# Prologue

The ACIO-2013 general-awareness answerkey (history, geography etc.) was given separately click me. This article contains the answerkeys for Aptitude portion (Maths, Reasoning, English.)

- Two MCQs in the english portion :debatable, because I’m unable to locate the rules.
- other than that, if you have any correction/faster techniques/shortcuts/ for the same MCQs, do share it as well.

and my thanks to **Manu Jha, Palas Nuwal, Shiva Ram and Rohith** for their valuable inputs.

# Maths questions

% | Percentage | 1 |

AVG. | Wine-Water | 1 |

NUMBERSYSTEM | Remainder | 2 |

Prime Number | 1 | |

Base System | 1 | |

STD | Time-Speed-Distance | 1 |

PCP | Permutation Combination | 3 |

Probability | 1 | |

APGP | Arithmetic Progression | 1 |

Total | 12 |

# Percentages

- If increasing 20 by p% gives same result as decreasing 60 by p%, then what is p% of 70?
- 50
- 140
- 14
**35**

p%=p/100;

Increase 20 By P% | Decrease 60 By P% |

(100% of 20 + p% of 20)=(20+ 20p/100) =20 (1+p/100)…….eq1 |
60 (1-p/100)…eq2 |

but as per the question, eq1=eq2

(1+p/100)*20=(1-p/100)*60

When you simplify this equation, you get p=50.

But question requires you to find p% of 70

Meaning 50% of 70=>half of 70=35. Answer (IV).

# Wine-water (Alligiation)

- In what ratio should a 20% methyl alcohol solution be mixed with a 50% methyl alcohol solution so that the resultant solution has 40% methyl alcohol in it?
**1:2**- 2:1
- 1:3
- 2:3

Make the table

conc.% | 20 | 40 | 50 |

volume | a | b |

apply the “visual” move

(50-40)=a, hence a=10

(40-20)=b, hence b=20

a:b=10:20=1:2, so answer is (i).

# Number System

## Prime number

- The difference between ages of two brothers is a prime number. The sum of their ages is also a prime number. If elder brother is 28 years old, how many values can age of younger brother take?
- 2
**3**- 4
- 1

(I’m going by trial and error method, but if you know a faster method, please do share in the comment.)

Prime numbers between 1 to 28= 2,3,5,7,11,13,17,19,23

Now go by trial and error

columnA | columnB | col.C=ColA-ColB | col.D | yes/no |

elder bro’s age | difference is prime number | younger bro’s age | elder bro+younger bro | is col.D a prime number? |

28 | 2 | 26 | 54 | no |

28 | 3 | 25 | 53 | yes |

28 | 5 | 23 | 51 | no |

28 | 7 | 21 | 49 | no |

28 | 11 | 17 | 45 | no |

28 | 13 | 15 | 43 | yes |

28 | 17 | 11 | 39 | no |

28 | 19 | 9 | 37 | yes |

28 | 23 | 5 | 33 | no |

from this table, we can see three possible numbers for younger brother’s age: 25,15 and 9.

hence answer is (ii): 3 possible numbers.

## Remainder

- Find the least five digit number, which when divided by 12, 18, 21 and 28, leaves the same remainder.

- 11019
**10081**- 10059
- 10289

for this type of question, you need to find LCM of given numbers first

LCM (12, 18, 21, 28)=252

meaning, if I divided 252 with any of the given number (12,18,21,28) then it’ll give remainder zero.

similarly, if I divided 252+1 =253 with any of those given numbers, I’ll get remainder 1.

now by trial and error, try to find first “five digit” multiple of 252

first do approximation (in your head)

25 x 4=100

250 x 4=1000

250 x 40=10,000

Meaning 252 x 40 will be higher than 10,000.

252 x 39 try karo: 9829 but this is four digit. so

252 x 40= 10080 is our first “five digit” multiple of 10080.

observe the options: (ii)=10081. Meaning 10080+1 so this number will give same common remainder “1” when divided by 12,18,21 or 28.

**Excel**

just for timepass (and for IBPS computer awareness) try to find remainders using excel. The cell formula will be =MOD(number,divisor). you’ll see that our answer is correct.

