## Prologue

- Intelligence Bureau (IB) had conducted written examination for requirement of Assistant central intelligence officer (ACIO) on 22nd February 2015.
- I’m preparing the topic wise ACIO Answer key in four parts.
- First part: History and Polity MCQs already published
- Second part: Economy and Geography MCQs also published
- Third part: Science and Persons in News MCQs published
- Now in this fourth and last part, we look at the Maths, English, Reasoning questions asked in the ACIO-2015 examination
- Since IB refuses to disclose cutoffs under right to information act (RTI), so not much point in dwelling into that. One exam is over then it’s time to prepare for another exam.

## Maths/Reasoning Questions in ACIO-2015

- By and large trend similar to last exam conducted in 2013 i.e. few questions from basic numeracy, few from speed-time-distance, few from permutation-combination-probability and arithmetic progression.
- Only new part is “logarithms” asked.
- Only 1 question from reasoning. No questions about coding-decoding, blood-relations, sitting arrangement, syllogism or non-verbal image based reasoning.
- Strategy for future ACIO exam:
- Fast track to Objective Arithmetic by Rajesh Verma
- And misc. topics such as logarithm from internet.
- For reasoning, just practicing old papers of SSC and Bank exams, with main focus on vocubulary and dictionary part.

### Basic Numeracy

**18. If the sum of 60% of a fractional number and the number’s square root is 5 greater than one fifth of the number, then the number is **

- 6.25
- 0.25
- 12.25
- 2.25

0.6x + sqrt(x) = 0.2x +5

0.4x + sqrt(x) = 5

We have to choose an option from the choices given and substitute it in this equation to get answer. Since the sum is 5, we can assume that the number must be greater than 5, as the 2 components we are adding are fraction of the number.

So taking 6.25.

0.4*6.25 = 2.5

Sqrt(6.25) = 2.5

Adding both we have 5.

So option (1) is correct

**22. A man sells an article at a certain price incurring 20% loss. If he had sold the same article for Rs.20 more, he would have earned 20% profit. What was the cost price of the said article? **

- Rs.20
- Rs. 40
- Rs. 50
- Rs. 60

1.2x – 0.8x = 20 => 0.4x = 20 => x = 50. Option (3)

**23. Numerator of a fraction is increased by 60%, and at the same time its denominator is decreased by 60%. The new fraction is **

- 2.56 times the older fraction
- Equal to the older fraction
- 4 times-the older fraction
- 0.36 times the older fraction

1.6N/0.4D = 4(N/D). Option (3)

**28. Log (40^2-20^2) is equal to **

- log 3
- log 60 + log 20
- log 40 – log 20
- log 20

=40^{2}-20^{2}

=(40-20)(40+20)

= 20*60

Log of this equation = log 60 +log20, Therefore, answer is #2.

=11/14, hence answer (2)

**26. The last digit of the number 3^2015 is **

- 1
- 3
- 5
- 7

The last digit comes in iteration of 4 numbers: 3,9,7,1.

So remainder when 2015 is divided by 4 leaves remainder 3. So the unit digit comes out to 7.

Option (4)

**27. What is the squareroot of 49%? **

- 0.7%
- 7.0%
- 70%
- Undefined

Sqrt(49/100) = 7/10 = 70% Options (3)

**31. (7+14+21+28………..+700) is equal to : **

- 35350
- 42714
- 49420
- 56707

A=7, d=7, n=100.

S = (last number + first number)*N/2 = (700 + 7)*100/2 = 35350. Option (1)

### Permutation Combination Probability (PCP)

**19. If ‘Head’ appears consecutively in the first three tosses of a fair/unbiased coin, what is the probability of ‘Head’ appearing in the fourth toss also? **

- 1/8
- 7/8
- 1/16
- 1/2

The answer would be (4) ½.

Consider we take into consideration probability of each toss. HHHH. Then probability of 4^{th} toss as Heads will be (1/2) ^ 4 = 1/16.

Now consider the corollary, when the 4^{th} toss **is not a head**. So it is HHHT. Once again the probability will be 1/16. If we were to do (1/2) ^ 4 for each separate toss, then for not getting head also we will get same 1/16. But the answer should have been 1 – 1/16 = 15/16. So our assumption that we take earlier tosses into consideration is wrong.

This is because, the probability of 4^{th} toss will not change due to earlier occurrences. This is a new toss.

