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Showing posts with label aptitude. Show all posts
Showing posts with label aptitude. Show all posts

Friday, 17 July 2015

Syllogism for bank exams

Solving syllogism is always confusing .No more confusion here onwards. Conventional methods are usually time consuming .It is okey if the problem is 2 statement syllogism. But it is not the case if the problem is 3,4 or 5 statement syllogism .Conventional method will eat your valuable time during exams. Please try to follow Venn diagram method explained below.
Before solving questions ,let us draw Venn diagram for possible statements.

1.Statement:”All A are B” 
Possible Venn diagrams.


syllogism-venn diagram
fig1


syllogism-venn diagram
fig2

Let us see whether following conclusions follows ‘ the above statement  or not. A Conclusion follows if and only if conclusion is satisfied in all possible conditions of the statement. That means conclusion must be possible in all Venn  diagrams we have drawn .
>
syllogism-venn diagram
You can see only conclusions 2 and 3  clearly  follows .But look at the conclusions 1 and 7,there is a possibility for these  conclusions to be true.If the conclusions 1 and 7 are modified as below
1=> All A being   B is a possibility(see fig.2). and
7=> Some B  not being  A is a possibility (see fig.1).
Then the answer will be’ YES’ and ‘YES’. Hope it is clear….Now let us go to next statement

2.Statement:”some A are B” 
Possible Venn diagrams.


syllogism-venn diagram
fig.3

fig4

fig.5

fig.6


Let us see whether following conclusions follows the above statement or not.




You can see only conclusion 3 clearly follows. But in some cases there is possibility for conclusions 1,2,6 and 7 to be true. If we  modify 1,2,6 and 7 as follows.
1=> All A being B is a possibility.(see fig.4 and fig.6)
2=>All B being A is a possibility.(see fig.5 and fig.6)
6=>Some A not being B is a possibility(see fig.3 and fig.5)
7=>Some B not being A is a possibility(see fig.3 and fig.4)
Then these conclusions follows the statement.


3.Statement:"Some A are not B"
 Possible Venn diagrams.

fig7
fig8
fig9


None of the conclusion follows directly. But there exist possibility for conclusion 2 to 7.If we modify them
2=>All B being A is a possibility? YES (fig.8)
3=>Some B  being A is a possibility? YES(fig.7 and fig.8)
4=>No A being B is a possibility ?YES(fig.9).
5=> No B being  A is a possibility ?YES (fig.9).
6=> Some A being  B is possibility?YES(fig.7 and fig.8).
7=> Some B  not being  A is a possibility.?YES(fig.7 and fig.9).
Hope you understood ….


4.Statement:"No A is B"
Possible Venn diagram



fig10
syllogism-venn diagram

Conclusions 4,5 and 7 follows. In this case there is only one Venn diagram possible ,therefore there is no possibility cases.
Now let us do some simple problems.

Q1)Statement :Some Pens are Pencils.
                        All Pencils are Books.
Conclusions:1.All the Books are Pencil
                     2. Some Pens are Book.
                     3. All Pen being Book is a possibility.
syllogism-venn diagram
or

 Ans:1-NO,2-YES,3-YES.

Q2)Statement:Some Dogs are Cat.
                       Some Cats are Cows.
 Conclusions:1.Some Dogs are Cows.
                     2. Some Cats are Dogs.
or 

 ANS:1-NO,2-YES

Q3):Statements:All cars are Chair.
                          No Chair is Mug.
Conclusions:1.No car is mug.
                     2.All Chair are cars.

ANS:1-YES,2-NO

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Click here to read solving 3,4 statement syllogism


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simon         8 comments:

Friday, 10 July 2015

Time distance and speed formulas and shortcuts for bank exams

Time distance and speed formulas and shortcuts for bank exams:On an average you can found 2-3 question on Time ,distance and speed in every bank exams.By understanding few formulas and shortcuts you can score full mark from this section.We have provided main formulas and shortcuts of time,distance and speed for IBPS Clerk and PO exams.
 