- A number when divided by a divisor, leaves a remainder of 24. when twice the original number is divided by same divisor, the remainder is 11. what is the value of divisor?
- 13
- 59
- 35
**37**

Suppose the number is “N”, division is “D”, quotient is “Q” and remainder is “R”. then we can write

N=DQ+R

N=DQ+24….first case given.

Twice of that number

2xN= 2 (DQ+24)=2DQ+(24 x 2)=2DQ + 48…..eq1

Question says when 2N is divided by “D”, then 11 remainder is obtained.

But 2N=(2DQ+48)

Imagine what will happen if we divide (2DQ+48) by “D”

(2DQ+48)/D

(2DQ/D) + (48/D)

First bracket will give zero remainder because D/D will cancel each other. Meaning whatever remainder is obtained- that we got from (48/D).

48/D=new remainder. But as per the question, new remainder was 11.

Think about this: when 48 divided by “D” gives 11 remainder. Meaning, when 48-11(=37) is divided by “D” then we get zero remainder. Hence “D”=37. (Since 37 is a prime number, D has to be 37. Suppose we got 32, then we might need to think about some smaller factors of 32 e.g. 16, 2 etc.)

Thus answer is 37. (choice iv)

**let’s verify:**

Original number when divided by 37 leaves remainder 24. One such number could be 37+24=61

if we’re correct then twice of 61, when divided by 37, should leave remainder 11. Try it in excel: =MOD(2*61,37) and you’ll get 11 as remainder. Meaning 37 is correct.

## Base system

- What will be the expression for 567 in binary system?
- 1010111001
- 1000110001
- 1000011101
**1000110111**

Method is explained here:

http://www.wikihow.com/Convert-from-Decimal-to-Binary

DIVIDED BY TWO |
NUMBER OR QUOTIENT |
REMAINDER |

2 | 567 | 1 |

2 | 283 | 1 |

2 | 141 | 1 |

2 | 70 | 0 |

2 | 35 | 1 |

2 | 17 | 1 |

2 | 8 | 0 |

2 | 4 | 0 |

2 | 2 | 0 |

2 | 1 | 1 |

now write those remainder from bottom to top

1000110111

Hence (567)_{10}=(1000110111)_{2}

# TSD (Time Speed Distance)

- A train covers certain distance between two places at a uniform speed. If the train moved 10 km/hr faster, it would take 2 hours less. And, if the train were slower by 10 km/hr, it would take 3 hours more than the scheduled time. Find the distance covered by the train.
- 300 kms
**600 kms**- 800 kms
- 1200 kms

**Shortcut (cross multiplication)**

Inspired from Sarvesh Kumar’s cross multiplication method, from his example 8 in chapter on Time, Speed and distance.

First, draw a regular STD table.

normal case | faster case | slower case | |

speed | s | +10* | -10 |

time | t | -2 | +3 |

distance | d |

*here we should be writing s+10 but instead just write +10. Same approach for other cells.

Now, speed x time = distance. So in faster case: +10 x -2=(-20) but distance cannot be negative, so write +20

normal case | faster case | slower case | |

speed | s | +10* | -10 |

time | t | -2 | +3 |

distance | d | 20 | 30 |

Now cross multiply speed and time from first two columns

-2s+10t=20…..eq1

Similarly cross multiple speed time from column 1 and column 3

+3s-10t=30….eq2

Add eq1+eq2, you get

(-2s+10t)+(3s-10t)=30+50

s=50kmph. plug this value back in eq1

-2(50)+10t=20

10t=120, hence t=12 hours.

And we know that speed x time = distance. Therefore 50 x 12=600km was the total distance. Answer (ii)

**Longer method:**

normal case | faster case | slower case | |

speed | s | s+10 | s-10 |

time | t | t-2 | t+3 |

distance | d | d | d |

here you’ve 3 variables (s,t,d) and 3 columns:

speed x time = distance and distance is same in all three cases. from the first column we get s x t=d.

