new - rec - intro - aptitude - june 2007

8/8/2019 New - Rec - Intro - Aptitude - June 2007

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An Initiative with a Difference


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QUANTATIVE APTITUDE, PUZZLES,ANALYTICAL or LOGICAL REASONING

Analytical reasoning questionsare based on a fictional situation

described by a group of rules orconditions that establishesrelationships among persons,

places,things, orevents.Analytical questioningfalls in three categories

:Order,Inclusion,Causation.


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Data SufficiencyData Sufficiency questions test your ability to"reason quantitatively." This stands in sharp

contrast to the problem solving section, whichis designed to test how well you manipulatenumbers. If you find yourself doing a lot of

number crunching on the data sufficiencyquestions, you are doing something wrong.


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The Answer ChoicesData Sufficiency questions will all have the exact same

answer choices. Memorize these answer choices beforeyou take the exam. It will help you better utilize your timein the quantitative section. The answer choices aresummarized below as you will see them on the exam.

A. Statement 1 alone is sufficient but statement 2 alone is not

sufficient to answer the question asked.B. Statement 2 alone is sufficient but statement 1 alone is not

sufficient to answer the question asked.C.Both statements 1 and 2 together are sufficient to answer

the question but neither statement is sufficient alone.D.Each statement alone is sufficient to answer the question.E. Statements 1 and 2 are not sufficient to answer the

question asked and additional data is needed to answerthe statements.


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The following table summarizes howelimination functions with Data Sufficiencyproblems.

Statement Choices Eliminated

(1) is sufficient B, C, E

(1) is not sufficient A, D

(2) is sufficient A, C, E

(2) is not sufficient B, D

(1) is not sufficient and (2) is not sufficient A, B, D


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Ifkis a positive integer, is ka multiple of 40 ?Statement (1) kis multiple of 4Statement (2) kis a multiple of 10

The correct answer is choice (5).You're asked about whetherkis a multiple of 40. This will be true ifkisdivisible by 40.Statement 1 tells you that kis a multiple of 4. That means that kcouldbe, for instance, 8 or 80. 8 is not a multiple of 40 while 80 is a multiple of40, so Statement 1 is not sufficient to answer the question in the stem.

Statement 2 tells you that k is a multiple of 10. That means that kcouldbe, for instance, 20 or 80. 20 is not a multiple of 40 while 80 is a multipleof 40, so Statement 2 is not sufficient to answer the question in thestem.Now combine the statements. This is the tricky part. You might haveassumed that since 40 is the product of 4 and 10, that kmust be amultiple of 40. But again, try finding a number that's a multiple of both 4and 10, but not of 40. In fact, kcould equal 20. So the statements, evenwhen combined, are not sufficient to tell you whetherkis a multiple of40 or not.


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Data Sufficiency

The set S of numbers has the followingproperties: I) If x is in S, then 1/x is in S.

II) If both x and y are in S, then so is x + y.

Is 3 in S? (1) 1/3 is in S. (2) 1 is in S.


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Data Sufficiency

Are the majority of salespeople employed by XYZCompany commissioned?

1. The number of salespeople employed by XYZCompany exceeds the number of employees atXYZ

Company who are not salespeople.2. The percentage ofXYZCompany's salespeoplewho are commissioned exceeds the percentage ofemployees at XYZCompany who are salespeople.

1. This problem involves the concept of proportion.2. In order to answer the question posed here, you need

information about the number of commissionedsalespeople relative to the number of non-

commissioned salespeople.


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How much more does it cost to send a parcel weighing 16.5 pounds byexpress delivery than to send the same parcel by ground delivery?(A) $3.45(B) $9.00(C) $11.55(D) $15.00

(E) $16.60


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By approximately what percent does the average air delivery cost perpound for a 21-pound parcel exceed the average ground delivery cost

per pound for a 28-pound parcel?(A) 33(B) 46(C) 67(D) 80(E) 130


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Marketing expenses trailed production expenses by about the same

percentage during which of the following two years?(A) 1990 and 1992(B) 1991 and 1992(C) 1991 and 1993(D) 1992 and 1993(E) 1990 and 1994


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Consider aggregate legal and production expenses for each year shown.With respect to the two years during which this aggregate amount wasmost nearly the same, average annual marketing expenses totaledapproximately(A) $5.5 million(B) $6.1 million(C) $6.5 million(D) $7.2 million(E) $8.0 million


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Probability = (# of favorable outcomes) / (# of

possible outcomes)

Example 2. Two fair six-sided dice arerolled; what is the probability of having 5 asthe sum of the numbers?

