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Quantitative Problems for Bank Tests
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Bank Probationary Officer Test has a Quantitative section whose difficulty will be much lesser than Competitive entrance exams like CAT,MAT etc.Here most important factor is your speed.so always try to practice more.Here we have some sample bank Quantitative questions

One night 18 percent of the female officers on a police force were on duty. If 180 officers were on duty that night and half of these were female officers, how many female officers were on the police force?
(A) 90
(B) 180
(C) 270
(D) 500
(E) 1,000

If an integer n is divisible by both 6 and 8, then it must also be divisible by which of the following?
(A) 10
(B) 12
(C) 14
(D) 16
(E) 18

On the number line, if x is halfway between -5 and 3, and if y is halfway between -2 and 6, what number is halfway between x and y ?
(A) -1
(B)
(C) 0
(D)
(E) 1

Out of their annual net income, a couple spent 25 percent for food, 13.5 percent for entertainment, 20 percent for housing, 8 percent for car expenses, 15 percent for clothing, and saved the rest. What was the ratio of the amount saved to the amount spent for entertainment?
(A)19/27
(B) 6/5
(C) 37/27
(D) 19/9
(E) 7/3

If z+3/(z-1) + z+1/(z-3) =2, then z =
(A) 2
(B) 1
(C) -1
(D) -2
(E) -3

The population of city X increased from 325,000 in 1980 to 350,000 in 1990, and it is projected that the population will increase by the same number from 1990 to 2000. Approximately what is the projected percent increase in population from 1990 to 2000 ?
(A) 7.1%
(B) 7.7%
(C) 8.3%
(D) 14.3%
(E) 15.3%

Of the z students at a certain college, x are studying French and y are studying German. If w are studying both French and German, which of the following expresses the number of students at the college not studying either French or German ?
(A) z + w – x – y
(B) z – w – x – y
(C) z – w – x + y
(D) w + x + y – z
(E) w – x – y – z

Of the science books in a certain supply room, 50 are on botany, 65 are on zoology, 90 are on physics. 50 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same science?
(A) 81
(B) 159
(C) 166
(D) 285
(E) 324

A certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint. If 2 gallons of the mixture is needed and the individual colors can be purchased only in one-gallon or half- gallon cans, what is the least amount of paint, in gallons, that must be purchased in order to measure out the portions needed for the mixture?
(A) 2
(B) 2.5
(C) 3
(D) 3.5
(E) 4

–2 (– 4 – (– 3 + 5)) =
(A) – 16
(B) – 10
(C) 6
(D) 12
(E) 16

On a certain test, 3 students each had a score of 90, 9 students each had a score of 80, 4 students each had a score of 70, and 4 students each had a score of 60. What was the average (arithmetic mean) score for the 20 students ?
(A) 70.5
(B) 75.0
(C) 75.5
(D) 80.0
(E) 80.5

. In the manufacture of a certain product, 5 percent of the units produced are defective and 4 percent of the defective units are shipped for sale. What percent of the units produced are defective units that are shipped for sale?
(A) 0.125%
(B) 0.2%
(C) 0.8%
(D) 1.25%
(E) 2.0%

The numbers in which of the following pairs do NOT have a pair of distinct prime divisors in common ?
(A) 10 and 20
(B) 12 and 18
(C) 24 and 32
(D) 21 and 63
(E) 22 and 88.

A certain fraction is equivalent to 2/5 . If the numerator of the fraction is increased by 4 and the denominator is doubled, the new fraction is equivalent to 1/3 . What is the sum of the numerator and denominator of the original fraction?
(A) 49
(B) 35
(C) 28
(D) 26
(E) 21

If all of the telephone extensions in a certain company must be even numbers, and if each of the extensions uses all four of the digits 1, 2, 3, and 6, what is the greatest number of four-digit extensions that the company can have?
(A) 4
(B) 6
(C) 12
(D) 16
(E) 24

The product of the first twelve positive integers is divisible by all of the following EXCEPT
(A) 210
(B) 88
(C) 75
(D) 60
(E) 34

Concepts in Unit Digits for CAT QA and DI
================================
Unit digit concepts play a lot of time saving tricks in the CAT format.We can use the concept of unit digits in eliminating answer options in all the objective type competitive examinations.

The unit digit has got huge significance when it comes to eliminate the answer options.Lot of questions involving rigorous multiplications can be solved within no time by eliminating the answer options

CASE 1...
---------
Lets take the case of the product of two successive numbers,n(n+1)
We will see the possible unit digits of the products.

0*1=0
1*2=2
2*3=6
3*4=2
4*5=0
5*6=0
6*7=2
7*8=6
8*9=2

we can see that, the unit digits of products of successive numbers will end in 0,2,6 only.
Now we have the formula for sum of first n natural numbers, n(n+1)/2
So we will see the possible unit digits for these products.
We know that,n(n+1) ends in 0,2,6.
So we consider the possible digits, we will get, when we divides n(n+1) by 2.
0 gives 0,5
2 gives 1,6
6 gives 3,8
So these are the possible unit digits for the sum of first n natural numbers.

*Product of successive numbers,n(n+1) ends in 0,2,6

*The sum of first n, natural numbers will never end in 2,4,7,9

*Perfect squares never end in 2,3,7,8

*If there are n terms in an AP, the difference between sum of odd terms and sum of even terms is (n/2)*d where d is the common difference.

