Tips to approach a direction sense test

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Hey guys,
Thanks for your views and comments. Today we will pick one more interesting as well as important topic of reasoning i.e directions.

Many students feel that this is very complex as they find that this topic includes lots of diagrams but let me know one thing , do all of you know that sun rises from the east and sets in west?

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Kashmir is in north and kanyakumari in south? West bengal is in east and Gujarat in west ? Do you agree with me on these points, look at the map of India and check it once and if you already know these things 50% of the job is done and for the rest 50% scroll down.

Directions questions asked in the exam are based on two principles

  1. Distance
  2. Direction

You might be asked to calculate either of this. The first thing you need to do is either visualize or draw a basic map.

map

 

 

 

 

 

 

Let’s take a case :

A. If I move 4 km towards east and then I travel 3 km towards north. What is my distance from the starting point?

Soln– First thing that you should keep in your mind is that your starting point is always the center of the direction map.

Now draw the map according to the directions.

b

Ohhh !! This is a right angled triangle and here I am supposed to calculate nothing bur hypotenuse and for that Mr. Pythagoras has already given a theorem, let us use it to find the answer.

Pythagoras says:  Hypotenuse2  =  Perpendicular2 +Base2
H2 = 32 + 42
= 9+16 

=25
Hence , H = 5 km.

So, I am 5 Km away from my starting point. Simple ??

B. What if you are asked to find the direction, Let suppose If I move 4 km towards east and then I travel 3 Km towards north. In which direction I am from the starting point ?

Soln Draw the map and try to superpose the direction map like this

 

c

Now, can you tell me where am I ? I am in North east direction from my starting point.

C.What if I walked 3 km towards south and then 4 km towards west?  In which direction I am from starting point now ?

d

Ohhh!! I reached south west. Now are you getting idea how to calculate distance and analyze directions ??

Let’s solve some miscellaneous cases.
D.  A person starts from position A. He goes towards the east and then takes a right turn .Again the person takes a left turn and moves and then again he move 45 degree right. In which direction he is from the starting position?

Soln Whenever such question comes consider yourself in place of the person mentioned and enjoy walking.

e

So, the person is in south east direction of the starting point. Look at the way I am drawing the maps , follow the same and you will never make a mistake in solving these questions. Always draw a reference map of NSEW  as drawn above so that you are clear with the direction.

E.  A person P is standing at a point , another person Q is standing in the north of P. Q’s friend R is in right of Q and P’s friend S is standing left of P.In which direction S is standing with respect to R.

f

Can you figure out the answer now ? S is in south west direction w.r.t R.

And in which direction is R with respect to S ?

g

R is in North east direction w.r.t S .

F. I start from my house and go straight and come at a cross road. The road which is coming from opposite direction ends at a hospital. When I walk from my house and turn right , there is a park on that road and opposite to park there is a school.What would be the direction of my house from the school.

Soln–  When such case come where you are allowed to walk straight and no particular direction is given, you can assume any direction. Let’s suppose I am walking towards EAST.

h

So, My house is in south west direction from the school.Many students face difficulties to determine the direction even after successfully drawing the diagram.

Remember this point.
Can you see I have drawn a reference map above. Whenever you are asked questions  like -in which direction is my house from school, consider school at the middle point of you reference map and then look at the superpose figure, you will find that your house is in south west direction. This is very simple.

What would be direction of school from my house ?

Now in this case just consider your house at the middle point of the reference map, now can you determine direction of the school ?

i

School is in North east direction from my house.

SUNRISE AND SUNSET

Always remember these two points:
1. Sun rises in the EAST then it shadow will be in the WEST.
2. Sun sets in the WEST then it shadow will be in the EAST.

You can be asked questions related to these such as:

G. Ranbir kapoor went for a shooting and is facing towards the NORTH. At sunrise where will his shadow be? And if he is facing SOUTH. Then where will his shadow be?

j

If Ranbir is facing north, his shadow will be in west or to his left.

k

And If he is facing south his shadow will be in west or towards his right.

I hope you guys enjoyed reading this post, There are few points you need to remember before approaching to directions problem.

  1. Direction : N S E W.
  2. Left –Right.
  3. Straight / opposite.
  4. Sunrise and sunset.

Stay tuned, leave back your comments and till then Eat Pray Calculate Analyze Repeat.