Solution

There are 36 possible outcomes when a pairof dice is thrown (six outcomes for the first

die times six outcomes for the second one).Since four of the outcomes have a total of 5[(1,4), (4,1), (2,3), (3,2)], the probability of thetwo dice adding up to 5 is 4/36 = 1/9.


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Probability of Multiple Events

NOT tool If you know that the probability of an event (or one of the outcomes) is p,

the probability of this event NOT happening (or the probability of it NOThaving this given outcome), is (1-p).

p(not A) + p(A) = 1

AND tool If two (or more) independent events are occurring, and you know the

probability of each, the probability of BOTH (or ALL) of them occurringtogether (event A and event B and event C etc) is a multiplication of theirprobabilities. p(A and B) = p(A) * p(B) p(A and B and C ... and Z) = p(A) *p(B) * p(C) * ... * p(Z) Suppose I will only be happy today if I get an emailand win the lottery. I've a 90% chance to get an email and 0.1% chanceto win the lottery. What are my chances for happiness? Since email andlottery are independent (getting an email doesn't change my lotterychances, and vice versa), we can use the AND tool: p(email and lottery)= p(email) * p(lottery) = 90% * 0.1% = 0.09%; So I have 9 chances in10,000... Not bad.


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Probability of Multiple Events

OR tool If two (or more) incompatible events are occurring, the

probability of EITHER of them occurring (event A or event Bor event C etc) is a sum of their probabilities.

p(A or B) = p(A) + p(B) p(A or B or C ... or Z) = p(A) + p(B) +... + p(Z) Incompatible means that they can't happentogether, i.e. p(A and B) = 0. In case of two compatibleevents, the OR tool looks a bit more complicated:

p(A or B) = p(A) + p(B) - p(A and B) If we know that A and Bare independent, we can apply AND tool to rewrite:

p(A or B) = p(A) + p(B) - p(A) * p(B) Suppose I will now behappy in both cases - either getting an email or winning thelottery. What are my chances to happiness now? p(email orlottery) = p(email) + p(lottery) - p(email) * p(lottery) = 90% +0.1% - 0.09% = 90.01%; My chances are 9,001 in 10,000

now. I'd rather choose this one.


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ORDER

A sales representative plans to visit each of 6 companies-

M, N, P, Q, R, S exactly once during the course of oneday.He is setting up his schedule for the day according tothe following conditions:

1.He must visit M before N and before R

2.He must visit N before Q

3.The third company he visits must be P.

Which of the following could be the order in which thesales representative visits the six companies?

A) M,R,N,Q,P,S B)M,S,P,N,R,Q

C)P,R,M,N,Q,S

D)P,S,M,R,Q,N

E)Q,N,P,R,S,M


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ORDER

Three men (Tom, Peter and Jack) and three women

(Eliza, Anne and Karen) are spending a few months at ahillside. They are to stay in a row of nine cottages,each one living in his or her own cottage. There are noothers staying in the same row of houses.

Anne, Tom and Jack do not want to stay in any cottage,

which is at the end of the row.

Eliza and Anne are unwilling to stay besides anyoccupied cottage..

Karen is next to Peter and Jack.

Between Anne and Jacks cottage there is just onevacant house.

None of the girls occupy adjacent cottages.

The house occupied by Tom is next to an end cottage.


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1. How many of them occupy cottages next to avacant cottage ?

A. 2B. 3C. 4D. 5E. 6

Ans : C

1 2 3 4 5 6 7 8 9

TOM KAREN PETER JACK ANNE ELIZA

Anne, Tom and Jack Tom Tom Eliza

X O X O


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1. Which among these statement(s) are true ?I. Anne is between Eliza and Jack.II. At the most four persons can have occupied

cottages on either side of them. .

III. Tom stays besides Peter.

A. I onlyB. II onlyC. I and III onlyD. II and III only

E. I, II and III

Ans : C

1 2 3 4 5 6 7 8 9

TOM KAREN PETER JACK ANNE ELIZA

Anne, Tom and Jack Tom Tom Eliza

X O X O


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INCLUSION

Two collectors Ram and Lakshman are each selecting agroup of three wild life prints from a group of seven prints-T,U,V,W,X,Y, and Z. No print can be in both groups. Theselection made by Ram and Lakshman are subject tofollowing restrictions:

If U is in Rams group W must be inLakshmans group.

If X is in Rams group then Z must be inLakshmans group.

T and Z cannot be in the same group.

W and Y cannot be in the same group.

IfX is in Rams group any one of the following could be in

Lakshmans group except: A)T

B)U

C)V

D)W

E)Z


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CAUSATION

A scientist is conducting an experiment with sevensubstances:F,G,M,N,O,R,and X

O destroys R if either X or M is present.