CAT Lessons-Progressions
======================

Progressions is a comparatively easy section that comes in CAT.
Once you understand the concepts in progressions, you can answer almost all the questions. Identifying that the questions belong to progressions is the most difficult part. Now we can go to the detailed study of the Progressions.
For a person aiming very high score in QA section,I would advise that he should definitely do the Progressions questions

Progressions can be divided into
------------------------------------------
Arithmetic Progression (AP)
Geometric Progression (GP)
Harmonic Progression. (HP)
Arithmetic Geometric Progression. (AGP)



Arithmetic Progression (AP)
-------------------------------------------

In Arithmetic Progression, the successive terms always has a constant difference between them. The example of an AP is given below.

1,3,5,7,9…….This is an AP series with first term (a or t1)=1 and the constant difference (common difference or cd)=2.
2,4,6,8,10…… This is an AP series with first term (a or t1)=2 and the constant difference (common difference or cd)=2.

The nth term for an AP with first term =‘a’ and cd=’d’ is
tn =a+(n-1)d.
The sum of first n terms of an AP is
Sn=n/2{2a+(n-1)d}


Take the case of AP,2,4,6,8,10……

The 5th term can be found out by
t5=2+ (5-1)2
=2+4*2
=2+8
=10.
As we can see from the series the 5th term is indeed 10.

The sum of first 5 terms can be found out by
S5=5/2{2*2+(5-1)*2)
=5/2{4+8}
=5*6
=30.

Also we can see that sum of first 5 terms are 2+4+6+8+10=30.

Arithmetic Mean (AM)
----------------------------------
AM of an AP with terms a and b is AM = (a+b)/2.
Between two terms of an AP we can put any number of AMs.

Eg.
Suppose we need to put 4 AMs between a and b.,
Now the total number of terms in AP is 6.
Now the common difference in the AP is (b-a)/(4+1)= (b-a)/5..


Properties useful in solving questions in APs
----------------------------------------------------------------------
****
If in an AP, mth term is n and nth term is m, then (m+n)th term is always zero.
Eg. Consider the AP 4,3,2,1,0,-1,-2…..
1st term is 4 and 4th term is 1,therefore (4+1) term ie 5th term ,according to the property should be 0.We can see that the property holds true here.

****
If in an AP, sum of first m terms is equal to sum of first m tems, then sum of first (m+n) term is always zero.
Eg. Consider the AP -2.-1,0,1,2,…..
Sum of first 1 term is -2.
Sum of first 4 terms is -2.
Therefore according to property, sum of first (1+4) ie 5 terms should be 0.
We can verify that the property holds true.

Geometric Progression (GP)
----------------------------------------

In Geometric Progression, the successive terms always has a constant ratio between them. The example of an GP is given below.

1,3,9,27,81…….This is a GP series with first term (a or t1)= 1 and the constant ratio (common ratio or cr)=3.
2,4,8,16,32…… This is a GP series with first term (a or t1)= 2 and the constant ratio (common ratio or r)=2.

The nth term for an GP with first term =‘a’ and common ratio=’r’ is
tn =ar^(n-1)
The sum of first n terms of a GP is
Sn=a{r^(n-1)/(r-1)} r>1
&
Sn = a{r^(n-1)/(1-r)} r<1

Geometric Mean (AM)
------------------------------
GM of a GP with terms a and b is GM = (a*b)^0.5
Between two terms of an GP we can put any number of GMs.

Eg.
Suppose we need to put 4 =GMs between a and b.
Now the total number of terms in =GP is 6.
Now the common ratio of the GP is (b/a)^(4+1)= (b/a)^0.5

But in Competitive exams like CAT,GMAT etc, in GP, sum to infinity is more significant than sum of n terms.
Sum to infinity of GP is infinity if r>1,so the cases where, r<1 only we will get a definite sum.
Sum to infinity of a GP with first term,a and common ratio,r is
S∞=a/(1-r).

Eg. Find the sum to infinity of the series 1,1/2,1/4,1/8,1/16…….
a=1,r=1/2
S∞=1/(1-1/2)=2.

Harmonic Progression
-----------------------------------

If a,b,c are in Harmonic Progression(HP),then 1/a,1/b,1/c are in AP.
This is the standard definition of an HP.


Also we have the general rules
1. AM>=GM>=HM
2. GM^2=AM*HM



Strategies for solving problems in Progressions.
----------------------------------------------------------------------

**
In all questions that has Tn and Sn variable, n, always put values for n and check for the answer option.

**
Always try to make up a progression satisfying the conditions given in the questions and solve that progression only instead of doing with unknown numbers.

**
Suppose we need to take one AP,one GP and one HP having 3 terms with same first and last terms,then we an take the following progressions,

AP: 1, 2/3,1/3 cd=1/3
GP : 1,1/(3^.5),1/3 cr=1/(3^.5)
HP: 1,1/2,1/3 HM=1/2.

**
Find the 625th term of the series 1,2,2,3,3,3,4,4,4,4,5………

Analysing the series, we see

Last 2 is the 3rd term ie 2*3/2
Last 3 is the 6th term ie 3*4/2
So we got the pattern,Last n will be the n(n+1)/2 th term
Also the previous n terms will be same,n only.

So if we consider,the case of 625th term, consider 35*36/2 gives 630.
Means 630th term will be 35,also previous 35 terms will be same 35 only.
So our answer is 625th term is 35.