(Written by Yeshu)

 

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Missing Series

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Hi Guys,

Hope you liked our last post on different approaches to calculate averages, today we will be discussing about missing series. A very clear instruction- To be proficient in solving series you have to practice a lot because series can be made by using any of the mathematical operation known so you need to practice as much type of questions as you can. But today we will discuss certain questions that are frequently asked in exams also I will provide you with some tips which will help you determine the missing number in series.

Let us take a question:

A.   9   11   16   26   ?   69.    

How do i solve this ? Look at the series above. Numbers are increasing from left to right so suddenly only two things comes in mind either they are getting added by certain number or multiplied. Now, which one of the two should I choose ‘multiplication or addition’. Just look at the series again, all the numbers are very close to each other there is no such two numbers which has a big difference so this strictly tells us that addition must be going on between them. Let us see.

9+2=11
11+5=16
16+10=26
26+17=43
43+26=69

So. basically an addition of 2 , 5 , 10, 17 , 26 took place where each of these numbers had a difference of 3 , 5 , 7 , 9 . (Common difference of 2).

So, the missing number was 43

Look at this series:

B.  3   4   10   33   136   ?

In this case you can see that 33 is preceded by 10 and immediately followed by 136 which simply says that this must be a case of multiplication, you cannot obtain 136 by adding certain number to 33 if you have obtained 33 by adding certain number to 10. so this is only possible in case you are multiplying. Let us see:

3*1 + 1 = 4
4*2 + 2 = 10
10*3 + 3= 33
33*4 + 4 = 136

You have the series now, thus the missing number would be 136*5 + 5 = 685

C.  6   3    3    6    24    ?

What could be the answer in this case ? here we have a decreasing – increasing series of numbers. But can you notice one thing- 6 is followed by 3 and how can you get that ?

Either you do 6-3=3 but no, I can see that series increases further so subtraction will not work or you divide 6/2=3 but again you can see that 24 is preceded by 6 which means there must be multiplication going on.

But did you notice one thing in above line I wrote 6/2=3 , which also means 6*0.5=3 . Let us see if this works.

6*0.5=3
3*1=3
3*2=6
6*4=24
24*8=192

So the numbers were getting multiplied by 0.5, 1, 2,  4,  8 and each of them are getting multiplied by (*2).

Let us take another case :

D.  3   4   12   16    48    ?

Can you identify which type of series is this ? look at the numbers.

3*4=12
4*4=16
12*4=48
16*4=64

Did you notice there was a relation between alternate numbers and the mathematical operation used was multiplication (*4). Such series are known as Alternate series. 

Try this out :

E.  2   3    4    9    8    27   ?

2*2=4
3*3=9
4*2=8
9*3=27
8*2=16

Did you notice? Here the consecutive elements of series don’t have relations, but the alternate elements have a relation.

2-4-8- these elements have a relationship- they are elements of table of 2.

3-9-27- these elements have relationship- they are elements of table of 3.

This was also an alternate series but here the multiplying factor wasn’t common unlike the previous questions.You will have to keep a check as your multiplying factors may also appear in series.

So these were certain tips that you can keep in mind while solving missing series and I am sure this will save your time and help you obtain missing numbers.

It’s Practice time, Try yourself :

1) 5, 25, 7,______, 9, 19

a) 23
b) 22
c) 25
d) 32
e) None of The Above

 2) 62, 64,______, 32, 14,16

a) 26
b) 28
c) 30
d) 32
e) None of The Above

3) 100, 50, 52, 26, 28,______

a) 30
b) 32
c) 14
d) 16
e) None of The Above

4) 980, 392, 156.8,______, 25.088, 10.0352

a) 62.72
b) 63.85
c) 65.04
d) 60.28
e) None of The Above

5)113, 225, 449,_____, 1793

a) 789
b) 786
c) 897
d) 987
e) None of The Above

Answers:

  1. Solution (Option B)
  2. Solution (Option C)
  3. Solution (Option C)
  4. Solution (Option A)
  5. Solution (Option C)

Were you able to get all your answers correct ? Here are few points that will help you approach to an unknown question.

  1. When ever you find a series, look for relations between two numbers, you can find relations between consecutive numbers, alternate numbers, or numbers at a gap of two, three etc.
  2. Once you identify these two numbers, try to recognize which mathematical operation has been done between the two, above mentioned examples will help you find the trick to do so.
  3. Just follow the series to reach out to your answer.

 

(Written by Yeshu)