Relation between time distance and speed is given by the equation
speed=distance/time 
Unit of speed is km/hr or m/s
If speed is given in km/hr,then inorder to convert it  in to m/s multiply by 5/18
1km/hr=5/18m/s
If speed is given in m/s,then inorder to convert it  in to km/hr multiply by 18/5

Ratio 

  • If ratio of speed of two moving object is a:b, then ratio between times taken for covering same distance is b:a.
  • If two objects A and B moving in opposite direction from two different places  reach at common point in t1 and t2 hrs respectively                 Then Speed of A:Speed of B=sqrt(t2/t1)
Average speed 
  • average speed=total distance/total time taken.
  • If a moving object covers a certain distance with a speed of x km/hr and again covers same distance with a speed of ykm/hr, then average speed is 2xy/(x+y).
  • If a moving object covers a certain distance with a speed of x km/hr and again covers same distance with a speed of ykm/hr and again with zkm/hr,then average speed is=3xyz/(xy+yz+xz)

Points to be noted while doing 'train and time' problems

  • If two trains are travelling in same direction ,then their relative speed is equal to difference of their speeds.Then Time taken by the fast train to cross the slower train is                                                                            =Sum of       lengths of both trains/difference of their speed
  • If two trains are travelling in opposite direction ,then their relative speed is equal to sum of their speeds.Then time taken to pass one another is   =Sum of lengths of both trains/sum of their speed.
  • when a train is clearing a pole or a point, then distance covered by train is equal to its length
  • When a train is covering a platform or bridge or tunnel ,then distance covered by train is equal to sum of the length of train and the length of platform/tunnel/bridge.
  • When a moving train crosses another train, then distance covered is equal to sum of lengths of both trains. 
Example:A 480-metre-long train crosses a platform in 140 seconds. What is the speed of the train?
Ans:Cannot be determined,since length of platform is not given

Example:A train 100m long is running at 21km/hr and another train 150m is running at 36km/hr in the same direciton.how long will the faster train take to pass the other train?
Sum of length of both train=100+150=250m
difference of their speed is=36-21 km/hr=15km/hr=15*(5/18) m/s=25/6 m/s
Time taken=250/(25/6)=60 seconds.

Boat and stream problems

  • If speed of stream=xkm/hr and speed of boat in still water is ykm/hrthen speed of boat in downstream=x+y km/hr                                           speed of boat in upstream=y-x km/hr
  • If speed of boat in upstream and speed of boat in down stream is given then,                                                                                        speed of boat in still water=1/2(speed in upstream+speed in downstream)                                                                                                      speed of stream=1/2(Speed in downstream - speed  in upstream)
Example: A boat is moving at 30 km/hr upstream, when it travels down stream its speed is 36km/hr.What is the speed of boat in still water and what is the speed of stream?
Speed of boat in still water=1/2 (30+36)=66/2=33 km/hr.
speed of stream=speed of boat downstream-speed of boat in still water
                =36-33=3km/hr
Note:
A person walks at x kh/hr he reaches destination t1 hrs late,if he walks at y km/hr,then reaches t2 hrs early
then distance to the destination =(xy/(y-x)) * (t1+t2)

Example:A person walking at 2km/hr reaches his office 6 minutes late .If he walks at 3km/hr he reaches there 6 minute early. How far is the  office from his house?
Distance=(2*3)/(3-2) *((6+6)/60)=6*12/60=1.2 km .


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simon         No comments:

Thursday, 9 July 2015

Work and Time problems shortcuts for bank tests

Work and Time shortcut tricks for bank exams:In every competitive exam we have to deal with varieties of quantitative aptitude questions .In almost every competitive exam, work and time problem is a regular question under quantitative section.In bank PO and clerk exams there will be at least 2-3 questions on work and time.By understanding the basic concept and memorizing a few shortcut formulas, you  can score full mark for these questions.Here we are sharing some useful Work and Time shortcut tricks for bank exams.
Basic point to remember while solving work and time problems:First of all work done in 1 day is calculated.If a person completes a work in x days,then Work done by that person in one day is 1/x.
work and time problem shortcuts

Shortcut formula for solving work and time problems

If A can do a work in x days and B can do the same work in y days,then  A and B together can finish the work in 
work and time formula
This is the first and foremost shortcut formula for solving work and time problems.For understanding better, derivation of this formula is given below.
Derivation of above formula:
    Work done by A in one day=1/x
    Work done by B in one day=1/y
    Work done by A and B together in 1 day=1/x+1/y
    Then  total days taken to complete the work by A and B together=1/ Work done by A and      B together in 1 day
    =1/(1/x+1/y)
    =1/((x+y)/xy))
    =xy/(x+y)

Example:If A can do a work in 8 days and B can do the same work in  days,in how many days A and B together can finish the work
Ans:Applying above formula 
 no of days taken to finish the work=8*6/(8+6)
 Instead of solving this directly take the LCM of 8 and 6
 8*6/(8+6)=LCM(8,6)/(LCM(8,6)/8 + LCM(8,6)/6)=24/(3+4)=24/7=3 3/7

Important points to be noted while solving work and time problems

  1. If A completes a work in x days and B completes the same work in y days then ratio of work done by A and B in one day will be y:x
  2. If A can finish the work in x days ,B can finish the same work  in y days and C finishes it in z days, then number of days taken to complete the work if all three work together is  work and time shortcut trick formula 
  3. If A&B together can finish the work in x days,B&C together finishes in  y days and C&A together finishes in z days,then work done by A,B and C together in 1 day is                            work and time shortcut trick formula
  4. If a man can do x/y of work in 1 hr,then he will take y/x hrs to finish the work.