G and F together produce R

M produces N

X is destroyed by F if N is present

If F,O,R ,and X are present which of the following musthappen:

A) F destroys X

B)F produces R C)O destroys R

D)O produces M

E)X destroys N


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X or M G & F

IfF,O,R ,and X are present which of the following must happen:

A) F destroys X

B)F produces R

C)O destroys R

D)O produces M

E)X destroys N

X

F

N

R

G F

RO

X M

N

M


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WHO'S TELLING THE TRUTH?

A says B lies.B says C lies.C says A & B both lie.Is anyone telling the truth?

If A is telling the truth, then B's lie means that C is tellingthe truth.If A is lying then B is telling the truth.IfB is telling thetruth, then A must have lied.That also means that C is lying,which IS possible since hesaid that BOTH A and B were lying, and that is a lie aboutB.So B alone is telling the truth.


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A recent murder case centered around six men Mark, Fillip, Graham, Walt, Hunt and Clarkwho play the roles of Murderer, Victim, Witness, Judge, Policeman, Hang man, but not in thesame order. The victim died instantly.The witness did not see the crime committed but swore thearing the altercation followed by a shot.After a lengthy trial the murderer was convicted and

sentenced to death and hanged.

1. Mark knew both the victim and the murderer.2. In court judge asked Clark to give his account of the shoo ting3. Walt was last of the six to see Fillip alive.4. The Police man testified that he picked up Graham near the place where the body was fou5. Hunt and Walt never met.

What role did each of the following play in the melodrama?

y Murderery Victimy Judgey Witness

Mark Fillip Graham Walt Hunt Clark

Murderer X O OVictim X O OWitness O

Judge O XPoliceman X OHang man O


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Sherl l es r. tson ere on the trail of a ang ofri inals. he gang onsisted of four en: ones,Brown,Smith,and

hite. wo of them were nown as ank robbers,another a knownforger,and the fourth a blackmailer. bserved by holmes,the four men

boardeda trainandsat inseparatecompartmentswhichwerenumbered, , ,and 4. ones,whowasnt abankrobbersat incompartment . hitewas incompartment number and the forger incompartment . olmesalso knew that Smith had worked with one of the bank robbers in thepast but not theother.

anyou identify the forger?

ones Brown Smith hite

bankrobbers

forger

blackmailer

4

bankrobbers

forger

blackmailer

Smith ones hite Brown


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Kim Jones,Jan, Robinson & Pat Smithare are the officers of thespaceship.They serve as the crafts pilot engineerand biochemist, thoughnot necessarily in the same order. Because they have difficulty withMartians names, they nickname the 3 Martians who work with them as

Jones, Smith & Robinson.1. Robinson is a Yomi.2. Jones doesnt speak any language otherthan Martian.3. All Martians linguists are Uti.4. The Martian, who serves as interpreter, respects the Martian whose

name is the same as the biochemists5. The Martian whose name is same as the biochemist is a Grundi.6. Jan Robinson beat the engineerat Chess.

ho is the Pilot?

Jones Smith Robinson

Uti X O

Yomi O

Grundi O

Kim Jones Jan Robinson Pat Smithare

pilot O

engineer X O

biochemist O X


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A Jeweler is preparing a window to display gems. There is a leftdisplay case & a right display case. In each display case, he willshow 3 of the 7 gems: an amethyst, a diamond, an emerald, agarnet, an opal, a ruby and a sapphire. The gems must be shown

as per the following instructions:---The amethyst must be included in the window & shown in theleft display case.--The diamond must be included in the window & shown in theright display case.--The ruby can neither be shown in the same display case as thediamond or garnet.--The emerald and the sapphire must be included in the window& shown together in the same display case.

LEFT

amethyst

emerald

sapphire

amethyst ruby opalamethyst garnet opal

RIGHT

diamond emerald sapphirediamond garnet opal


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LEFT

a et yst e eral sa ire

a et yst r y opal

a et yst garnet opalI T

ia ond e erald sapphire

dia ond garnet opal

. hichoneof the followingcombinationsofgemscanbeshown in the

left displaycase a. methyst, opal , r byb. methyst, emerald, opalc. methyst garnet sapphired. methyst, diamond, r bye. iamond, emerald, sapphire


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LEFT

a e hys e erald sapphirea e hys ruby opala e hys garne opal

RIGHTdia ond e erald sapphire

dia ond garne opal

1. I sapphire is shown in he righ display case,which one o he ollowing pairs could be shownin he le display case?

a. Emerald & garneb. Emerald & opalc. Emerald & diamondd. Garne & rubye. Opal & ruby


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WORD PROBLEMS

The most difficult part of a word problem iscorrectly translating words to an algebraicequation. Here are our best tips for approachingword problems:

1) First, choose a variable to stand for the leastunknown quantity and then write the otherunknown quantities in terms of that variable.2) Second, write an equation based on the

situation given. Most test problems pivot on twoquantities being equal.3) Solve the equation and interpret the result.


