BANK PO LOGICAL ABILITY SOLVED PAPER

1.If GRAMMAR is written as MAMRAGR, the ENGLISH is written as:
(a) LIGNSEH
(b) GINESHL
(c) LGINSEH
(d) NHSELGI
(e) None of these
Ans (c)

2. Which of the following replaces the question mark?
MILD : NKOH :: GATE?
(a) HCWI
(b) HDVQ
(c) IBUP
(d) HDUR
(e) None of these
Ans (a)

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3. If DBMDVUUB stands for Calcutta, How will you write Bombay?

(a) DQUDDXB

(b) CPMCBZ

(c) DPNCB

(d) CPNCBZ

(e) None of these

Ans (d

4.Insert the word that completes the first word and begins the second

Clue: boy

BAL(....)DER

(a) ERS

(b) OCK

(c) LAD

(d) LIES

(e) None of these

Ans (c)

5. A man travels three miles due North, then travels eight miles due East and further travels three miles due North. How far is he from the starting point?

(a) 14 miles

(b) 10 miles

(c) 100 miles

(d) 15 miles

(e) None of these

Ans (b)

6. Which is the wrong member among the following?

(a) Microscope

(b) Stethoscope

(c) Telescope

(d) Periscope

(e) None of these

Ans (b)

7. From the following select the member that does not belong to the set

(a) Whale

(b) Crocodile

(c) Lizard

(d) Snake

(e) None of these

Ans (a)

8. Which is not related in the following set?

(a) Othello

(b) King Lear

(c) Macbeth

(d) Oliver TwistV

(e) None of these

Ans (d)

9. Which is the wrong member in the following set?

(a) Graphite

(b) Diamond

(c) Pearl

(d) Coal

(e) None of these

Ans (c)

10. From the following select the word that does not belong to the set

(a) Cube

(b) Rectangle

(c) Rhombus

(d) Square

(e) None of these

Ans (a)

11. If in a certain code TWENTY is written as 863985 and ELEVEN is written as 323039 how is TWELVE written?

(a) 863584

(b) 863203

(c) 863903

(d) 863063

(e) None of these

Ans (b)

12. Showing a man Saroj said: “He is the brother of my Uncle's daughter”. What is the relation of Saroj with that man?

(a) Son

(b) Brother-in-law

(c) Nephew

(d) Cousin

(e) None of these

Ans (d)

13.In a certain code MONKEY is written as XDJMNL. How is TIGER written in that code?

(a) SDFHS

(b) SHFDQ

(c) QDFHS

(d) UJHFS

(e) None of these

Ans (c)

14.Choose the subject which is different from others

(a) Mathematics

(b) Arithmetic

(c) Geometry

(d) Algebra

(e) None of these

Ans (a)

15. Aluminium is to Bauxite as iron is to

(a) Pyrite

(b) Haematite

(c) Magnesite

(d) Iron Oxide

(e) None of these

Ans (b)

16. Which among the following is different from others?

(a) DE

(b) PQ

(c) TU

(d) MO

(e) None of these

Ans (d)

17. Which is the odd pair of words different from the following sets?

(a) Blacksmith : Anvil

(b) Carpenter : Saw

(c) Goldsmith : Ornaments

(d) Barber : Scissor

(e) None of these

Ans (c)

18. Which is the pair like Triangle : Hexagon?

(a) Cone : Sphere

(b) Rectangle : Octagon

(c) Pentagon : Heptagon

(d) Triangle : Quadrilateral

(e) None of these

Ans (c)

19. Bag is related to luggage in the same way as ship is related to

(a) Cargo

(b) Coal

(c) Stock

(d) Weight

(e) None of these

Ans (a)

20. Moon : Satellite :: Earth : ?

(a) sun

(b) solar system

(c) asteroid

(d) planet

(e) None of these

Ans (d)

21. Select the pair which has the same relationship as the given pair Traveler : Destination

(a) Beggar : Donation

(b) Teacher : Education

(c) Refugee : Shelter

(d) Accident : Hospital

(e) None of these

Ans (c)

22. A man is facing north-west. He turns 90o in the clockwise direction and then 1350 in the anticlockwise direction. Which direction is he facing now?