Sample Aptitude Questions for Competitive Exams
===========================================

The 180 students in a group are to be seated in rows so that there is an equal number of students in each row. Each of the following could be the number of rows EXCEPT
(A) 4
(B) 20
(C) 30
(D) 40
(E) 90

A parking garage rents parking spaces for Rs.10 per week or Rs.30 per month. How much does a person save in a year by renting by the month rather than by the week?
(A) 140
(B) 160
(C) 220
(D) 240
(E) 260

Of the following, which is the best approximation to (0.0026)^0.5
(A) 0.05
(B) 0.06
(C) 0.16
(D) 0.5
(E) 0.6

In the expression (a/b)/c above, a, b, and c are different numbers and each is one of the numbers 2, 3, or 5. What is the least possible value of the expression?
(A)1/30
(B)2/15
(C)1/6
(D)3/10
(E)5/6

What is the total number of integers between 100 and 200 that are divisible by 3?
(A) 33
(B) 32
(C) 31
(D) 30
(E) 29

Dan and Karen, who live 10 miles apart meet at a cafe that is directly north of Dan’s house and directly east of Karen’s house. If the cafe is 2 miles closer to Dan’s house than to Karen’s house, how many miles is the cafe from Karen’s house?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10

What percent of 50 is 15?
(A) 30%
(B) 35%
(C) 70%
(D) 300%

If 2x = 3y = 10, then 12xy =
(A) 1,200
(B) 200
(C) 120
(D) 40
(E) 20

If Jack walked 5 km in 1 hour and 15 minutes, what was his rate of walking in km per hour?
(A) 4
(B) 4.5
(C) 6
(D) 6.25
(E) 15

After paying a 10 percent tax on all income over $3,000, a person had a net income of $12,000. What was the income before taxes?
(A) $13,300
(B) $13,000
(C) $12,900
(D) $10,000
(E) $9,000

1-[2-(3-{4-5}+6)+7]=
(A) –2
(B) 0
(C) 1
(D) 2
(E) 16

Working alone, R can complete a certain kind of job in 9 hours. R and S, working together at their respective rates, can complete one of these jobs in 6 hours. In how many hours can S, working alone, complete one of these jobs?
(A) 18 (B) 12 (C) 9
(D) 6 (E) 3

If 0.497 mark has the value of one dollar, what is the value to the nearest dollar of 350 marks?
(A) $174 (B) $176 (C) $524
(D) $696 (E) $704

If a sequence of 8 consecutive odd integers with increasing values has 9 as its 7th term, what is the sum of the terms of the sequence?
(A) 22 (B) 32 (C) 36
(D) 40 (E) 44

Reserve Bank of India (RBI)-Sample Objective Paper
====================================

RBI selection is held through Written Examinations (WE) and Interview.

'WE' will be held in two phases as under:

Phase I-Objective Type

Phase II-Descriptive Type

i) Phase I (Objective Type Test): This Paper of 3 hours duration for 200 marks will be held on Sunday, the October 11, 2009.

The Paper consists tests of 4 areas

i) General Awareness

ii) English Language

iii) Quantitative Aptitude

iv) Reasoning.

ii) Phase II (Descriptive Type Test): This paper has the following sections
1) Paper I – English

2) Paper II – Economic and Social Issues

3) Paper III – Finance and Management.
Each of these papers is of 3 hours duration carrying 100 marks.


Phase I- Reasoning section
---------------------------
Answer the following questions by marking the answer options a,b,c,d or e.
a.The question can be answered by statement 1 alone.
b.The question can be answered by statement 2 alone.
c.The question can be answered by either statement alone.
d.The question can be answered only by combining both statements together.
e.The question cannot be answered by given data.


John and Aby each received a salary increase. Which one received the greater salary increase?
(1) John’s salary increased 8 percent.
(2) Aby’s salary increased 5 percent

At a certain picnic, each of the guests was served either a single scoop or a double scoop of ice cream. How many of the guests were served a double scoop of ice cream?
(1) At the picnic, 60 percent of the guests were served a double scoop of ice cream.
(2) A total of 120 scoops of ice cream were served to all the guests at the picnic.

By what percent was the price of a certain candy bar increased?
(1) The price of the candy bar was increased by 5 Rs.
(2) The price of the candy bar after the increase was 45 Rs.

Is it true that a > b?
(1) 2a > 2b
(2) a + c > b + c

If m and n are consecutive positive integers, is m greater than n?
(1) m – 1 and n +1 are consecutive positive integers.
(2) m is an even integer

If x + 2y + 1 = y – x, what is the value of x?
(1) y2 = 9
(2) y = 3

If n is an integer, then n is divisible by how many positive integers?
(1) n is the product of two different prime numbers.
(2) n and 23 are each divisible by the same number of positive integers

If x and y are positive, what’s the value of x ?
(1) x = 3.927y
(2) y = 2.279

What is the value of the sum of a list of n odd integers?
(1) n = 8
(2) The square of the number of integers on the list is 64

What is the ratio of x to y?
(1) x is 4 more than twice y.
(2) The ratio of 0.5x to 2y is 3 to 5.

What was the average number of kilometers per litre of petrol for a car during a certain trip?
(1) The total cost of the petrol used by the car for the 180-km trip was Rs12.00.
(2) The cost of the petrol used by the car for the trip was Rs.1.20 per litre.

Is the prime number p equal to 37?
(1) p = n2 +1, where n is an integer.
(2) p2 is greater than 200.

Data Sufficiency Questions
=====================

Data sufficiency questions are a good source for scoring marks in competitive entrances using very less time.The advantage is that you never has to find the exact answers.You have to find whether the given statements are enough to find out the answer to the question.
This needs a bit of practice,since we need to analyse the given statements,individually first and then combined form.Also the answer options will be tricky sometimes.But practice it and you can increase your score easily .Also in lot of exams like CAT,GMAT,XAT etc,Data Sufficiency appears in both Quantitative section and Data Interpretation section.So its very easy to clear the cut-off marks if you can convert 4-5 DS questions.Also DS is now appearing in Bank entrances also
Here are some examples of DS questions for competitive exams...

Data Sufficiency Questions
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Answer the following questions by marking the answer options a,b,c,d or e.
a.The question can be answered by statement 1 alone.
b.The question can be answered by statement 2 alone.
c.The question can be answered by either statement alone.
d.The question can be answered only by combining both statements together.
e.The question cannot be answered by given data.


