Mensuration Tricks - 2

Mensuration Tricks - 2

This is a famous question. Just remember whenever you are forming a circle and then a square,

the side of that square is given by, a = 1.6*r (approx.), where r = radius of the circle

I have written approx. because the actual formula is 1.57*r, but it will make the calculations a bit lengthy. So, just find 1.6*r and the answer will be little less than that. Like here

Side = 1.6*84 = 134.4, so the answer is 132 cm

Answer: (A)

When the wire is bent in the form of a circle of radius 84cm, that means the circumference (or the length of the wire) of the circle is 2*p*84 = 44*12 cm

Now this wire forms a square of (let�s say) side �a�

Then, 4a (perimeter of the square) = 44*12

Hence a = 132 cm

If the given rectangular sheet of paper (length =l, breadth = b) is rolled across its length to form a cylinder, having a height b, then volume of cylinder = (l*l*b)/4p

If rolled across its breadth, then = (b*b*l)/4p

In this question the sheet is rolled along its length, so volume = (l*l*b)/4p = 12*12*5/(4* p)

Volume = 180/ p cm³

Answer: (C)

In this question, the ratio of surface areas is given and they are asking the ratio of volumes. The word �sphere� is useless here. In such questions, just imagine area as A² and volume as A³. Now A³ is given and you have to find A³. How will you do it? Simple, first take the square-root of A² to convert it into A, and then take the cube of A to find A³.

So for solving this question, we just have to take the square-root of 4:9. The ratio will become 2:3. Then take the cube of 2:3. Hence the answer is 8:27

Answer: (C)

Here again ratio of areas is given, that means A² is given, and we have to find A. So 4:9 will become 2:3

Answer: (A)

Diameter and perimeter are directly proportional, P = D*p, where P is the perimeter and D is the diameter.

Hence a 75% increase in diameter means a 75% increase in perimeter

 Answer: (D)

The area of base and the volume of a cone are directly proportional V = A * h/3, where V = volume and h = height of the cone

Hence a 100% increase in the area of the base would mean a 100% increase in the volume

Answer: (B)

A is increased by 50% hence A² (or surface area) will increase by (1.5*1.5 � 1)*100 % = 125%

Note: Similarly A³ (or volume) will increase by (1.5*1.5*1.5 � 1)*100 % = 237.5%

Answer: (A)

Where ever the word �melting� is used in mensuration, it means only one thing � equate the volume

The volume of the rectangular block = l*b*h = 21*77*24 cm³

Now this volume will be equal to the volume of the sphere formed after melting the block

Volume of sphere = (4/3) * p * r³= 21*77*24

Hence, r = 21 cm

Answer: (A)

The water rises by 5.6 cm. Take this 5.6 cm as the height of the cylindrical beaker and find its volume.

Volume of a cylinder = p*r*r*h = p * (7/2) * (7/2) * 5.6

Volume of the marbles (spherical in shape) = (4/3) * p * r³ = (4/3) * p * 0.7 * 0.7 * 0.7

No. of marbles dropped = Volume of beaker/Volume of a marble = 150

Answer: (B)

Let the radius of the big sphere be R.

Volume of a cone = (1/3) * p * R³ (since radius and volume are same as the radius of the sphere)

Let the radius of the smaller sphere = r

Then volume of cone = volume of smaller sphere

(1/3) * p * R³ = (4/3) * p * r³

r : R = 1 : 2^2/3

Surface area of smaller sphere(s) = 4 * p * r²

Surface area of larger sphere(S) = 4 * p * R²

S/s = (r/R)² = 1 : 2^4/3

Answer: (D)

When a cone is hollowed out from a cylinder, we get the above figure

The whole surface area of the remaining solid = Area of A + Area of B + Area of C

A = curved surface area of the cone

B = curved surface area of the cylinder

C = area of the cylindrical base

A = p * r * l, where l = slant height of the cone, which is  or

Hence A = p*3*5 = 15p

B = 2prh = 2p*3*4 = 24p

C = pr² = p*3² = 9p

The whole surface area of the remaining solid = 15p + 24p + 9p = 48p

Answer: (C)

Given, AB = 3 cm, BC = 6 cm and OF = 1 cm

Height of the cone (AC) = v(6^2 - 3^2 ) = 3v3 cm

Triangles ABC and CFO are similar (RHS similarity)

So, OC/BC = OF/AB

OC = 2 cm, therefore CG = 3 cm (OG = 1 cm)

Now, ABC and CEG are similar

GE/AB = CG/AC

So, GE =

Required volume = Volume of cone (CDE) - Volume of Sphere

                                = 3p � (4/3)p

                                = (5/3)p

Answer: (C)

Please check the link for Part-1

• Mensuration Tricks Part-1

If you have any doubt in this article, please drop a comment.