So instead of “d”, I can write “st” everywhere.

normal case | faster case | slower case | |

speed | s | s+10 | s-10 |

time | t | t-2 | t+3 |

distance | st | st | st |

now observed:

column | speed x time = distance |

first column | s x t =d |

second column | (s+10)(t-2)=styou simplify it further, you get -s+5t=10…eq1 |

third column | (s-10)(t+3)=styou simplify it further, you get 3s-10t=30….eq2 |

-s+5t=10…eq1

3s-10t=30….eq2

now if I multiply eq1 with x2 and add in eq2, it’ll cut -10t.

-2s+10t=20

3s-10t=30

from this we get

s=50kmp. plug it back in eq1, you get t=12 hrs.

and distance = st=50×12=600km. Answer choice (ii)

# Permutation Combination Probability

## Men and task

- 6 tasks and 6 persons. task 1 can’t be assigned to either person 1 or 2. task 2 must be assigned to either person 3 or 4. Every person has to be assigned a task. How many ways can the assignment be done?
- 144
- 180
**192**- 360

Imagine these are not ‘tasks’ but chairs. And we’ve to pick candidate for each chair.

chair | person choice (number of candidates) | choice |

1 | 4 persons (because 1 and 2 out) | 4 |

2 | 2 person (either 3 or 4) | 2 |

3 | previous two chairs took away “2” people, so remaining 4 candidates | 4 |

4 | 3 candidates | 3 |

5 | 2 candidate | 2 |

6 | 1 candidate | 1 |

total choice

=choice for chair#1 AND chair#2 AND…..

but “and” means multiplication

=4 x 2 x 4 x 3 x 2 x 1

=192 ways

**Another approach:**

chair 1 | chair 2 | chair number 3 to 6 |

one chair four candidates | one chair two candidates | four chairs remaining four candidates |

4P1 | 2P1 | 4P4 |

4p1 x 2p1 x 4p4

=4 x 2 x 24

=192 ways. Choice iii.

## word arrangement

- In how many ways can the letters of the word ASSASSINATION be arranged so that all the S are together?
- 10!
- 14!/(4!)
**1,51,200**- 36,28,800

given word has 13 letters

letter | occurs __ times |

A | 3 |

S | 4 |

I | 2 |

N | 2 |

T | 1 |

O | 1 |

TOTAL | 13 |

As such there are 13 candidates and 13 seats. but we want 4 s’ to be together. And 13-4=9.

Imagine there are 10 seats: 9 seats for those other letters and 1 seat where those 4 “S” will sit together.

So first, out of those 10 seat, pick this one seat where four “S” can sit together.

Total ways

=(Pick one out of 10 seats for that S group) AND (arrangement for remaining 9 seats)

=10C1 x (arrangement for 9 seats)….eq1

Now let’s just focus on those 9 seats

A | 3 |

I | 2 |

N | 2 |

T | 1 |

O | 1 |

total | 9 |

=9!/(3! x 2! x 2!)

^why this way? Because A repeats 3 times, I repeats 2 times, N repeats 2 times. (Theory was explained in separate article long time ago.)

anyways, back to eq1. total ways

=10C1 x (9!/(3! x 2! x 2!)

=(10) x [9!/(3! x 2! x 2!)]
=151200 hence answer is (iii).

## Round table

- In how many ways can 15 people be seated around two round tables with sitting capacities 7 and 8 people.
- 15!/8!
- 7!x8!
**(15c8)x6!x7!**- 15c8 x 8!

circular arrangement of “n” objects= (n-1)! Ways.

what are we supposed to do here?

=(out of given 15, pick any 8 people) AND (arrange those 8 in a round table) AND (arrange remaining 7 in the second round table)

=15C8 AND (8-1)! AND (7-1)!

=15C8 x (8-1)! x (7-1)! (because AND means multiplication)

=15c8 x 7! x 6! Hence (iii) is the answer.

## Probability

- In a lottery 10,000 tickets are sold and ten prizes are awarded. What is the probability of not getting a prize if you buy one ticket ?
- 9/10,000
- 9/10
**999/1000**- 9999/10,000

Favorable outcomes meaning out of those 10 tickets, one is yours=10C1=10

Total outcomes= out of those total 10000 tickets, one is yours=10000C1=10000

Hence probability of winning

=favorable outcomes / total outcomes

=10/10000

And probability of NOT winning

=1 MINUS probability of winning

=1-10/10000

=9990/10000

=999/1000 hence answer (iii)

# AP-GP

- What is the sum of all positive integers lying between 200 and 400 that are multiples of 7?
**8729**- 8700
- 8428
- 8278

Think in your head

7 x 3 =21

7 x 30=210

Therefore 7 x 29 has to be 210-7=203. This is the first number in our series.

so far our series is 203, 210,….. last multiple of “7” before 400

What could be the last number?