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Examples:

1) A certain book costs $12 more in the local retail bookstore than onAmazon.com.If Amazon's price is 2/3 of the retail price, how much does the book costretail?Solution: We are told to determine the retail price, R.From the narrative, we know that:Retail Price R = Amazon price + 12, or R = 2/3 R + 12

Solving for R, we find that the retail price is $36.00

2) During a spill the amount of milk in a tank was reduced by a third.If the amount of milk in the tank was 8,000 gallons immediately after thespill, how many gallons of milk were lost during the spill?

Solution: We are told that one third of the milk was spilled,leaving 8,000 gallons.Let M equal the total amount originally in the tank:M - 1/3 (M) = 8,000M = 72,000

The amount lost is 1/3 of 72,000, or 2 ,000 gallons


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A restaurant has 27 employees. If there are seven morewaitresses than managers, how many employees arewaitresses?Solution: Let W be the number of waitresses, which iswhat we are being asked to calculate. We know that thenumber of waitresses plus the number of managers = 27.We also know there are 7 more waitresses than managers.

This translates to:Managers + 7 = W or Managers = W - 7Substitute this into the first equation to get:(W - 7) + W = 27Solving for W, we find W = 17. There are 17 waitresses in

the restaurant and 10 managers, totaling 27 employees.

One advantage to the test problems is that the correctanswer will ALWAYS be listed as one of your answer

choices.


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The length of each side of square A is increased by 100% tomake square B. If the length of the side of square B isincreased by 50% to make square C, by what percent is

the area of square C greater than the sum of the areas ofsquares A and B?

(A) 75%(B) 80%(C) 100%

(D) 150%(E) 180

Choice B is correct. We begin by choosing 10 as the

length for a side of square A. This makes the length of aside of square B = 20, and the length of a side of C = 30.The area of squares A, B and C are 100, 00 and 900,respectively. The area of C is greater than the sum of thearea of A and B by 00, or(900 - 500). The percentage

difference is 00/500 x 100 = 80%.


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If the diameter of a circle increases by 50%, by whatpercent will the area of the circle increase?

(A) 25%(B) 50%(C) 100%(D) 125%

(E)225%

Choice D is correct. The fastest way to solve is toselect values for the diameter of the circle and determine

the effect on the area. If the diameter is , the radius is 2and the area is times pi. Increasing the diameter by50% to 6, makes the new radius = 3, and the new area is9 times pi. The percent increase is (9- ) / = 5/ , or 125%.


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Joe and Alex are miles apart. If Joe starts walking toward Alexat 3 miles per hour and at the same time Alex starts walkingtoward Joe at 2 miles per hour, how much time will passbefore they meet?

(A) 20 minutes(B) 28 minutes(C) 3 minutes(D) 8 minutes(E) 60 minutes

Choice D is correct. The distance Joe walks is x. Thismakes the distance Alex walks - x. When they meet, eachwill have walked an equal amount of time. Using the equationDistance = Rate x Time, we get:

Time = Distance/RateJoe's time = Alex's timex / 3 = (4 - x) / 2.Solving for x, the total distance walked is x = 12/5. Plugging this

number back into the rate equation yields: T = D/R = (12/5) / 3

= 4/5 of an hour, or48 minutes.


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Theresa is 10 years older than Cindy. However, 5 years ago,Theresa was twice as old as Cindy. How old is Cindy?

(A) 5(B) 10(C) 12(D) 15

(E) 25

Choice D is correct. Let x be Cindy's age and x + 10be Theresa's age.

5 years ago Cindy's age was x - 5 and Theresa's age was(x + 10) - 5 = x + 5. At that time, Theresa was twice as old asCindy, giving us the following equation: x + 5 = 2(x - 5)solving for x, we get x = 15.


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If crate Q contains only sweaters, how many sweaters arein the crate?(1) If one quarter of the sweaters were removed, the crate

would be filled to one half its capacity(2) If 100 sweaters were added to the crate, it would be full

While neither statement alone allows us to answer thequestion, with both pieces of information, we can

determine the number of sweaters in the crate. Bycombining the capacity of the crate with details of itscontents, we can determine the current number ofsweaters inside.

Let x be the no. of sweaters in a full crate.Let y be the no.ofsweater as in situation 1.Then.75y=.5x. or x=1.5 yAs per situation 2 . y+100=x.Solving for y . y+100=1.5y or 1.5y-y=100 or .5y=100 ory=200 and x=300.