Who types at a faster rate, Raju or Renju?
(1) The difference between their typing rates is 10 words per minute.
(2) Renju types at a constant rate of 80 words per minute.

What was Anil’s average (arithmetic mean) grade for all of his courses?
(1) His grade in social studies was 75, and his grade in science was 75.
(2) His grade in mathematics was 95.

If today the price of an item is $3,600, what was the price of the item exactly 2 years ago?
(1) The price of the item increased by 10 per-cent per year during this 2-year period.
(2) Today the price of the item is 1.21 times its price exactly 2 years ago.

If the Eden ground is rectangular, what is its width?
(1) The ratio of its length to its width is 7 to 2.
(2) The perimeter of the playground is 396 meters

What is the value of x –1?
(1) x + 1 =3
(2) x – 1 <> r – s?
(1) x > r and y < y =" 2," s =" 3," r =" 5," x =" 6." y =" 7" y =" 3"> 9
If x and y are consecutive odd integers, what is the sum of x and y?
(1) The product of x and y is negative.
(2) One of the integers is equal to –1.

What is the value of x?
(1) 3 + x + y = 14 and 2x + y = 15
(2) 3x + 2y = 12 + 2y

If John is exactly 4 years older than Anil, how old is Aby?
(1) Exactly 9 years ago Aby was 5 times as old as Anil was then.
(2) Anil is more than 9 years old.

CAT Data Interpretation-Interesting Question
============================================
Matchstick problem
----------------------------------

The Matchstick problem is a cult problem, which is frequently appearing in TIME-AIMCATs and its variants appear in lot of competitive exams like CAT,XAT,MAT, Campus placement papers….This problem appears in various forms,like two people going for a drive taking turns while driving for a max. & min. kilometer limits.
The variants of same question came 2-3 times in original CAT papers.

Mainly 2 variants are there for this problem, we will discuss the type 1 variant in this post.

Type 1.
=================

There are n matchsticks, and 2 players A and B. One person should take minimum of 1 stick and can take maximum of 5 sticks at a time. The person who takes the last stick is the loser. Each player will play intelligently in order to win.
a.If there are 10 matchsticks and A has to play next, how many sticks he has to take to ensure that he wins?
b.If there are 21 matchsticks, and B is to play, Is there a chance for B to win?

Explanation:-

Consider the situation of 8 matchsticks and A has to play.
A can take max 5 and min 1.
Consider the sequence of steps that will follows if A plays intelligently to win

1. A will take 1 and remaining is 7.
2. Now B can take a max of 5, suppose he takes 5,then ,2 will remaining.
3. A will take 1 and 1 will remain.
4. B has to take min. 1.so he will lose and A will win.

Consider another sequence where in step 2,B takes min 1.

1. A will take 1 and remaining is 7.
2. Now B takes 1,then ,6 will remaining.
3. A will take 5 and 1 will remain.
4. B has to take min. 1.so he will lose and A will win.
So in both these extreme cases, irrespective of B’s play, A is winning.

This leads us the conclusion that, in this problem,
‘Winner is decided by initial number of matchsticks and the first play.”

Also, the aim of the player who plays first will always be to leave
{(min. limit + max. limit)+1}
ie here {(1+5)+1}=7 numbers of matchsticks to his opponent.
The same scenario will occur even if he leaves the multiples of this number.
ie in our question, the player who plays first, should aim to leave either 7 or a multiple of 7 matchsticks to his opponents so that irrespective of the future moves he is sure about his success.
So, in a game with the above min and max limits, the first player should aim at leaving the number of matchsticks as 7,14,21,28,35……..

The aim of the player who plays first will always be to leave
{(min. limit + max. limit) +1} numbers of matchsticks to his opponent.

Note:
Here if initially the number of matchsticks is a multiple of 7, then the first player will always lose.

Variant of Type 1:
----------------------------
In the above case the min. limit was 1.
Suppose the min. limit has been increased to a higher number,say2.
Then also we need to apply our general formula,
ie the aim of the player who plays first will always be to leave
{(min. limit + max. limit) +1} or {(min. limit + max. limit) +2} numbers of matchsticks to his opponent.

So in this case, the player who plays first, should aim to leave either 8 or 9 or a multiple of 8 or 9 matchsticks to his opponents so that irrespective of the future moves he is sure about his success

Type 2 --will be discussed in coming posts...

Bank Tests-Aptitude Paper
----------------------------------

Aptitude questions frequently asked in Banks-PSUs and Private
-----------------------------------------------------------------
SBI, ICICI,Central Bank,Federal Bank,Corporation Bank and other banks include aptitude tests in their recruitment. Some sample Bank test questions are given taken from different bank tests



A man buys 12 lts of liquid which contains 20% of the liquid and the rest is water. He then mixes it with 10 lts of another mixture with 30% of liquid.What is the % of water in the new mixture?

If a man buys 1 lt of milk for Rs.12 and mixes it with 20% water and sells it for Rs.15, then what is the percentage of gain?

Pipe A can fill a tank in 30 mins and Pipe B can fill it in 28 mins.If 3/4th of the tank is filled by Pipe B alone and both are opened, how much time is required by both the pipes to fill the tank completely ?