7*50=350? Nope, it has to be higher. how about we add another 49 to 350, that could be very close to 400.

7*50 + 7*7=350+49=399 this is the closest multiple of 7, near 400.

And, 7*50 + 7*7=7 (50+7)=7*57

It means our series is going in this fashion:

(7 x 29) + (7 x 30) + …. + (7 x 57)

If I take “7” common then

sum=7 (29 + 30 + …+57)…..eq1=(this will be our final answer)

Now, just focus on the () bracket part. This is a continuous series in arithmetic progression.

Sum of AP

=[average of first and last term] x number of terms

=[(29+57)/2] x 29*

**=1247**

Plug this value back in eq1

= 7 x **1247** = 8729 hence answer is #1 (**8729**)

**how did I find number of terms is 29? => because this is a continuous number series: 29-30-31-32….-57*

*In such series, number of terms will be (last term minus first term + 1)=57-29+1=29 terms.*

**longer approach:**

By trial error you find first term and last term (203 and 399)

after that use “last term”= a+(n-1)*d

where “d”=7 and “a”=203. So you get number of terms “n”

finally sum of AP=n/2 x [2a+(n-1)d].

^but this method will require lengthy calculations. The first method is quicker, slimmer.

# Reasoning: Internal Breakup

Direction Sense Test | 1 |

Sitting Arrangement | 1 |

Blood Relation | 1 |

Missing Numbers | 2 |

Coding Decoding | 2 |

Calendar | 2 |

# Direction Sense Test

- Rajnikanth left his home for office in car. He drove 15 kms straight towards north and then turned east-wards and covered 8 kms He then turned to left and covered 1 km. He again turned left and drove for 20 kms and reached office. How far and in what direction is his office from the home?
- 21 kms west
- 15 kms north east
**20 kms north west**- 26 kms north west

follow direction, make diagram, you’ll get a right side angle whose two sides measure 16km and 12km. Then apply Pythagoras,

AB^{2}+BC^{2}=AC^{2}

Hypotenuse=square root of (16^{2}+12^{2})=square root of 400=20km. hence answer (iii)

# Sitting arrangement

- There are five different houses, A to E, in a row. A is to the right of B and E is to the left of C and right, of A. B is to the right of D. Which of the houses is in the middle?
**A**- B
- C
- D

Do the arrangement:

- A is to the right of B.
- B is to the right of D

From this two statement, we can make D-B-A

E is to the left of C and right, of A

Apply this in above arrangement

D-B-A-E-C.

Hence “A” is in the middle. Answer (i)

# Blood relation

- A’s mother is sister of B and daughter of C. D is the daughter of B and sister of E. How is C related to E?
- Sister
- Mother
- Father
**Grandmother or Grandfather**

- Arun/Aruna’s mom is sister of Bina.(because we don’t know whether A is male/female).
- Arun/Aruna’s mom is daughter of Chandu/Chameli. (because we don’t know the gender yet)
- It means Bina is also the daughter of Chandu/Chameli. (because Bina is sister of Arun/Aruna’s mom)
- Divya is daughter of Bina. And Sister of Elisha/Ehsan (because we don’t know E’s gender yet)
- But either way Chanu/Chameli (C) => their daughter Bina (B)==> their son/daughter Elisha/Ehsan (E)
- Meaning Chandu/Chameli(C) is grandfather or grandmother of E. Answer (iv)

## Missing Numbers

- Find the missing number in this series: 4, 18, ??, 100, 180, 294

- 32
- 36
**48**- 40

The pattern is: n(n+1)^{2}

Put n=1, n=2,n=3,n=4 and so on

since missing term “??” is at third place in this series. So, Put n=3 then

3(3+1)^{2}= 3*16=48

- Which number should replace the question mark?