(a) east

(b) west

(c) north

(d) south

(e) None of these

Ans (b)

23. Which is the irregular member of the following group?

(a) RQPA

(b) MLKA

(c) STUA

(d) HGFA

(e) None of these

Ans (c)

24.Choose which is least like the other words in the group?

(a) Club

(b) hotel

(c) hostel

(d) inn

(e) None of these

Ans (a)

25. Which among the following is same as Violet : Orange : Yellow?

(a) Purple

(b) White

(c) Pink

(d) Blue

(e) None of these

Ans (d)

Tips and Tricks- Successive Discounts

Formula for successive discounts
a+b+(ab/100)
This is used for successive discounts types of sums.like 1999 population increases by 10% and then in 2000 by 5% so the population in 2000 now is 10+5+(50/100)=+15.5% more that was in 1999 and if there is a decrease then it will be preceded by a -ve sign and likewise.

Tips and Tricks- General Quantitative

Product Vs HCF-LCM
Product of any two numbers = Product of their HCF and LCM . Hence product of two numbers = LCM of the numbers if they are prime to each other

AM GM HM
For any 2 numbers a>b a>AM>GM>HM>b (where AM, GM ,HM stand for arithmetic, geometric , harmonic menasa respectively) (GM)^2 = AM * HM

Sum of Exterior Angles
For any regular polygon , the sum of the exterior angles is equal to 360 degrees hence measure of any external angle is equal to 360/n. ( where n is the number of sides)
For any regular polygon , the sum of interior angles =(n-2)180 degrees
So measure of one angle in
Square-----=90
Pentagon--=108
Hexagon---=120
Heptagon--=128.5
Octagon---=135
Nonagon--=140
Decagon--=144

Problems on clocks
Problems on clocks can be tackled as assuming two runners going round a circle , one 12 times as fast as the other . That is , the minute hand describes 6 degrees /minute the hour hand describes 1/2 degrees /minute . Thus the minute hand describes 5(1/2) degrees more than the hour hand per minute .
The hour and the minute hand meet each other after every 65(5/11) minutes after being together at midnight. (This can be derived from the above) .

Co-ordinates
Given the coordinates (a,b) (c,d) (e,f) (g,h) of a parallelogram , the coordinates of the meeting point of the diagonals can be found out by solving for [(a+e)/2,(b+f)/2] =[ (c+g)/2 , (d+h)/2]

Ratio
If a1/b1 = a2/b2 = a3/b3 = .............. , then each ratio is equal to (k1*a1+ k2*a2+k3*a3+..............) / (k1*b1+ k2*b2+k3*b3+..............) , which is also equal to (a1+a2+a3+............./b1+b2+b3+..........)

Finding multiples
x^n -a^n = (x-a)(x^(n-1) + x^(n-2) + .......+ a^(n-1) ) ......Very useful for finding multiples .For example (17-14=3 will be a multiple of 17^3 - 14^3)

Exponents
e^x = 1 + (x)/1! + (x^2)/2! + (x^3)/3! + ........to infinity 2 <>GP
-> In a GP the product of any two terms equidistant from a term is always constant .
-> The sum of an infinite GP = a/(1-r) , where a and r are resp. the first term and common ratio of the GP .

Mixtures
If Q be the volume of a vessel q qty of a mixture of water and wine be removed each time from a mixture n be the number of times this operation be done and A be the final qty of wine in the mixture then ,
A/Q = (1-q/Q)^n

Some Pythagorean triplets:
3,4,5----------(3^2=4+5)
5,12,13--------(5^2=12+13)
7,24,25--------(7^2=24+25)
8,15,17--------(8^2 / 2 = 15+17 )
9,40,41--------(9^2=40+41)
11,60,61-------(11^2=60+61)
12,35,37-------(12^2 / 2 = 35+37)
16,63,65-------(16^2 /2 = 63+65)
20,21,29-------(EXCEPTION)

Appolonius theorem
Appolonius theorem could be applied to the 4 triangles formed in a parallelogram.

Function
Any function of the type y=f(x)=(ax-b)/(bx-a) is always of the form x=f(y) .