If on an item a company gives 25% discount, they earn 25% profit. If they now give 10% discount then what is the profit percentage.
(a) 40%
(b) 55%
(c) 35%
(d) 30%
(Ans . D)

A certain number of men can finish a piece of work in 10 days. If however there were 10 men less it will take 10 days more for the work to be finished. How many men were there originally?
(a) 110 men
(b) 130 men
(c) 100 men
(d) none of these
(Ans . A)

In simple interest what sum amounts of Rs.1120/- in 4 years and Rs.1200/- in 5 years ?
(a) Rs. 500
(b) Rs. 600
(c) Rs. 800
(d) Rs. 900
(Ans . C)

If a sum of money compound annually amounts of thrice itself in 3 years. In how many years will it become 9 times itself.
(a) 6
(b) 8
(c) 10
(d) 12
(Ans A)

Two trains move in the same direction at 50 kmph and 32 kmph respectively. A man in the slower train observes the 15 seconds elapse before the faster train completely passes by him. What is the length of faster train ?
(a) 100m
(b) 75m
(c) 120m
(d) 50m
(Ans B)

How many mashes are there in 1 square meter of wire gauge if each mesh
is 8mm long and 5mm wide ?
(a) 2500
(b) 25000
(c) 250
(d) 250000
(Ans B)

x% of y is y% of ?

(a) x/y
(b) 2y
(c) x
(d) can t be determined

The price of sugar increases by 20%, by what % should a housewife reduce the consumption of sugar so that expenditure on sugar can be same as before ?
(a) 15%
(b) 16.66%
(c) 12%
(d) 9%
(Ans B)

A man spends half of his salary on household expenses, 1/4th for rent, 1/5th for travel expenses, the man deposits the rest in a bank. If his monthly deposits in the bank amount 50, what is his monthly salary ?
(a) Rs.500
(b) Rs.1500
(c) Rs.1000
(d) Rs. 900
(Ans C)

The population of a city increases @ 4% p.a. There is an additional annual increase of 4% of the population due to the influx of job seekers, find the % increase in population after 2 years ?

The ratio of the number of boys and girls in a school is 3:2 Out of these 10% the boys and 25% of girls are scholarship holders. % of students who are not scholarship holders.?

15 men take 21 days of 8 hrs. each to do a piece of work. How many days of 6 hrs. each would it take for 21 women if 3 women do as much work as 2 men?
(a) 30
(b) 20
(c) 19 }
(d) 29
(Ans . A)

A cylinder is 6 cms in diameter and 6 cms in height. If spheres of the same size are made from the material obtained, what is the diameter of each sphere?
(a) 5 cms
(b) 2 cms
(c) 3 cms
(d) 4 cms
(Ans C)

A rectangular plank (2)1/2 meters wide can be placed so that it is on either side of the diagonal of a square shown below.(Figure is not available)What is the area of the plank?
( Ans :7*(2)1/2 )

What is the smallest number by which 2880 must be divided in order to make it into a perfect square ?
(a) 3
(b) 4
(c) 5
(d) 6
(Ans . C)

A father is 30 years older than his son however he will be only thrice as old as the son after 5 years what is father s present age ?
(a) 40 yrs
(b) 30 yrs
(c) 50 yrs
(d) none of these
(Ans . A)

An article sold at a profit of 20% if both the cost price and selling price would be Rs.20/- the profit would be 10% more. What is the cost price of that article?

If an item costs Rs.3 in 99 and Rs.203 in 00.What is the % increase in price?
(a) 200/3 %
(b) 200/6 %
(c) 100%
(d) none of these
(Ans . A)

5 men or 8 women do equal amount of work in a day. a job requires 3 men and 5 women to finish the job in 10 days how many woman are required to finish the job in 14 days.
a) 10
b) 7
c) 6
d) 12
(Ans 7)

A simple interest amount of rs 5000 for six month is rs 200. what is the anual rate of interest?
a) 10%
b) 6%
c) 8%
d) 9%
(Ans 8%)

In objective test a correct Ans score 4 marks and on a wrong Ans 2 marks are ---. a student score 480 marks from 150 question. how many Ans were correct?
a) 120
b) 130
c) 110
d) 150
(Ans 130)

An artical sold at amount of 50% the net sale price is rs 425 .what is the list price of the artical?
a) 500
b) 488
c) 480
d) 510
(Ans 500)

A man leaves office daily at 7pm A driver with car comes from his home to pick him from office and bring back home.One day he gets free at 5:30 and instead of waiting for driver he starts walking towards home. In the way he meets the car and returns home on car He reaches home 20 minutes earlier than usual. In how much time does the man reach home usually?
(Ans . 1hr 20min)

A works thrice as much as B. If A takes 60 days less than B to do a work then find the number of days it would take to complete the work if both work together?

How many 1 s are there in the binary form of 8*1024 + 3*64 + 3
Ans . 4

In a digital circuit which was to implement (A B) + (A)XOR(B), the designer implements (A B) (A)XOR(B) What is the probability of error in it ?

A boy has Rs 2. He wins or loses Re 1 at a time If he wins he gets Re 1 and if he loses the game he loses Re 1.He can loose only 5 times. He is out of the game if he earns Rs 5.Find the number of ways in which this is possible?
(Ans . 16)

If there are 1024*1280 pixels on a screen and each pixel can have around 16 million colors. Find the memory required for this?
(Ans . 4MB)

On a particular day A and B decide that they would either speak the truth or will lie. C asks A whether he is speaking truth or lying? He Ans wers and B listens to what he said. C then asks B what A has said B says "A says that he is a liar" What is B speaking ?
(a) Truth
(b) Lie
(c) Truth when A lies
(d) Cannot be determined
Ans . (b)

What is the angle between the two hands of a clock when time is 8:30
Ans . 75(approx)

A student is ranked 13th from right and 8th from left. How many students are there in totality ?

A man walks east and turns right and then from there to his left and then 45degrees to his right.In which direction did he go ]
(Ans . North west)

A student gets 70% in one subject, 80% in the other. To get an overall of 75% how much should get in third subject.