Keep reading :)

[Banking] Machine Input-Output

Machine Input-Output

Machine input-output is a very important topic for banking exams. I will tell you a short-cut that would help you in solving such questions in a single line, instead of writing all the steps.

Q. 1)

Input: mix  12   in   form   35  are  20   with  47  given
Step I: 47   mix  12   in  form   35   20  with   given   are
Step II: 47   35  mix  12   in   20   with  given   are  form
Step III: 47   35   20  mix  12   in  with   are   form  given
Step IV: 47  35  20  12  mix  with  are  form  given  in

Step V: 47  35  20  12  with  are  form  given  in  mix

Step VI: 47  35  20  12  are  form  given  in  mix  with

As per the rules given above, solve the below input

Input: when  11  given  fine  37  provide  zero  90  over  45  is  29  team  89

Solution: 

First try to find the pattern.

In the given question, each step moves the biggest number to the left and the smallest word to the right. So ultimately are the numbers are sorted in the descending order on the left and all the words are sorted in the ascending order on the right.

Once you have deciphered the pattern, write down the input

Input: when  11  given  fine  37  provide  zero  90  over  45  is  29  team  89

Now in the 1st step the biggest number, i.e., "90" will move to the left, while the smallest number, i.e., "fine" will move to the right. Hence strike-through the words "fine" and "90" and write "1R" and "1L" above them, respectively. Like this:

1R means in the 1st step, "fine" will move to the extreme right and 1L means in the first step, "90" will move to the extreme left.

Now, "89" is the next biggest number and "given" is the next smallest word. Hence, strike-through them and write "2L" and "2R" above them, respectively.

Similarly strike-through the rest of the words.

Your input will look something like this-

That's it, you can now solve all the questions, just by looking at the above figure.

Q. 1(a) Which number/word would come on the fourth position(from the left) in step II ?

From our figure we can see that in the 2nd step, the words having the code "1L" and "2L" will move  to the left and the words having the code "1R" and "2R" will move to the right. All the other words/numbers won't change their positions. Hence, step II will look like this: (I am writing the whole step just for the sake of explanation. You can easily imagine the step in your head)

Step II: 90  89  when  11  37  provide  zero  over  45  is  29  team  89  fine  given

So the fourth word from the left is "11"

Q. 1(b) How many step would be needed to complete the arrangement?

The farthest our code reached was 8R. Hence the total number of steps is 8.

Q. 1(c) In step IV, which word would be 8th from the left?

In step IV - 1R, 2R, 3R and 4R would be on the right, while 1L, 2L, 3L and 4L would be on the left. Rest of the words/numbers would remain unchanged.

Step IV: 90  89  45  37  when  11  provide  zero  29  team  fine  given  is  over

So the 8th word from the left is "zero".

Short-cut: You have to count from the left. so just look at the image and imagine 1L, 2L, 3L and 4L on the left and count the leftover words (ignoring 1R, 2R, 3R and 4R because they would be on the extreme right).

5th word = when

6th word = eleven

7th word = provide

8th word = zero

Q. 1(d) Which step number would be the following output?

90  89  45  when  11  37  provide  zero  over  29  team  fine  given  is

You can see that three numbers have been arranged on the left and three numbers have been arranged on the right. So it is the 3rd step.

Let us take another question

Q. 2) Input: gone name 43 39 18 for again 66

Step 1 : 66 gone name 43 39 18 for again
Step 2 : 66 again gone name 43 39 18 for
Step 3 : 66 again 43 gone name 39 18 for
Step 4 : 66 again 43 for gone name 39 18
Step 5 : 66 again 43 for 39 gone name 18
Step 6 : 66 again 43 for 39 gone 18 name

Based on the above rule, sort the below input-

Input: their 19 27 dent are 91 hour zero 31 16 chairs

The pattern is simple: Numbers and words are arranged alternatively, with numbers following descending order and words following ascending order.

After sorting, the input will look like this:

Note few things:

1. I have only written 1L, 2L, etc. and no "R" because the words/numbers are only moving to the left. 1L means in the first step the word coded "1L" will move to the left and "2L" means in the second step, the word coded "2L" will move to the second position from the left.
2. I have not numbered "their" and "zero" because after striking-through 16 (i.e. 9L), you will notice that the words "their" and "zero" are already sorted in the ascending order. So no need to  write 10L over "their" and 11L over "zero". Had the situation been something like this-

          Then you would have written "10L" over "their" and 11L over "zero".