Finding Squares
To find the squares of numbers from 50 to 59
For 5X^2 , use the formula
(5X)^2 = 5^2 +X / X^2
Eg ; (55^2) = 25+5 /25 =3025
(56)^2 = 25+6/36 =3136
(59)^2 = 25+9/81 =3481

Successive Discounts
Formula for successive discounts
a+b+(ab/100)
This is used for successive discounts types of sums.like 1999 population increases by 10% and then in 2000 by 5% so the population in 2000 now is 10+5+(50/100)=+15.5% more that was in 1999 and if there is a decrease then it will be preceded by a -ve sign and likewise.

Rules of Logarithms:
-> loga(M)=y if and only if M=ay
-> loga(MN)=loga(M)+loga(N)
-> loga(M/N)=loga(M)-loga(N)
-> loga(Mp)=p*loga(M)
-> loga(1)=0-> loga(ap)=p
-> log(1+x) = x - (x^2)/2 + (x^3)/3 - (x^4)/4 .........to infinity [ Note the alternating sign . .Also note that the logarithm is with respect to base e ]


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Tips and Tricks- Inequalities

-> x + y >= x+y ( stands for absolute value or modulus ) (Useful in solving some inequations)
-> a+b=a+b if a*b>=0 else a+b >= a+b
-> 2<= (1+1/n)^n <=3 -> (1+x)^n ~ (1+nx) if x<<<1> When you multiply each side of the inequality by -1, you have to reverse the direction of the inequality.

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Tips and Tricks - Maximum/Minimum problems

-> If for two numbers x+y=k(=constant), then their PRODUCT is MAXIMUM if x=y(=k/2). The maximum product is then (k^2)/4
-> If for two numbers x*y=k(=constant), then their SUM is MINIMUM if x=y(=root(k)). The minimum sum is then 2*root(k) .


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Tips and Tricks - Reciprocal Roots

The equation whose roots are the reciprocal of the roots of the equation ax^2+bx+c is cx^2+bx+a
Roots
Roots of x^2+x+1=0 are 1,w,w^2 where 1+w+w^2=0 and w^3=1
Finding Sum of the rootsFor a cubic equation ax^3+bx^2+cx+d=o sum of the roots = - b/a sum of the product of the roots taken two at a time = c/a product of the roots = -d/a
For a biquadratic equation ax^4+bx^3+cx^2+dx+e = 0 sum of the roots = - b/a sum of the product of the roots taken three at a time = c/a sum of the product of the roots taken two at a time = -d/a product of the roots = e/a

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Tips and Tricks - Finding number of Imaginary Roots

For an equation f(x)=0 , the maximum number of positive roots it can have is the number of sign changes in f(x) ; and the maximum number of negative roots it can have is the number of sign changes in f(-x) .
Hence the remaining are the minimum number of imaginary roots of the equation(Since we also know that the index of the maximum power of x is the number of roots of an equation.)

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Tips and Tricks - Quantitative Aptitude Tests - Finding number of Positive Roots

If an equation (i:e f(x)=0 ) contains all positive co-efficient of any powers of x , it has no positive roots then.
Eg: x^4+3x^2+2x+6=0 has no positive roots

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Tips and Tricks - Quantitative Aptitude Tests - To find the squares of numbers

To find the squares of numbers near numbers of which squares are known
To find 41^2 , Add 40+41 to 1600 =1681
To find 59^2 , Subtract 60^2-(60+59) =3481

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Tips and Tricks - Quantitative Aptitude Tests - Sum of n natural numbers

-> The sum of first n natural numbers = n (n+1)/2
-> The sum of squares of first n natural numbers is n (n+1)(2n+1)/6
-> The sum of first n even numbers= n (n+1)
-> The sum of first n odd numbers= n^2

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Tips and Tricks - Quantitative Aptitude Tests -Finding number of Factors

To find the number of factors of a given number, express the number as a product of powers of prime numbers.
In this case, 48 can be written as 16 * 3 = (24 * 3)
Now, increment the power of each of the prime numbers by 1 and multiply the result.
In this case it will be (4 + 1)*(1 + 1) = 5 * 2 = 10 (the power of 2 is 4 and the power of 3 is 1)

Therefore, there will 10 factors including 1 and 48. Excluding, these two numbers, you will have 10 – 2 = 8 factors.

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Vedic Maths Tricks - Is it divisible by four?

1. Whether a number is divisible by four or not?

Let's look at 1234 - Does 4 divide evenly into 1234?

