Aptitude and Reasoning Questions

Q:

A class is 6 meters 24 centimeters in length and 4 meters 32 centimeters in width. Find the least number of square tiles of equal size required to cover the entire floor of the class room ?

A) 115 B) 117
C) 116 D) 114
 
Answer & Explanation Answer: B) 117

Explanation:

Length = 6 m 24 cm = 624 cm
Width = 4 m 32 cm = 432 cm
HCF of 624 and 432 = 48
Number of square tiles required = (624 x 432)/(48 x 48) = 13 x 9 = 117.

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Q:

A number is selected at random from the numbers 1 to 30. What is the probability that it is divisible by either 3 or 7 ?

A) 1/30 B) 2/30
C) 1/25 D) 1/2
 
Answer & Explanation Answer: A) 1/30

Explanation:

Let A be event of selecting a number divisible by 3. B be the event of selecting a number divisible by 7.

  Proability tutorial

 A = { 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 }, so n(A)=10
 B = { 7, 14, 21, 28 }, n(B)= 4 

Probability problems 

Since A and B are not mutually exclusive So :

Probability addition rule

Probability problems

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Q:

12 boys decided to constribute Rs. 750 each to an Orphange. Suddenly few of them boys dropped out and consequently the rest had to pay Rs. 150 more. Then the number of boys who dropped out?

A) 4 B) 6
C) 2 D) 3
 
Answer & Explanation Answer: C) 2

Explanation:

Total money decided to contribute = 750 x 12 = 9000

Let 'b' boys dropped

The rest paid 150/- more

=> (12 - b) x 900 = 9000

=> b = 2

Hence, the number of boys who dropped out is 2.

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Q:

While travelling in a train, you observe some college students pulling the alarm chain simply to get down at their desired point. You would :

A) with the help of some passengers, check them from doing so B) let them pull the chain but check them from detraining.
C) inform the guard of the train as soon as it stops. D) keep quiet and do nothing.
 
Answer & Explanation Answer: A) with the help of some passengers, check them from doing so

Explanation:

 

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Q:

How many ways are there to deal a five-card hand consisting of three eight's and two sevens?

A) 36 B) 72
C) 24 D) 16
 
Answer & Explanation Answer: C) 24

Explanation:

If a card hand that consists of four Queens and an Ace is rearranged, nothing has changed.

 

The hand still contains four Queens and an Ace. Thus, use the combination formula for problems with cards.

 

We have 4 eights and 4 sevens.

We want 3 eights and 2 sevens.

C(have 4 eights, want 3 eights) x C(have 4 sevens, want 2 sevens) 

C(4,3) x C(4,2) = 24

 

Therefore there are 24 different ways in which to deal the desired hand.

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Q:

At a game of billiards, A can give B 20 points in 60 and A can give C  15 points in 60. How many points can C give B in a game of 90 ?

A) 9 points B) 10 points
C) 11 points D) 8 points
 
Answer & Explanation Answer: B) 10 points

Explanation:

a:b = 60:40
a:c = 60:45
c/a x a/b = 45/60 x 60/40 = 45/40 = 90/80
So C gives B => 10 points.

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Q:

A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?

A) 2.91 m B) 3 m
C) 5.82 m D) None of these
 
Answer & Explanation Answer: B) 3 m

Explanation:

Area of the park = (60 x 40) = 2400 sq.m  

Area of the lawn = 2109  sq.m 

Area of the crossroads = (2400 - 2109) = 291 sq.m   

 

Let the width of the road be x metres. Then,   

60x + 40x - (x * x) = 291  

=>(x * x) - 100x + 291 = 0    

=>(x - 97)(x - 3) = 0  

=>x=3

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Q:

The probabilities that drivers A, B and C will drive home safely after consuming liquor are 2 / 5, 3 / 7 and 3 / 4, respectively. What is the probability that they will drive home safely after consuming liquor ?

A) 3/70 B) 4/70
C) 9/70 D) 1/50
 
Answer & Explanation Answer: C) 9/70

Explanation:

Let A be the event of driver A drive safely after consuming liquor. 

 

Let B be the event of driver B drive safely after consuming liquor. 

 

Let C be the event of driver C drive safely after consuming liquor. 

 

P(A)=2/5,P(B)=3/7,P(C)=3/4

 

The events A, B and C are independent . Therefore,

 

PABC=P(A)P(B)P(C)=25*37*34=970

 

Therefore, The probability that all the drivers will drive home safely after consuming liquor is 9/70

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