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BIRDS IN A TREETwenty-one birds are sitting in a tree. If a manshot into the tree and killed one-seventh of

them, how many would remain?Zero. After killing three birds (one-seventh),the other 18 would surely fly away, leaving

none in the tree.


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What's the next number in this series?

4 16 37 58 89 145 42 20 (?)

4. The series consists of the sum of the

squares of the digits of the previous number.16 = (4*4)37 = (1*1)+(6*6)58 = (3*3)+(7*7)

and so on.So the next number would be 4, and theseries repeats.


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You have an appointment to meet your friend,the logic professor during the winterholidays when she is on vacation. Today isSaturday. She has told you to meet her threedays after the day before the day after

tomorrow. What day does she expect you?Solution:

Day after tomorrow is Monday us today isSaturday. Day before the day after tomorrowis Sunday. Three days after Sunday is aWednesday


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BANANAS AND TARANTULASThere are three boxes in a South American warehouse,one marked "Tarantulas," one marked "Bananas," and the thirdmarked "Tarantulas and Bananas." You are told that all threeboxes are marked wrong, and you must rearrange the labelscorrectly. Without peeking, you may withdraw only one item fromeach box.What is the minimum number of boxes from which you wouldhave toremove an item in order to be able to correctly label all three?

There are two key elements here: ALL the boxes are labeledwrong, and you pick from the one marked "Bananas andTarantulas."Doing so will allow you to determine the contents of all threeboxes in ONE PICK with absolute certainty:If the B&T pick is a banana, then that box can only be bananas(remember, it's labeled wrong). That means the B box istarantulas, and the T box is bananas & tarantulas.


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You have 9 golf balls, 8 of which are equal in weight.The ninth is slightly heavier then the rest.

You also have a balancing scale.

How can you use this scale two times and only two timesin order to tell which ball is heavier?Solution:Separate the balls into 3 groups of 3.Place 3 balls on the left side of the scale and 3 balls on the right.

If they balance out, you know that the heavier ball is not one ofthose 6.If one side is heavier, you know that the heavier ball is one ofthose 3.

Now for your second use of the scale, place one of theremaining 3balls on the left and one on the right. If they are equal, then it isthe ball that was left out that is heavier. If either side is heavier,then that is the heavier ball.


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I started 2 watches at the same time & foundthat one of them , was running slow by 2mts

per hr., while the other was running fast byone mt. per hr. When I looked at them again,the faster one was exactly one hr ahead of theother. How long had the watches been running?Solution:At zero time say 12 noon watch 1 was behindby 2 minutes and watch 2 ahead by 1 minute.In other words watch 2 was ahead of watch1by 3 minutes. If watch 2 was ahead of watch 1by one hour the watches must have run for(60/3-1) hours or 19 hours.


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A horse travels half its route, with no load,

at 12miles per hr. The rest of the journey aload slows him to 4miles per hr. What is hisaverage speed?

SOLUTION:Let x be the total distance. Let AS beaverage speed.

Therefore X/2*12 + X/2*4=X/AS orX/24+X/8=X/AS or 32X/192=X/AS.1/6=1/AS or AS=6


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Find the missing number in the followingsequences:a)46,656,3125,256,27,----,1

b)3,10,7,8,---,12,9,16Solution:a)4 1,2*2,3*3*3,4*4*4*4,.b) 3,10,7,8,11,12,9,16

3+16=10+9=7+12=8+X


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23 5 12 3 15 13 ?Answer:WELCOME

100 365 24 60 ?Answer: 60. 100 years in a century, 365 days in a year, 24hours in a day, 60 minutes in an hour, & 60 seconds in aminute.3 10 21 44 65 102 ?Answer:133.A very tough one! The numbers represent theodd prime numbers, multiplied by the number for theirplace in the series of odd prime numbers. 3 is the first oddprime number, & because it is first, it is multiplied by 1; 5 is

the second odd prime number, & is thus multiplied by 2,which yields 10, & so on.6 6 7 9 8 6 ?Answer:8. Beginning with Sunday, each numberrepresents the number of letters in each day of the week.


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Example:

If Juan runs 4 km in 30 minutes, how many hours will ittake him to run 1 km?Be careful not to confuse the units of measurement.While Juan's rate of speed is given in terms of

minutes, the question is posed in terms of hours. Onlyone of these units may be used in setting up aproportion. To convert to hours, multiply4 km/30 minutes 60 minutes/1 hour = 8 km/1 hourNow, let n be the number of hours it takes Juan to run

1 km. Then running 8 km in 1 hour is the same asrunning 1 km in n hours. Solving the proportion,8 km/1 hour = 1 km/n hours, we have 8 n = 1, so n =1/8.


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Multiplication and Division

If two positive numbers are multiplied together ordivided, the answer is positive.

