# IQ Test, Mental Aptitude, Logical Reasoning & Mathematical Tests

### Test Report

#### Question No 1

9 excavators working 10 hours a day remove 2500 cubic feet of earth in 3 days. How many excavators working 6 hours a day are required to remove 5000 cubic feet of earth in 2 days?

Solution!
Let x excavators are required.
As excavators are inversely proportional to hours and days and directly proportional to work progress so
x/9 = (10/6)*(5000/2500)*(3/2)
x = 45

Hence 45 excavators are required to remove 5000 cubic feet of earth..

#### Question No 2

Choose the word which is different from the rest.

Solution!
Swan is the only water bird in the group..

#### Question No 3

The calendar for the year 2007 will be the same for the year ...

Solution!
Count the number of odd days from the year 2007 onwards to get the sum equal to 0 odd day.

Year 2007 has 1 odd day
2008 has 2 odd day
2009 has 1 odd day
2010 has 1 odd day
2011 has 1 odd day
2012 has 2 odd day
2013 has 1 odd day
2014 has 1 odd day
2015 has 1 odd day
2016 has 2 odd day
2017 has 1 odd day

Sum = 14 odd days = 0 odd days.

Hence, Calendar for the year 2018 will be the same as for the year 2007..

#### Question No 4

A said to B, My mother gave birth to a child, who was neither my brother nor my sister. Can you guess who was the child?

Solution!
A's mother gave birth to A and A has no brother and no sister.
He is just talking about himself..

#### Question No 5

A train travelling at he speed of 72km/h can cross a platform in 17 seconds. If length of the train is 180 meters, what is the length of the platform?

Solution!
Speed of train = v = 72Km/h = 72*(5/18) = 20m/s

Time = t = 17s
Length of the train = L1 = 180m
Length of the platform = L2 = ?

t = (L1+L2)/v
By putting values
17 = (180+L2)/20
340-180 = L2
L2 = 160m

Hence length of the platform is 160m..

#### Question No 6

Which of the following is an integer that has a remainder of 1 when it is divided by 4,5 and 6?

Solution!
Least common multiple of 4,5 and 6 is 60 so 61 is an integer that has a remainder of 1 when it is divided by 4,5 and 6..

#### Question No 7

What is the largest 4 digit number exactly divisible by 88?

Solution!
No answer description available for this question..

#### Question No 8

What is the angle between the hands of a clock at 2:30?

Solution!
Hour hand is nearly at 2
Minute hand is at 6

Angle between 2 and 6 is 120 degree.

Hour hand move 1/2 degree in one minute.

In 30 Minutes hour hand will move 1/2 * 30 = 15 degree

Hence, Angle between hands is 120 - 15 = 105 degree.

#### Question No 9

Tina is twice as old as David. 15 years ago, Tina's age was 5 times the age of David. What is the present age of Tina?

Solution!
Let David's age is x and Tina's age is y.

Given that
y = 2x
y-2x = 0 ...(1)

and also given that
y-15 = 5(x-15)
y-15 = 5x-75
y-5x = -60 ...(2)

By simultaneously solving equation(1) and equation(2)
y = 40

Hence Tina's present age is 40 years..

#### Question No 11

A man can row 1 km upstream in 20 minutes, and downstream in 15 minutes. What is the speed of the current?

Solution!
20 minutes = 20/60 = 1/3 hours
Upstream distance covered in 1/3 hours = 1 Km
Upstream distance covered in 1 hour = 1/(1/3) = 3 Km
Upstream speed = y = 3 Km/h

Now
15 minutes = 15/60 = 1/4 hours
Downstream distance covered in 1/4 hours = 1 Km
Downstream distance covered in 1 hour = 1/(1/4) = 4 Km
Downstream speed = 4 Km/h

speed of water = (1/2)*(4-3) = 1/2 = 0.5 Km/h.

#### Question No 12

230 meters long train crosses a man sitting on the platform in 46 seconds. What is the speed of the train?