Q. 2(a) Which of the following will be step 4 ?

A.) 91 are 31 their 19 27 dent hour zero 16 chairs
B.) 91 their 19 27 dent are hour zero 31 16 chairs
C.) 91 are 31 chairs their 19 27 dent hour zero 16
D.) 91 are 31 chairs 27 dent 19 their hour zero 16

Look at the solution figure: 

In the fourth step- 1L, 2L, 3L and 4L will move to the left and rest of the words/numbers will remain as it is. So the fourth step will look like this:

91 are 31 chairs their 19 27 dent hour zero 16

Answer: (C)

Q. 2(b) How many steps would be needed to sort the input?

Answer: 9 (because the highest numbering is 9L)

Q. 2(c) Which of the following would be final arrangement ?

A) 91 are their 27 19 dent hour zero 31 16 chairs
B) 91 are 31 chairs 27 dent 19 hour 16 their zero
C) 91 are 31 chairs 27 19 dent hour 16 their zero
D) 91 are 31 chairs 27 dent 19 zero hour 16 their

It's easy. Sort the numbers and words alternatively with numbers following descending order and words following ascending order.

Answer: (B)

I think by now you must have understood this method. Solve some questions to get a hold of it.

If you have any doubt in this article, please drop a comment.

Keep reading :)

[Banking] Coded Inequality

Almost all of you are appearing for Banking exams along side SSC, so I decided to write few important articles on it. This post deals with "Coded-Inequality".

Q. (1) Statement: F < B = A = C > D
          Conclusion: (1) B = C              (2) F > C

You have to find whether the conclusions (1) and (2) are true or false.

How to solve such questions quickly? The answer is "Magic Square"

When you get the rough sheet in the examination hall, immediately draw this magic square. Although after solving more and more questions, soon you would be able to memorize it.

Rules of magic square:

1. Always prefer smaller value:
   
2. Simple and (`) do not have any relation
   
3. "3" is universal

Now let's move to the question

Conclusion 1 (B = C)

The first conclusion is B = C. We know from the magic square that = evaluates to "2". Now, note the positions of B and C in the statement and solve all the signs between them.

Note: There is a typo in the above image. It should be F < B

We know that among two numbers, we choose the smaller one. Hence 2 and 3 evaluate to 2.

The statement as well as the conclusion evaluates to "2". This means that this conclusion is correct.

Conclusion 2 (F > C)

Second conclusion F > C. We know from the magic square that > evaluates to 1. Now, note the positions of F and C in the statement and solve all the signs between them.

You won't be able to solve the statement because the first two symbols do not have a relation between them. So no need to check the rest.

If at any point in the statement you encounter "no relation" between symbols, you can be sure that the conclusion is wrong.

Q. 2)  Statement: F < A = B = C = D

          Conclusion: (1) B > F              (2) A = C

Conclusion 1 (B > F)
Notice that in the statement, the direction is from F to B, but in the conclusion (B > F), the direction is from B to F. Hence to make the directions same, we will write the conclusion as F < B. So it evaluates to 1`.

The statement evaluates to 1` and the conclusion too evaluates to 1`. Hence the conclusion is right.

Conclusion 2 (A = C)
Here the direction is same. So simply, the conclusion evaluates to 2. Now evaluate the statement.

The statement as well as the conclusion evaluates to 2. Hence the conclusion is right.

In the similar manner you can solve all the questions of Coded Inequality quickly. But make sure the question is in the desired format. Notice the below question for instance,

Q.  Statements F % T, T @ J, J # W.

Conclusions 1) J @ F. 2) J # F

Note that:

P is neither smaller than nor equal to Q means P > Q

P is neither greater than nor smaller than Q means P = Q

P is neither greater than nor equal to Q means P < Q

P is not greater than Q means P = Q

First convert the statement in the desired format.

Statement: F = T = J > W

Conclusion: (1) J = F        (2) J > F

Now solve the question with magic square method.

If you have any doubt in this article, please drop a comment.

Keep reading :)

Averages Tricks - 1

Q. 1) The average weight of 4 men is increased by 3 kg when one of them who weighs 120 kg is replaced by another man. What is the weight of the new man?