If two negative numbers are multiplied together ordivided, the answer is positive.

If a positive and a negative number are multipliedor divided, the answer is negative.

Examples(-2) (-4) =

(8) (-2) = (-4)2 (-3) = (-6)(-2) (-2) = 4


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A. BASIC ARITHMETICPerfect squares include 1, 4, 9, 16, 25, 36,

49, 64, 81, 100Perfect cubes include 1, 8, 27, 64 and 125Commutative property: x + y = y + xAssociative property: (x + y) + z = x + (y +z)Transitive property: If x < y and y < z, thenx < zLike inequalities can be added: If x < yand w < z, then x + w < y + z

Multiplying both sides of an inequality bya negative number reverses the inequality:

If x > y and c < 0, then cx < cy


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Common measurements and conversions:1 foot = 12 inches

1 yard = 3 feet1 quart = 2 pints

1 gallon = 4 quarts1 pound = 16 ounces

1 inch = 2.54 centimeters

1 liter = 1.06 quarts1 kilogram = 2.2 pounds


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Permutation and Combination

Permutation : Permutation meansarrangement of things. The wordarrangement is used, if the order of

things is considered. Combination: Combination means

selection of things. The word selection is

used, when the order of things has noimportance.


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Permutation and Combination

Example: Suppose we have to form a number

of consisting of three digits using the digits1,2,3,4, To form this number the digits have tobe arranged. Different numbers will get formeddepending upon the order in which we arrange

the digits. This is an example of Permutation. Now suppose that we have to make a team of 11

players out of 20 players, This is an example ofcombination, because the order of players in

the team will not result in a change in the team.No matter in which order we list out the playersthe team will remain the same! For a differentteam to be formed at least one player will haveto be changed.


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Addition rule : If an experiment can be performed inn ways, & another experiment can be performed inm ways then either of the two experiments can beperformed in (m+n) ways. This rule can be extendedto any finite number of experiments

Multiplication Rule : If a work can be done in mways, another work can be done in n ways, thenboth of the operations can be performed in m x nways. It can be extended to any finite number ofoperations.Factorial n : The product of first n natural numbersis denoted by n!.

n! = n(n-1) (n-2) ..3.2.1.

Ex. 5! = 5 x 4 x 3 x 2 x 1 =120

Perm tation


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PermutationNumber of permutations of n different things taken r at a time isgiven by:-

nPr = n!/(n-r)!Number of permutations of n different things taken all at a time isgiven by:-nPn = n!Examples

Q. How many different signals can be made by 5 flags from 8-flags of different colours?Ans. Number of ways taking 5 flags out of 8-flage = 8P5= 8!/(8-5)!= 8 x 7 x 6 x 5 x 4 = 6720Q. How many words can be made by using the letters of the wordSIMPLETON taken all at a time?Ans. There are 9 different letters of the word SIMPLETONNumber of Permutations taking all the letters at a time = 9P9

= 9! = 362880.

N b f C bi i f diff hi k i i


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Number of Combination of n different things, taken r at a time isgiven by:-nCr= n! / r ! x (n-r)!Restricted Combinations

(a) Number of combinations of n different things taken r at a time,when p particular things are always included = n-pCr-p.(b) Number of combination of n different things, taken r at a time,when p particular things are always to be excluded = n-pCrExample: In how many ways can a cricket-eleven be chosen out of

15 players? if(i) A particular player is always chosen,(ii) A particular is never chosen.Ans:(i) A particular player is always chosen, it means that 10 players areselected out of the remaining 14 players.

=. Required number of ways = 14C10 = 14C4= 14!/4!x10! = 1001(ii) A particular players is never chosen, it means that 11 playersare selected out of 14 players.=> Required number of ways = 14C11

= 14!/11!x3! = 364


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QuestionA piece of equipment cost a certain factory Rs. 600,000. If it depreciatesin value, 15% the first year,13.5 % the next year, 12% the third year, and so on, what will be itsvalue at the end of 10 years,all percentages applying to the original cost?

(1) 2,00,000(2) 1,05,000

(3) 4,05,000(4) 6,50,000

Explanatory AnswerLet the cost of an equipment is Rs. 100. Now the percentages ofdepreciation at the end of 1st, 2nd, 3rd years are 15, 13.5, 12, which arein A.P., with a = 15 and d = - 1.5. Hence, percentage of depreciation inthe tenth year = a + (10-1) d = 15 + 9 (-1.5) = 1.5 .Also total valuedepreciated in 10 years = 15 + 13.5 + 12 + ... + 1.5 = 82.5Hence, the value of equipment at the end of 10 years=100 - 82.5 = 17.5.The total cost being Rs. 6,00,000/100 * 17.5 = Rs. 1,05,000.