Solution!
Length of the train = L = 230m
Time = t = 46s
Speed = v = ?

V = L/t
By putting values
v = 230/46 = 5m/s

Hence speed of the train is 5m/s..

#### Question No 13

APOCRYPHAL is to CERTAINTY as CHAOTIC is to..

Solution!
No answer description available for this question..

#### Question No 14

How many times in a day, the hands of a clock are straight?

Solution!
In 12 hours, the hands coincide or are in opposite direction 22 times.

So, In 24 hours, the hands coincide or are in opposite direction 44 times a day..

#### Question No 15

0 , 1 , 4 , 9 , 16 , 25 , 36 , 49 , ?

Solution!
Add 1, 3, 5, 7, etc..

#### Question No 16

2664/12/6=?

Solution!
(2664/12) * (1/6) = 37.

#### Question No 17

Ten years ago, P was half of Q in age. If the ratio of their present ages is 3/4, what will be the total of their present ages?

Solution!
Let the present age of P and Q be 3x and 4x respectively.

Ten years ago, P was half of Q in age.

(3x - 10) = 1/2 * (4x - 10)
6x - 20 = 4x - 10
2x = 10
x = 5

total of their present ages
= 3x + 4x = 7x = 7 * 5
= 35.

#### Question No 18

If m is an even integer and 3m < 48 and 2m > 24 then m = ?

Solution!
3*14 = 42 (lesser than 48)
and
2*14 = 28 (greater than 24)..

#### Question No 19

0 , 100 , 6 , 94 , 12 , 88 , 18 , 82 , ? , ?

Solution!
There are two sequences interwoven.

Add 6 starting at 0 and deduct 6 starting at 100..

#### Question No 20

Choose the word which is different from the rest.

Solution!
All except Mathura are cities situated on the banks of Ganga river..

#### Question No 21

South is to North-West as West is to?

Solution!
As North-West is 135 degree clockwise from South in the same were North-East is 135 degree clockwise from the West..

#### Question No 22

Choose the word which is different from the rest.

Solution!
All except Groundnut are spices..

#### Question No 23

A and B can do a job together in 7 days. A is 7/4 times as efficient as B.The same job can be done by A alone in

Solution!
(A's 1 day's work) / (B's 1 day's work) = 7/4

Let A's and B's 1 day's work be 7x and 4x respectively.

Then,
7x + 4x = 1/7
11x = 1/7
x = 1/77

Hence, A's 1 day's work = (1/77 * 7) = 1/11.

#### Question No 24

100 , 96.75 , 93.5 , 90.25 , 87 , ?

Solution!
Deduct 3.25 each time..

#### Question No 25

Pointing to a boy in the photograph Reena said, "He is the only son of the only child of my grandfather." How Reena is related to that boy?

Solution!
The boy in the photograph is the only son of Reena's grandfather's only son; i.e., the boy is the only son of Reena's father.

Hence, the boy is the brother of Reena or Reena is the sister of the boy..

#### Question No 26

If P + Q means P is the brother of Q; P x Q means P is the wife of Q and P % Q means P is the daughter of Q then which of the following means D is the uncle of A?

Solution!
No answer description available for this question..

#### Question No 27

The angle between the minute hand and the hour hand of a clock when the time is 4:20, is ?

Solution!
Angle traced by hour hand in 13/3 hrs = (360/12 * 13/3) = 130 degree

Angle traced by minute hand in 20 min = (360/60 * 20) = 120 degree

So, required angle = 130 - 120 = 10 degree.

#### Question No 28

The sum of ages of 5 children born at the intervals of 3 years each is 50 years. Find out the age of the youngest child?

Solution!
Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.

Then,
x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50
5x = 20
x = 4

Hence, Age of the youngest child = x = 4 years.

#### Question No 29

paw is to cat as hoof is to..

Solution!
As cat has Paw similarly Horse has Hoof..

#### Question No 30

Which number is the odd one out, 8, 27, 64, 100, 125, 216, 343