17 | 8 | 5 | 5 |

13 | 7 | 5 | 4 |

6 | 12 | 6 | 3 |

10 | 6 | 4 | ?? |

**4**- 5
- 6
- 7

The pattern is: (from right cell towards left cell in each row)

5*5=25 and 25-8=17.

5*4=20 and 20-7=13

6*3=18 and 18-12=6

like this ans will be 4, because 4*4-6=10

## Coding decoding

- ACEG : DFHJ:: QSUW
- TVNZ
- TVZX
**TVXZ**- XVTZ

Pattern is: Skip one alphabet and start the 2^{nd} analogy after the 2^{nd} alphabet of the 1^{st} word that means 2bd word starts with D which comes after C which is the 2^{nd} alphabet of 1^{st} word.

A_{B}C_{D}E_{F}G : D_{E}F_{G}H_{I}J :: Q_{R}S_{T}U_{V}W : T_{U}V_{W}X_{Y}Z .

Answer (iii)

- 165135 is to peace as 1215225 is to
- lead
**love**- loop
- Aura

the approach:

A =1

B = 2

E = 5

. . .

Z = 26

accordingly: P = 16 , E = 5 A =1 C =3 E = 5

Hence Peace = 16| 5|1|3|5

Now question is: what does 1215225 mean?

And since the options are only 4 letter words

We have to choose with cancelling the options

last two numbers: “25”

It could be |5 OR 25.

- if last number is “25”, then “Y”. but there is no word ending with “Y” among given choices.
- it means last number is |5=”E”. Meaning E is the last letter.

so eliminate all options that don’t have “E” as last letter.

- lead
- love
- loop
- Aura

thus we’re left with answer (ii) Love. But we should verify:

LOVE = L =12 || O = 15 || V = 22 || E =5 =>1215225 correct.

# Calendar

- The day before the day before yesterday is three days after Saturday. What day is it today?
- Tuesday
- Wednesday
- Thursday
**Friday**

Start from end part of the sentence.

this part | equal this part |

day before the day before yesterday | three days after Saturday. |

3 days before today. | =Three days after Saturday=Sun, Mon, Tuesday. |

3 days before today= | Tuesday |

Meaning Today MINUS 3 days=Tuesday.

Then today has to be Friday.

- If the republic day of India in 1980 falls on Saturday. X was born on March 3 1980 and Y is older than X by four days. then Y’s birthday fell on?
**Thursday**- Friday
- Wed.
- None of these

first understand the calendar technique from this article click me

- X born on March 3
- Y is four days older=>March 3 + 4= 7th March.
- In short, we’ve to find the day on 7th March 1980.
- As per the information: Republic day (26th March) 1980= on Saturday.

find the odd days

remaining days in January= 27 to 31 | 5 |

February (leap) but b’day is on 28th. | 28 |

total days | 33 |

divide total days (33) by 7= you get 5 as remainder.

Required day (28th Feb)

=Saturday (on 26t Jan) + 5 days 28th Feb

=Saturday+ 5 days

=Thursday.

**Verification:**

**There is site called “dayoftheweek.org”, you enter the date and it’ll tell you its day.**

So, as per www.dayoftheweek.org/?m=January&d=26&y=1980&go=Go , 26^{th} Jan 1980 was indeed Saturday

And 28th Feb, 1980 was indeed Thursday.

# English internal breakup

sentence correction/meaning | 4 |

idioms-phrases | 3 |

vocabulary/ fill in the blanks | 4 |

total | 11 |

# Sentence correction / meaning

- Choose the correct sentence among the following
- The danger will continue its growth
**The danger will continue to grow**- The danger will continue its growing
- The danger will continue growth

“Continue” should following with “to-infinitive”. Hence Danger will continue to grow. Answer (ii)

- Complete the following sentence, This is the best book __
- of all others on History
- of any other on History
- of all on History
- of any other in History

Debatable because I’m unable to locate the rule. Your inputs welcome.

- Choose the correct sentence among the following,
- I have one chance in a thousand of winning tonight
- I have one chance in a thousand for winning tonight
- I have one in a thousand chances to win tonight
- I have one chance in a thousand that I will win tonight

Debatable because I think (iii) but Unable to locate the rule. Your inputs welcome.