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Question The average age of a family of 5 members is 20 years. If the

age of the youngest member be 10 years then what was theaverage age of the family at the time of the birth of the

youngest member?

1. 13.52. 143. 154. 12.5

Correct Answer is 12.5. Correct Choice is (4)

Explanatory Answer

At present the total age of the family = 5 * 20 = 100

The total age of the family at the time of the birth of the youngest member= [100-10-(10*4)] = 50

Therefore, average age of the family at the time of birth of the youngestmember = 50/4 = 12.5.


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A circle of maximum possible size is cut from a square sheet of board.Subsequently, a square of maximum possible size is cut from the resultantcircle.

What will be area of the final square?

(1)75% of the of the original square(2)50% of the size of the original square(3)75% of the size of the circle(4)25% of the size of the original squareCorrect Answer - (2)Solution:Let the side of the original square be 'a' units. Therefore, the area of theoriginal square = a2 units.The diameter of the circle of maximum possibledimension that is cut from the square will be 'a' units. The diagonal of the

square of maximum possible dimension that can be cut from the circle willbe 'a' units.If the diagonal of the final square is 'a' units, then its area =a2 /2units.Therefore, the area of the new square will be 50% of the area of the originalsquare.


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A father left a will of Rs.35 lakhs between his two daughters aged8.5 and 16 such that they may get equal amounts when each of

them reach the age of 21 years.The original amount of Rs.35 lakhshas been instructed to be invested at 10% p.a. simple interest. Howmuch did the elder daughter get at the time of the will?1)Rs. 17.5 lakhs2)Rs. 21 lakhs3)Rs. 15 lakhs

4)Rs. 20 lakhsCorrect Answer - (2)

Solution:Let Rs.x be the amount that the elder daughter got at the time ofthe will. Therefore, the younger daughter got (35- x).The elder daughters money earns interest for (21 - 16) = 5 years

@ 10% p.a simple interestThe younger daughters money earns interest for (21 - 8.5) =12.5 years @ 10% p.a simple interest.

As the sum of money that each of the daughters get when theyare 21 is the same

X+X*10*5/100 = (35-X)+(35-X)*10*5/100


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The difference between the compound interest and the simpleinterest on a certain sum at 12% p.a. for two years is Rs.90.What will be the value of the amount at the end of 3 years?

(1) 9000(2) 6250(3) 8530.80(4) 8780.80Correct Answer - (4)Solution:

The difference in the simple interest and compound interest for twoyears is on account of the interest paid on the first year's interest,when interest is reckoned using compound interest, interest beingcompounded annually.Hence 12% of simple interest = 90 => simple interest = 90/.12=750.

As the simple interest for a year = 750 @ 12% p.a., the principal =750/.12= Rs.6250.If the principal is 6250, then the amount outstanding at the end of 3years = 6250 + 3(simple interest on 6250) + 3 (interest on simpleinterest) + 1 (interest on interest on interest) = 6250 + 3(750) + 3(90) +1(10.80) = 8780.80.


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The angle of elevation of the top of a tower 30 m high, from two points onthe level ground on its opposite sides are 45 degrees and 60 degrees.What is the distance between the two points?

(1) 30(2) 51.96(3) 47.32(4) 81.96Correct choice (3). Correct Answer - 47.32


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Let OT be the tower.

Therefore, Height of tower = OT = 30 mLet A and B be the two points on the level ground on the opposite side oftower OT.Then, angle of elevation from A = TAO = 45o and angle of elevation fromB = TBO = 60o Distance between AB = AO + OB = x + y (say)Now, in right triangle ATO,tan 45o = OT/AO=30/x

=> x = 30/ tan 45o = 30 mand in right traingle BTO tan 60o = OT/OB=30/y=> y = 30/ tan 60o = 17.32 mHence, the required distance = x + y = 30 + 17.32 = 47.32 m


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Two merchants sell, each an article for Rs.1000. If Merchant Acomputes his profit on cost price, while Merchant B computes his profiton selling price, they end up making profits of 25% respectively.

By how much is the profit made by Merchant B greater than that ofMerchant A?

Rs.66.67Rs.50

Rs.125Rs.200Correct Answer - Rs.50. Choice (2)

Merchant B computes his profit as a percentage of selling price.He makes a profit of 25% on selling price of Rs.1000. i.e. his profit = 25%

of 1000 = Rs.250.Merchant A computes his profit as a percentage of costprice.Let C be the cost price.Therefore,C+.25C =1000.C=1000/1.25=800.

Profit=1000-800=Rs200.Hence, Merchant B makes Rs.50 more profit than Merchant A.