Work and Time - Practice questions(Solved)

Question1:Ganesh ,Ram and Sohan together can do a work in 16 days. If Ganesh and Ram together can do a the same work in 24 days then, how long will take Sohan to do the same work?
Solution: Work done by three of them together in 1 day= 1/16............(1)
               Work done by Ganesh and Ram together in 1 day= 1/24.....(2)
               So,work done by Sohan in one day=(1)- (2)=(1/16) - (1/24)=1/48
               =>Total days taken by Sohan to complete the work alone= 48 days.

Question2:15 men can complete a work in 10 days while 20 boys can complete the same work in 15 days .How many days will 10 men and 10 boys together take to complete the same work
Solution:Work done by one man in one day=1/(15*10)
              Work done by one boy in one day=1/(20*15)
              Work done by 10 men and 10 boys in one day=10[ 1/(15*10) + 1/(20*15)] 
              Days taken=1/Work done by 10 men and 10 boys in one day
                                =10 days

Question3:16 men can do a piece of work in 16 days .4 days after they started the work, 8 more men joined them. How many days will they now take to complete the remaining work
Solution:Work done by 1 man in 1 day=1/(16*16)
              Work completed by 16 men in 4 days= 4[1/(16*16)]*16=1/4
               Remaining work= 1- 1/4= 3/4
               Total men now= 16+ 8=24
               24 men do 3/4 work 
                =>24*number of days*Work done by 1 man in 1 day=3/4
                =>24*number of days* 1/(16*16)=3/4
                =>number of days=8 days

Download Work and Time Practice questions PDF ebook
Question4:A and B together can complete a piece of work in 6 days. B and C can complete the same work in 8 days.A and C can finish it in 12 days. If they all work together, how long it will take to finish the work
 Solution:Applying the formula
               Work done by A,B & C together in one day= ½(1/6 +1/8 + 1/12)=9/48
                => days taken to complete the work by A,B & C together =48/9 days


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simon         3 comments:

Monday, 6 July 2015

Ratio,proportions and Fractions for competitive exams(bank po,clerk,ssc,cat,mat,upsc etc..)

Ratio and Fractions shortcuts and tricks:In most of the competitive exams quantitative part will be time consuming when compared with other sections.This is same in case of bank exams also.To improve your overall quantitative aptitude speed ,you must me thorough with basic maths rules and shortcuts. Here we are sharing some important rules and shortcut tricks for ratio proportion and fractions. This will not only help you in solving ratio and fraction questions faster, but also improve your overall maths speed.Here we have covered all important rules and formulas of ratio,proportion and fractions and examples are included for better understanding.

Ratio and proportion-Important rules and shortcuts

Example:If P:Q=2:3, Q:R=4:5 then P:R=?
P/R=(P/Q)*(Q/R)=2/3*4/5=8/15,thus P:R=8:15

Example:P:Q:R=2:3:4,then P/Q:Q/R:R/P=?
P/Q:Q/R:R/P=2/3:3/4:4/2=8:9:24


Example:If 2P=3Q=4R then P:Q:R=?
Let 2P=3Q=4R=K, 
we get P=K/2,Q=K/3,R=K/4 
=> P:Q:R=K/2:K/3:K/4=1/2:1/3:1/4=6:4:3

Example:P:Q=1:2,Q:R=4:5,R:S=10:3 then P:Q:R:S=?
 Make the  Q term in first and second fraction same and make the R term similar in second and third fractions as follows

P:Q:R:S=2:4:5:3/2=4:8:10:3

Comparison of ratios and Fractions

Method1:To compare two fractions  we can  make either denominators same or numerators same.
Example:2/5 and 3/10
To find out which is greater, make denominators same.We get 4/10 and 3/10.From this we can conclude,2/5>3/10
                            or make numerator same
Fractions will become 6/15 and 6/20,obviously 6/15>6/20.

Method2:This method can be applied if difference between numerator and denominator is same for all given fractions.
Example:1/2,3/4,7/8. Here 2-1=4-3=8-7=1.In such cases, just look at the numerator .Smaller the numerator will be smaller fraction.1/2<3/4<7/8.