For 4 to divide into any number we have  to make sure that the last number is even
If it is an odd number, there is no way it will go in evenly.
So, for example, 4 will not go evenly into 1233 or 1235
Now we know that for 4 to divide evenly into any number the number has to end with an even number.
Back to the question... 4 into 1234, the solution:
Take the last number and add it to 2 times the second last number
If 4 goes evenly into this number then you know that 4 will go evenly into the whole number.
So
4 + (2 X 3) = 10
4 goes into 10 two times with a remainder of 2 so it does not go in evenly.
Therefore 4 into 1234 does not go in completely.

Let’s try 4 into 3436546
So, from our example, take the last number, 6 and add it to
two times the penultimate number, 4
6 + (2 X 4) = 14
4 goes into 14 three times with two remainder.
So it doesn't go in evenly.

you can use it in working out whether the year you are calculating is a leap year or not.

Vedic Maths Tricks - Multiplying by 12

Example: 12 X 7
The first thing is to always multiply the 1 of the twelve by the
number we are multiplying by, in this case 7. So 1 X 7 = 7.
Multiply this 7 by 10 giving 70.

Now multiply the 7 by the 2 of twelve giving 14. Add this to 70 giving 84.
Therefore 7 X 12 = 84


Let's try another:
17 X 12
Remember, multiply the 17 by the 1 in 12 and multiply by 10
(Just add a zero to the end)
1 X 17 = 17, multiplied by 10 giving 170.
Multiply 17 by 2 giving 34.
Add 34 to 170 giving 204.
So 17 X 12 = 204
lets go one more
24 X 12
Multiply 24 X 1 = 24. Multiply by 10 giving 240.
Multiply 24 by 2 = 48. Add to 240 giving us 288
24 X 12 = 288

Vedic Maths Tricks - Converting Kilos to pounds

Let’s start off with looking at converting Kilos to pounds.
86 kilos into pounds:
Step one, multiply the kilos by TWO.
To do this, just double the kilos.
86 x 2 = 172
Step two, divide the answer by ten.
To do this, just put a decimal point one place in from the right.
172 / 10 = 17.2
Step three, add step two’s answer to step one’s answer.
172 + 17.2 = 189.2
86 Kilos = 189.2 pounds

Let's try:
50 Kilos to pounds:
Step one, multiply the kilos by TWO.
To do this, just double the kilos.
50 x 2 = 100
Step two, divide the answer by ten.
To do this, just put a decimal point one place in from the right.
100/10 = 10
Step three, add step two's answer to step one's answer.
100 + 10 = 110
50 Kilos = 110 pounds

Vedic Maths Tricks - Adding Time

A simple way to add hours and minutes together:
Let's add 1 hr and 35 minutes and 3 hr 55 minutes together.

Make the 1 hr 35 minutes into one number, which will give us 135 and do
the same for the other number, 3 hours 55 minutes, giving us 355 . Now you want to add these two numbers together:
135
355
___
490
So we now have a sub total of 490.
What you need to do to this and all sub totals is
add the time constant of 40.
No matter what the hours and minutes are,
just add the 40 time constant to the sub total.
490 + 40 = 530
So we can now see our answer is 5 hrs and 30 minutes!

Vedic Maths Tricks - Temperature Conversions

This is a shortcut to convert Fahrenheit to Celsius and vice versa.
The answer you will get will not be an exact one.. but approximate
Fahrenheit to Celsius:
Take 30 away from the Fahrenheit, and then divide the answer by two.
This is your answer in Celsius.

Example:
74 Fahrenheit - 30 = 44. Then divide by two, 22 Celsius.
So 74 Fahrenheit = 22 Celsius.
Celsius to Fahrenheit just do the reverse:
Double it, and then add 30.
30 Celsius double it, is 60, then add 30 is 90
30 Celsius = 90 Fahrenheit
Remember, the answer is not exact but it gives you a rough idea.

Vedic Maths Tricks – Converting Kilometres To Miles

This is a useful method for when traveling between imperial and metric countries and need to know what kilometers to miles are.
The formula to convert kilometers to miles is number of (kilometers / 8 ) X 5
So lets try 80 kilometers into miles
80/8 = 10
multiplied by 5 is 50 miles!
Another example
40 kilometers
40 / 8 = 5
5 X 5= 25 miles