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RATIO AND PROPORTIONA bag contains 50p,25p, and 10 p coins in the ratio 5:9:4 amounting to

Rs.206. ind the number of coins of each type?Solution: Let the number of50p,25p, and 10 p coins be 5x,9x,wx respectively.

Then 5x/2+9x/4+4x/10=206.50x+45x+8x=4120. or x=40Therefore number of 50p coins:5*40=200;Number of 25p coins=9*40=360;Number

of 10p coins:4*40=160.


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Time and Work

Important Concepts:If A can do a piece of work in n days ,the As I day work=1/n.If A is 3 times as good as B then ratio of work done by A and B=3:1 and Ratio of

times taken by A and B to finish work=1:3

Example: Worker A takes 8 hours to do a job.Worker B takes 10 hours to the samejob. How long would it take both A and B working together but independently todo the same job?

As 1 hours work-1/8.Bs 1 hours work=-1/10.

(A+B)s 1 hours work=(1/8+1/10)=9/40.Both A and B will finish the work in 40/9 hours.


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PIPES AND CISTERNS

Inlet pipe fills a tank,cistern or reservoir.Outlet pipe empties a tank,cistern orreservoir.

If a pipe can fill a tank,cistern or reservoir in x hours,or, minutes , or seconds then itfills in part 1/x in hour,or, minute , or second.

If a pipe can empty a tank,cistern or reservoir in y hours,or, minutes , or secondsthen it fills in part 1/y in hour,or, minute , or second.

If a pipe can fill a tank,cistern or reservoir in x hours,or, minutes , or seconds andanother empties a tank in y hours ,or minutes, or seconds then net part filled is(1/x-1/y) or (1/y-1/x). Why?

Two pipes can fill a tank in 10 hours and 12 hours respectively while a thirdemptiesthe full tank in 20 hours.If all the 3 pipes operate simultaneously , in howmuch time will the tank be filled?

Solution:Net part filled in 1 hour1/10+1/12-1/20)=8/60=2/15.The tank will be filled in 15/2

hours.


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Alligation or Mixtures:Concepts:Alligation is a rule that enables us to find the ratio in which 2 or more ingredients at

the given price must be mixed to produce a mixture of desired price.Mean Price:The cost price of unit quantity of the mixtureAlligation rule:If 2 ingredients are mixed then (qty.of cheaper/Qty. of dearer or

costlier)=(cost price of dearer - Mean Price)/(Mean Price Cost Price ofCheaper)

If from a container containing x units of a liquid y units are taken out and replacedwith water then after n operations the quantity of pure liquid=[x(1-y/x)n]

How much water must be added to 60 litres of milk to have a mixture worth Rs 10and and2/3 a litre?Cost of 1 litres of milk Rs.20

Cost of 1 litre of milk:Rs 20*2/3=Rs40/3Mean Price:Rs 10 2/-3 =32/3Ratio of water and milk=(40/3-32/3)32/3-0)=8/3:32/3=8:32=1:4Therefore Qty. of water to be added to 60 litres of milk:1/4*60=15 litres.


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Problems on trains:

A train is moving at a speed of 132 kmph.If the train length is 110 metres, how longwill it take to cross a railway platform 165 metres long?

Speed of train:132*1000/3600=110/3 metres per second.Distance Covered in passing the platform:(110+165)=275 metresTherefore time taken=275/(110/3)=3*275/110=15/2=7.5 seconds


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Boats and Streams:Direction along the stream downstream. Direction against the stream upstream.If the speed of a boat in still water is u kmph and speed of the stream v kmph then

speed downstream:u+v)kmphSpedd upstream:(:(u-v)kmphIf the speed upstream is u kmph and downstream is d kmph then speed in still

water: (d+u)Speed of stream:1/2(d-u)

A man takes 3 hours 45 minutes to row a boat 15 km downstream of a river and 2hours and 30 minutes to cover a distance of 5 kms upstream. ind the speed ofriver current in kmph.

Rate downstream=15/(3 and )=15/(15/4)=4 kmph.Rate upstream=5/(2 and )=5/(5/2)=2 kmph.Rate of stream=1/2*(4-2)= 1 kmph.


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Distribution of leaflets and delivering speeches on government property should beoutlawed. Radicals and fanatics have no right to use public property whenpeddling their unsavory views.

The argument above is based on the postulateA. The general public has a special concern in the free exchange of different

political views.B. Radicals and fanatics prefer the use of public property while propagating

their viewpoint.C. Every person who hands out leaflets and delivers speeches is a radical or

fanatic.D. Legal constraints which are applicable to one group need not be equally

applicable to all.E. Any political activity, which hinders the proper functioning of the government

should not be protected by the law.Ans : C


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THANK YOU

new - rec - intro - aptitude - june 2007

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