Method3:this method is applicable for all fractions.
If a/b and c/d are fractions under consideration,cross multiply numerator and denominator .ie a*d and c*b.
If a*d>b*c,then a/b>c/d

Example:7/11 and 3/5

cross multiply denominator and numerator.We get 7*5 and 11*3 


Since 7*5>11*3 ,7/11>3/5
Don't forget to share Ratios and Fractions shortcuts with your friends  .
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simon         1 comment:

Thursday, 2 July 2015

Square,square root,cube ,cube roots shortcuts and tricks

Square ,square roots ,cube,cube root shortcuts for bank exams:As you know in bank exams speed is a major factor.In most of the bank exams there will be 10-15 questions from basic maths and simplifications,out of which 2-4 questions will contain square/square root/cube/cube root.Many candidates take it lightly and commit unforced errors.By understanding some basic formulas you can avoid such errors.We are sure that our shortcuts and tricks for squares and cubes will improve your calculation speed considerably. In quantitative section you can save your precious time by practicing maths shortcuts and Tricks.Here we are sharing some useful shortcuts for finding square,square root,cube and cube roots.Hope you will find this useful in upcoming exams.




Square,square root,cube ,cube roots shortcuts and tricks:PDF ebook

Here is the ebook for squares,square roots,cubes cube roots shortcut trick.You can also download this ebook in pdf format from the link provided below.
Click here for Tricks&shortcuts for division&multiplication
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simon         3 comments:

Wednesday, 1 July 2015

Basic Maths Tricks and shortcuts for competitive exams:Multiplication and Division shortcut

Basic Maths Tricks and shortcuts for competitive exams:In every competitive exam, if you want to succeed you should manage your time well.To crack a bank exam , time management is a crucial factor.Understanding some shortcuts and tricks will definitely save your time during common written examinations.Here we are sharing some simple but powerful time saving shortcut tricks for division and multiplication.

1. Division-shortcuts

In division instead of direct division, use factoring method
Example:1848/264=(2*3*4*7*11)/(2*3*4*11)=7

2.Multiplication-shortcuts

SUM – 10 METHOD:
Example: 78 and 72.  These two numbers, if we add the numbers in the unit's place, the resultant is 10 and thenumbers in the ten's place are both the same. In such cases, we can have a simple solution.
Step1: multiply the numbers in the unit's place and write down the resultant. (8*2 = 16)
Step2: say, the number in the ten's digit is a, then multi a*(a+1) and write down the resultant. => (7*(7+1) = 56)
Step3: write the final result: 5616
Example:118*112 follow above steps
 8*2 = 16; and 11*(11+1) = 11*12 = 132. And hence
the result is: 13216.
In short: ab*ac = (a*(a+1))(b*c)

Base Method:

Base numbers, in general, are nothing but multiples of 10. If the given numbers are nearer to
base numbers, then you can follow this method to multiply them.
Example: 98*95 =?
Here 98 is ,2 less than the base number 100 and 95 is ,5 less than 100. We can write them like this:
98  -2
95  -5
The first step will be deducting/subtracting the resultant of the diff between the base number and the given number with the given number in a cross-way! That is, you need to subtract 98 and 5 (which is the resultant of difference between the base number and 95) or you can also cross-subtract 95 and 2, the result will be same. This result forms the 1st part of the resultant at the start. The last part of the resultant will be multiplication of the differences from base numbers (i.e., 2 * 5 = 10)
98  -2
95  -5
(98 – 5) (-2 * -5)
Hence, the answer will be: 9310

Example: 998*997 =?
998  -2
997  -3
Observe carefully, in the second part, the multiplication of difference yield in a single digit number, but no. of zeroes in the base number, here 1000, is three. Hence add two zeroes before the result. Therefore, the answer will be: (998-3) | (-2 * -3) = 995006
What if the numbers we get are like this? I mean, the base is 50 here. We will follow the same procedure as above but a small difference that the resultant in the first part will be halved. And if the base is 200, then the number will be doubled and so on based on the base number.

Multiplication with 5,25,50 etc...




Substitute 5 by 10/2,25 by 100/4 and 50 by 100/2.
Examples:

  1. 5*18=18*10/2=180/2=90
  2. 24*25=24*100/4=2400/4=600
  3. 73*50=73*100/2=7300/2=3650

Multiplication with 9, 99,999 etc..

Examples:
  1. 13*9=13*(10-1)=130-13=117
  2. 26*99=26*(100-1)=2600-26=2574
  3. 350*999=350*(1000-1)=350000-350=349650
Click here for square,square root and cube root shortcuts 
Hope this shortcuts will help you do better.Share it if you find this shortcuts useful.
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