A man shows his friend a woman sitting in a park and says that she the daughter of my grandmother s only son.What is the relation between the two
Ans . Daughter

CAT Lessons--Quantitative Aptitude
================================

Targeting High marks in CAT,Improve your Quant.....

Numbers
=========
In last post we discussed about finding unit digit of a large power using Fermat's theorem and co-prime Technique.Now move 1 step forward,Find last 2 digits.
To find tens digit or last two digits, we will follow the same techniques except for this time we will divide by 100. 100 has 40 relative primes.
100(1-1/2)(1-1/5)=40

So to find tens digit of 69^83 we will divide 83 by 40 [power by relative primes]. We will get 3 as remainder. So we are left with 69^3 divided by 100.
this can be done manually by multiplying only the last 2 digits.
we will get 69.

Similarly we can do it for last three digits, method remains same but this time we will divide by 1000.
also remember,no. of co-primes for 1000=1000(1-1/2)(1-1/5)=400


Some examples are given
========================
* “What will be the remainder when 68^66 is divided by 5”.

First find relative primes of 5 [ 5 is prime so its relative primes are 4]
Now divide the power of 68^66 by 4, so we get 2.
Now we are left with 68^2 divided by 5.
Do 8^2/5, will get remainder as 4.

Suppose the base of numerator and denominator are not relative primes then take out the relative prime from Nr and Dr and multiply it in the end.


*Find the remainder when 78^67 is divided by 8.

Here we take out 2 from base of Nr and Dr. Hence we are left with
2*{39^67/4}.
Applying our usual method to get remainder as 3 multiplying with 2 to get the result as 6.


More posts on quant and DI are coming soon......

Important Number Questions
===========================
Some typical number questions are given in this posts.The variants of the same questions are frequently coming in CAT and various other competitive exams like XAT,GMAT,MAT,IIFT,Symbiosis....So have a look at these questions...


1*Find the number of factors 24 has?

Explanation:-
24 can be written as 2^3*3.
We know that if N=a^m*b^n. Then the number of factors of N is (n+1)*(m+1)
Here we have, number of factors= (3+1) (1+1) = 8.

2*Find the least number with no. of factors as 24.

Explanation:-
A number can have 24 factors,
If its in the form, N=a^23,
or a*b^11
or a^2*b^7
or a^3*b^5
or a*b*c^5
or a*b*c*d^2 .

Here if we want to find the smallest number we need to fit in the smallest prime numbers as far as possible.
So better if you put the last choice, a*b*c*d^2, also put d=2,c=3,b=5,a=7
So the number becomes 2^2*3*5*7 ie
4*3*5*7= 420.
So this is the smallest number with 24 factors.
If we put any other forms of the number, the resulting number will be higher than 420.

*A number has unequal prime factors and the total number of factors is 4.
The sum of the factors without 1 and the number itself is 30. Find the smallest number with this characteristics.

Explanation:-
The number with 4 factors can be with the form a^3 or a*b.
Since its given that number has unequal prime factors, it can take the form of a*b.
Then the factors are 1, a, b, ab where ab is the number itself.
The condition given is a+b=30, where a and b are prime numbers.
a,b can be 7 & 23
11 & 19
13 & 17.
Then the smallest number is 7*23 = 161.

*How many numbers are there <1000, which has exactly 3 factors.

Only squares of prime numbers have exactly 3 factors.
So we need to find the number of prime number squares<1000.
The highest prime number square less than 1000 is 31^2.
So all prime number squares up to 31 can be regarded as the answer.
They are squares of 2,3,5,7,11,13,17,19,23,29,31.So there are total 11 numbers.
So answer is 11.

Feel free to post new questions in these topics..

Data Interpretation for CAT--Introduction & Basic Fundas
===================================================

Data interpretation is one most critical section in CAT and other management exams which can become a nightmare for a lot of students. In this section, different caselets with 4-5 questions will be there. The questions and pattern in this section may change year after year, so always make sure that you score the cut-off marks for DI section and be safe.

The questions can be normal puzzles, numbers based puzzles, pattern matching, graph based caselets, game based caselets….

You must be fast in calculations, especially with fractions and percentages, in order to score high marks in DI section. Also in lot of graph based questions, you can answer them by mere observation alone.

If you analyze the DI questions, in recent CATS, a lot of reasoning questions are also appearing in CAT DI.

Some important concepts helpful in CAT-DI

Percentage concepts
===================

When a number becomes double, we say that it increased by 100%.
Also if it becomes thrice,the number increased by 200%.
ie the percentage increase ,if number got multiplied by ‘n’ times is
(n-1)*100.
If the number increases 14 times,the percentage increase is (14-1)*100=1300%

Similarly,if we say that a number got percentage increase of 1200,we mean that it became,{(1200/100) +1} ie 13 times its original value.

Also finding the squares of numbers, quickly is another important need for scoring high marks in DI section.

Fast way of finding Squares of numbers.
===================================
For finding squares of all numbers,we have a rather easy way.

Eg 1.Find the square of 32.

(32-2)*(32+2)+2*2= 30*34+4=1020+4=1024.

The advantage of this method is that we are converting the squaring procedure to a single digit multiplication plus addition. This is quite easy compared to the usual 2-digit multiplication.
In the example given above,the 32*32 multiplication is changed to a simple single digit multiplication of 34*3. and addition.

Eg. 2. Find the square of 26.

(26-6)*(26+6)+6*6=20*32+36=640+36=676
or this can be done in one more way,
(26+4)(26-4)+4*4=30*22+16=660+16=676.

Both ways are easier than the original multiplication of 26*26.

We can do any square using this method; however we need to improve our speed in single digit multiplication.

