) = 45.

69

After distributing the sweets equally among 25 children, 8 sweets remain. Had the number of children been 28, 22 sweets would have been left after equal distribution. What was the total number of sweets ?

A) 328 B) 348 C) 358 D) Data inadequate

Discuss

Answer & Solution

Answer: Option C

Solution:

Let the total number of sweets be (25x + 8).
Then, (25x + 8) - 22 is divisible by 28
⇔ (25x - 14) is divisible by 28 ⇔ 28x - (3x + 14) is divisible by 28
⇔ (3x + 14) is divisible by 28 ⇔ x = 14.
Therefore Total number of sweets = (25 x 14 + 8) = 358.

70

A group of 1200 persons consisting of captains and soldiers is travelling in a train. For every 15 soldiers there is one captain. The number of captains in the group is

A) 85 B) 80 C) 75 D) 70

Discuss

Answer & Solution

Answer: Option C

Solution:

Clearly, out of every 16 persons, there is one captain. So, number of captains (1200/16) = 75.