- Choose the answer that is closest in meaning to the following sentence, Yeuk Yee had her house painted white yesterday
- She had to paint her house white yesterday
- Her house was not blue last week
**They painted her house white for her yesterday**- She painted her house yesterday

She had her house painted…meaning she didn’t paint is by herself, she got some other person(s) to get house painted. Therefore, choice #3.

# idioms and phrases

- Choose the idiom from the following options which means “to be modest about one’s achievements”
**to hide one’s light under a bushel**- to take to the bush
- to hide behind the bush
- to beat about the bush

Oxford dictionary website says to hide one’s light under a bushel = keep quiet about one’s talents or accomplishments. Hence #1 is the answer.

- Choose the idiom from the options, which means ‘a lot of excitement and discussion about a trivial matter’
- A cyclone in the cup
- A flood in the tea-cup
**A storm in the tea-cup**- A flood of air

Storm in the tea-cup= a disturbance or uproar about little or nothing. Hence choice #3.

- “What is bred in the bone will come out in the flesh” Choose the meaning that is closest in the meaning to this proverb
- Pedigree racing horse will always win
**Inherited characteristics cannot be concealed**- Good diet in childhood makes for good health in adulthood
- Brain washing can change the personality

This proverb means “a person’s behavior or characteristics are determined by heredity.” So, #2 is the closest choice.

# Vocabulary

- Docility is to surrender as unrest is to —–
- education
**rebellion**- illness
- hospital

Docility= the trait of being agreeably submissive. Meaning docile person likely to surrender, similarly unrestful person likely to rebel. Hence choice #2

- Mitigate is to punishment as alleviate is to
- promotion
- change
- order
**pain**

Mitigate punishment = reduce punishment. Alleviate pain = reduce pain. Hence choice #4.

- Choose the pair which represents closest the relationship expressed in the original pair in capital letters: MENDACITY HONESTY,
- Truth Beauty
- Sportsmanship Fortitude
**Courageous Craven**- Turpitude Depravity

Mendacity=The tendency to be untruthful. = this is opposite of honesty.

craven= An abject coward. So it is opposite of courageous. Answer #3.

- Choose the set of words that when inserted in the sentence, best fits the meaning of the sentence as a whole, Unable to ____ his wholehearted distaste for media events and publicity, the miffed minister continued to make ____ comments throughout his speech

- conceal , effusive
- control ; garbled
**disguise, caustic**- express , vitriolic

He was unable to disguise his distaste…..kept making caustic (harsh) comments.

# Essay

Write an essay in English language only on any one of the following topics in not more than 400 words. (50 marks)

- A Communal Conflict Scenario
- Causes of Violence in the World
- Divide Between ‘India’ and ‘Bharat’
- Dimensions of Rural Employment

Just listing the essay so if some future ACIO-2014/2015 aspirant comes to search, he can see it. + Similar topic might even be asked in CAPF 2013 Paper II.

**The ACIO-2013 general-awareness answerkey (history, geography etc.) was given separately ****click me**

## 156 Comments on “[ACIO-2013] Aptitude (Maths, Reasoning, English) Answerkey with explanations, shortcuts”

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QUESTION 2 SOLUTION ————

If the train moved a km/hr faster, it would take x hours less. And, if the train were slower by a km/hr, it would take y hours more than the scheduled time.Distance travelled by train=(a*x)*(b*y)

distance travelled by train=(10*2)*(10*3)=600km

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..

in men and task 1st question is wrong solved the correct ans is 144.

explanation : 1st task can be given in = 3 ways

2nd task given in = 2 ways

3rd task given in = 4 ways

4th task given in = 3 ways

5th task given in =2 ways

6th task given in = 1 ways

so possible ways = 3*2*4*3*2*1= 144

Calendar Part Q2: The Answer I’m getting is Friday. (1980 is a Leap Year). The Calendar also shows the same.

Maybe the calendar is showing wrong, as a leap is defined as the year which is divisible by 100 and 400, leaving remainder 0,

you can very well see that 1980 will not give a remainder 1.