Faster way of finding Square-roots of numbers
=========================================

Finding approximate roots of numbers can also be useful in DI sections.
We have an easy method for that too.

Eg1. Suppose we need to find the root of 30.

The largest number with its square within 30 is 5(5*5=25).
Now 30/5 is 6.
So square root of 30 is (5+6)/2 = 5.5

If you take the square root of 30,it will come to 5.477. Approximately 5.5.

Eg2. Find the root of 40.

The largest number with its square within 40 is 6(6*6=36).
Now 40/6 is 6.667
So square root of 40 is (6+6.667)/2 = 6.333.
If you take the square root of 40,it will come to 6.324. Approximately 6.333.

Quantitative Aptitude Techniques.
--------------------------------------------
Here we will discuss some more quantitative methods for typical MBA examination questions.


Highest power of a number in a factorial.
--------------------------------------------------

This is a typical CAT question, which is being asked for many competitive entrance exams.
To find out the highest power of a no. in a factorial, we should find the no. of times the particular no. is repeating in that factorial. Hence we will divide the factorial no. continuously until we get a no. less than the original divisor.


Eg.Find the highest power of 5 in 100!

5)100
5)20
5)4.
Therefore the max. power of 5 in 1001! is 20+4=24

If the divisor is a composite no, we need to find the highest power of all the prime no. components and we can fix the highest power of the no, as the power of largest prime num. component.

Eg. Find the highest power of 10 in 100!
As we know 10 =5*2( both are prime numbers.)
Also 5>2.
So we need to find the highest power of 5 in 100! And this will be the answer.
(Anyway the highest power of 2 is more than that of 5, but we can’t take that since,
for getting a 10 we need both 5 and 2, so whichever is least, only that many 10s will be there).

Number of zeroes in a factorial.(n!)

The num. of zeroes will depend on the highest power of 10 in that factorial. That in turn depends on the highest power of 5( as we mentioned earlier.)

****In any number system, the number of zeroes depends on the highest power of the base number of that factorial****




Expressing a number as the difference between 2 squares.
--------------------------------------------------------------------

Suppose we have a number N=a.b
We can express N as
N= a.b=(a+b/2)^2-(a-b/2)^2
So we conclude that
In order for N to be an integer, both a &b should be either odd or even.
****So any multiple of 4 can be expressed as the difference between 2 squares.****

Lets take an example.

a.How many ways we can express 24 as the difference between 2 squares?
Explanation:-

24=1*24(format N=a*b)
24=2*12
24=3*8
24=4*6

Here 2*12 and 4*6 are the 2 forms where both a and b are even or odd. So 24 can be expressed as the difference between 2 squares in 2 ways.

2*12 as 7^2-5^2
4*6 as 5^2-1^2

Odd
-----
All odd prime no. can be expressed in only 1 way
Odd composite no. can be expressed in more than 1 way

Even
-------
4 can be expressed in only 1 way.
Prime multiple of 4 can be expressed in only 1 form.
Other multiples of 4 can be expressed in more than 1 form.
Non multiples of 4 can’t be expressed as difference between 2 squares.

Eg.
How many no. are there below 1000,that can’t be expressed as a difference between two squares?
Explanation:-

All odd num. can be expressed as the difference between two squares.
In even num., only which are non-multiples of 4 can’t be expressed.
So in 999 num. 499 even numbers are there.
Out of which ,250 are multiples of 4.
So non- multiples are 499-250=249.
So the answer is 249.

Online CAT Lessons
-------------------------

In CAT ,in Quantitative section,we can save a lot of time by eliminating the answer options,and divisibility checks comes in handy in this process.especially if you know the checks for prime numbers like 11,13,17...
So lets check out this quantitative methods...

Divisibility Checks for 11

We know that rem (10^1/11)=-1
Therefore the rem(10^2/11)=+1

So for a no. in the form ‘abcdef’, the divisibility can be checked by taking the diff. b/w
Sum of the odd numbered digits and even numbered digits.Check whether that difference is divisible by 11.If that is divisible then the large no. is divisible by 11.

Eg. Take the no. 1331
D
Odd numbered dig. Are 1,3 from right, sum =4
Even numbered dig. are 3,1 from right , sum =4
Difference of the sum is 0. So its divisible by 11

Divisibility Checks for 13

We know that rem (10^3/13)=-1
Therefore the rem(10^6/13)=+1

So for a no. in the form ‘abcdef’, the divisibility can be checked by taking the diff. b/w
abc and def. Check whether that difference is divisible by 13.If that is divisible then the large no. is divisible by 13.

Eg. Check the divisibility of 214175?
Split the no. in to 2 as 214 and 175.
214-175= 39
Since the difference 39 is divisible by 13, the no. 214175 is also divisible by 13.

Divisibility Checks for 17

We know that rem (10^9/17)=-1
Therefore the rem(10^18/17)=+1

So for checking the divisibility of 17,we need to take blocks of 9 digits and do the same procedure as we do for that of 7 or 13.

The knowledge of divisibility of various numbers will help you to eliminate some answer options without doing a single calculation. This types of small time savings can make a big difference in the whole exam.(As I said earlier, reaching answer quickly is the important thing…..)

Online CAT Lessons:-
---------------------------
Divisibility Checks for various digits.
===============================================

Its always advantageous to know the divisibility rules of various digits so that we can save a lot of time during our calculations and its extremely useful for elimination of answer choices.
In an exam like CAT or GMAT, the most important thing is not to arrive at the answer, but arrive at the answer fast if possible, without doing any calculation you will have to find the answer. So,when you get an objective type question,uy first aim should be to eliminate at least 2 options. The knowledge in rules like divisibility, factors etc will come handy there.