Weight of new person = Weight of removed person + No. of persons * Increase in Average = 120+3*4
Weight of new person = 132 kg

Q. 2) The average marks obtained by 120 candidates in a certain examination is 35. If the average marks of passing candidates is 39 and that of the failed candidates is 15, what is the number of candidates who passed the exam?

Such questions are best dealt with allegation formula:
Mean value = 35, Dearer value = 39 and Cheaper = 15
Failed students : Passed students = (Dearer - Mean) : (Mean - Cheaper) = 39 - 35 : 35 - 15 = 4 : 20
No. of students who passed = (5/6) * 120 = 100

Q. 3)

Correct Average = Incorrect average + (Correct value - Incorrect value)/Total observations

Correct Average = 35 + (85 - 45)/20 = 37

Answer: (D)

Q. 4)

Take x = 1

Then A = (1 + 1)/2 = 1

Average of x^3 + 1/x^3 = (1 + 1)/2 = 1

Now put A = 1 in all the four options and check which one is giving '1' as the output

Answer: (D)

Q. 5)

For consecutive numbers:
If the number of terms is odd (e.g. A, B, C), then their average is the middle term(i.e. B).
If the number of terms is even(e.g. A, B, C, D) then their average is (B+C)/2
So here, the average of eight consecutive even numbers = (5th term + 4th term)/2
Given, (5th term + 4th term)/2 = 93
5th term + 4th term = 186
We know, 5th term - 4th term = 2
Adding the equations, we get 5th term = 94
Hence 8th term = 5th term + 2 + 2 + 2 = 100
Answer: (C)

Q. 6)

Average = (8*3 + 20*2 + 26*m + 29*1)/(3 + 2 + m + 1)
17 = (93 + 26m)/(6 + m)
102 + 17m = 93 + 26m
m = 1
Answer: (A)

Q. 7)

Given, (3a + 4b)/2 > 50

3a + 4b > 100

5a > 100  [Since a = 2b]

a > 20

Hence the smallest value of a is 21

Answer: (D)

Q. 8)

Average of six numbers a,b,c,d,e,f = (Average of a,b + Average of c,d + Average of e,f)/3

3.95*3 = 3.4 + 3.85 + x

x = 4.6

Answer: (C)

Q. 9) The average of 11 numbers is 50. The average of first six numbers is 49, and that of last six is 52. Find the sixth result.
This is a common CGL question and a short-cut to solve it is:
Sixth result = 50 + 6{(52 - 50) + (49 - 50)} = 50 + 6(2 - 1) = 56
Answer: 56


Q. 10)

Answer: (B)

Q.11)

If you have any doubt in this article, please drop a comment...
Keep reading :)

Profit-Loss Tricks - 2

Profit and Loss Tricks - 2

Please read Part-1 before reading this part.

'

Q. 6) 

CP of 1 article = Rs.8/10 = Rs. 4/5

SP of 1 article = Rs. 10/8 = Rs. 5/4
SP/CP = 25/16 = 1.5625
Hence profit% = 56.25

Answer: (A)

Q. 7)

Total investment = Total CP
Let the CP of 1 egg = C
Then total CP = 200C

Total eggs left = 200 - 38 = 162 eggs = 162/12 dozen
Total SP = (162/12)*4.8 = Rs. 64.8
f = 1.08
Hence CP = 64.8/1.08 = Rs. 60

Answer: (D)

Q. 11)

This question appeared in Tier-2 2014 and is one of the trickiest question asked by SSC from this topic. So much so that many question banks haven't published its solution. Although if your concepts are clear, then there is nothing tricky here.

Let the fruit-seller buys 100 oranges

Now, he has sold the oranges in two parts. First he sold 40 oranges and then he sold 48 (80% of 60) oranges.

Total SP = (SP of 40 oranges) + (SP of 48 oranges) 

Given, SP of 40 oranges = CP of 100 oranges

40S = 100C (where S = SP of 1 orange and C = CP of 1 orange)

S/C = 2.5

f = 2.5 and hence Profit = 150%

He sold 80% of remaining oranges at half the previous rate of profit.

That means he sold 48 oranges at 75% profit.

CP of 48 oranges = 48C

f = 1.75

SP of 48 oranges = 1.75*48C = 84C

Total SP = (SP of 40 oranges) + (SP of 48 oranges) = 100C + 84C = 184C

Total CP = 100C

f = SP/CP = 184C/100C = 1.84

Hence profit = 84%

Answer: (B)

If you have any doubt in this article, please drop a comment...

Keep reading :)