The basic rule in finding the divisibility of a number is that we should find a power of 10(if we r using decimal system) which is completely divisible by the specific digit.
Or we need to find the power which gives a rem. of +/-1.

Divisibility Checks for 2
----------------------------------
We know that rem (10/2)=0.
ie rem(10^1/2) = 0.So we need to check the last digit of a no. only for checking its divisibility by 2.
****The last digit should be 2,4,6,8 or 0.****

Divisibility Checks for 3
-----------------------------------
We can write any no. in decimal abc in the form 100a+10b+c
Again, abc = 99a+9b+(a+b+c)

Here except the last term,all terms are divisibe by 9 hence also by 3
Hence if the term ( a+b+c) which is the digit sum of the no. is divisible by 3,the no.abc is divisible by 3.

****The digit sum of a no. should be a multiple of 3****

Divisibility Checks for 4
----------------------------------
We know that rem (10^2/4)=0.
So we need to check the last 2 digits of a no. for checking its divisibility by 4.

****The last 2 digits should be divisible by 4.****

Divisibility Checks for 5
-----------------------------------
The last digit should be 5 or 0.

****The last digit should be divisible by 5 or 0.****


Divisibility Checks for 6
-----------------------------------
6=2*3.
A no. is divisible by 6,if its divisible by both 2 &3.

****The no. should be divisible by both 2 &3****

Divisibility Checks for 7
------------------------------------
We know that rem (10^3/7)=-1.
therefore rem(10^6/7) = +1.
So if we need to check the divisibility of a 6 digit number 'abcdef'
we need to split the number in to 2, 'abc' and 'def'
Now we need to take the difference between the two numbers and check whether its divisible by 7.If its divisible,then the large number is divisible by 7.

Divisibility Checks for 8
------------------------------------
We know that rem (10^3/8)=0.
So we need to check the last 3 digits of a no. for checking its divisibility by 8.

****The last 3 digits should be divisible by 8.****

Divisibility Checks for 9
-------------------------------------
We can write any no. in decimal abc in the form 100a+10b+c
Again, abc = 99a+9b+(a+b+c)

Here except the last term,all terms are divisibe by 9.
Hence if the term ( a+b+c) which is the digit sum of the no. is 9,the no.abc is divisible by 9.

****The digit sum of a no. should be 9****

The divisibility check for higher prime numbers will be given in next lesson

Lets start with the most important section in Quantitative section,Numbers..

Numbers
================
Numbers has lot of properties to be studied in detail and certain set piece questions are there.from where CAT questions are frequently coming..

Power cycle
Power cycle for digits 2,3,4,5,6,7,8,9

Divisibility checks
2,3,4,5,6,7,8,9,11,13…

Remainder questions
a) Using power cycle
b) Using binomial theorem

Highest power of a number in n!

Problems related to factors of a number
No. of factors.
Sum of factors
No. of co-primes
Product of factors

Express a no. in different forms
Expressing as difference of squares.

Fermats theorem
Eulers no.
Solving remainder questions using Fermat’s Theorem

Miscellaneous properties
1.Properties of a^n- b^n when ‘n’ is odd,even…
2.n^p-p when p is prime.

a. Lets start with Power cycles

****The frequency of the power cycles of various digits is very important.
This helps you to solve remainder questions involving large powers.*****

Let us take some example.

1. Find the remainder of 3^75/5?

Explanation:-

We know the power cycle frequency of 3.Its 4and the power cycle is 3,9,7,1
So convert the large power in the question (here 75) to a much smaller number using this freq. 75=4*18+3
Therefore 3^75 is now 3^{(4*18)+3},this can still be shortened as 3^3 only.
Since the other power frequencies will be repeating only.
Hence our question reduces to finding rem. of 3^3/5
This is quite easy, 27/5,rem. is 2.(or since we know power cycle of 3,3^3 ends with 7,so remainder is 7/5=2).

2.Find the remainder of 2^102/3?

Explanation:-
We know the power cycle frequency of 2.Its 4and the power cycle is 2,4,8,6.
Now we convert the large power in the question (here 102) to a much smaller number using this freq. 102=4*25+2.
Therefore 2^102 is now 2^{(4*25)+2},this can still be shortened as 2^2 only.
Since the other power frequencies will be repeating only.
Hence our question reduces to finding rem. of 2^2/3.Its 4 /3,remainder is 1.

OR

This question can be done in a very easy method.
We knew that rem. of 2/3 is -1.

3.Find the rem. of {(2^203)*(3^506)}/5?

Explanation:-
Here we can use the fact that ,

*****The rem. of a product is the product of the individual rem.****

So the ques. changes to rem(2^203)/5 * rem.(3^506)/5
Rem(2^203)/5 can be found out by using power cycle..
203 = 4*50 +3 (since 4 is power cycle freq of 2).
So rem(2^203)/5 changes to rem2^3/5 ie rem8/5 =3.

Rem(3^506)/5 can also be found out by using power cycle.
506=4*126+2 (since 4 is power cycle freq of 3).
So rem(3^506)/5 changes to rem3^2/5 ie rem9/5 =4

Now indiv. rem. are 3 and 4.
Whole remainder is rem(3*4/5) { since the product is greater than devisor,we need to take rem.of the product again.
So answer is rem(12/5) ie 2.


Now rem. of 2^102/3 is equivalent to (rem. 2/3) ^102 that is (-1)^102 =1.

****For finding out the unit place of a very large power of a no. we can use power cycle****



Points to be remembered.
===============================

The frequency of the power cycles of various digits is very important.
This helps you to solve remainder questions involving large powers.
The rem. of a product is the product of the individual rem.
For finding out the unit place of a very large power of a no. we can use power cycle.