**20. Archers ‘A’ and ‘B’ take aim at a target. If the probability of ‘A’ hitting the target is 90% and of ‘B’ missing the target is 90%, what is the probability that both ‘A’ and ‘B’ miss the target?**

- 90%
- 09%
- 01%
- 81%

Answer = A missing AND B missing

= 0.1 * 0.9 [“AND” means multiplication]
= 0.09 = 9%. Option (2)

**29. Twelve persons meet in a conference and each shakes hands with all the others. How many handshakes take place? **

- 66
- 72
- 144
- 132

**Approach#1:**

Readymade formula for handshakes is: n*(n-1)/2. Therefore, 12*11/2=66 handshakes take place. option #1 is right.

**Approach#2:**

1^{st} person shakes hands with = 11 persons.

2^{nd} person = 10 (excluding the already shaken hands of the 1^{st} person)

3^{rd} person = 9 (excluding the already shaken hands of the 1^{st} person and 2^{nd} person)

……

Final handshakes = 1+2+3+…+11 = 12*11/2 = 66. [arithmetic progression]

Option (1)

### Speed Time Distance (STD)

**21. If 12 persons working 12 hours a day dig 12 meters of a tunnel in 12 days, how many men are required to dig additional 04 meters of the tunnel (of the same dimension) given that they work 04 hours a day for 04 days? **

- 27
- 4
- 12
- 36

**Approach#1: STD method**

Suppose 1 man’s speed is “s”

12 people | |
---|---|

Speed | 12*s |

Time | 12 hrs x 12 days |

Distance | 12 meters |

Apply STD formula in first column

Speed x time = distance

(12 x s) x (12 x 12)=12

s=1/144

**Case#2:** we have to find no. of more men required (say “M”) for 04 meters of the tunnel (of the same dimension) given that they work 04 hours a day for 04 days?

Speed | (m) x (1/144) |
---|---|

Time | 4 hrs x days |

Distance | 4 meters |

((m)/144)*4*4=4

Solving this equation we get answer 36.Hence option #4.

**Approach#2:**

- For 12 persons, Per day Meter for 12 Hours = 1 meter is dug
- So for 12 persons, per day per hour = 1/12 meter is dug.
- So for 4 hours of work in 4 days by 12 persons = 4/3 meters. We need 4 meters.
- So we need to employ 12*3 = 36 persons.

**30. A man travels uphill to city C from city B in a car at the speed of 40 Km/hr, and returns to city B at a faster speed of 60 Km/hr. What is his average speed for the round trip? **

- 0
- 48 Km/hr
- 50 Km/hr
- Data insufficient

uphill from B to C | from C to B | |
---|---|---|

Speed | 40 | 60 |

Time | ||

Distance | D | D |

Apply speed x time = distance formula in both columns, then you get time = D/40 and D/60 respectively. Update the table

uphill from B to C | from C to B | |
---|---|---|

Speed | 40 | 60 |

Time | D/40 | D/60 |

Distance | D | D |

Average speed = (total distance)/(total time)

=(D+D)/((D/40)+(D/60))

Answer is 48 kmph. Option #2

### Geometry

**24. In a triangle ABC, one of the angles is average of the remaining two angles. Which of the following is always true about the triangle ABC? **

- Isosceles triangle
- Equilateral triangle
- One of its angles measures 60°
- Right angled triangle.

It can’t be isosceles. Since, the average of the greater angle with the smaller angle will be more than the smaller angle. It need not be equilateral. Though it can be an equilateral. So one of the angle is 60. Consider the angles – 45, 60,75. It fits into the average criteria. So option (3) is answer.

**25. If the area of a circle ‘C’ is equal to the area of a square ‘S’, then the ratio of the square of the perimeter of ‘C’ to the square of the perimeter of ‘S’ is nearly equal to **

- 22:7
- 11:14
- 88:7
- 1:1

Pi*r^{2} = a^{2} …..eq1

^{2}] / [(4*a)

^{2}]

= pi/4 (after substituting values from equation1)

=22/(7*4)

=2*11/(7*2*2)

### Reasoning

32. In a group of 5 persons, P is taller than Q, but is shorter than both R and S. Both R and T are taller than Q, but shorter than S. This implies that

- R is taller than P, but shorter than T/ R
- T is taller than Q, but shorter than R/ T
- R is taller than Q, but shorter than T/ R
- S is taller than T while P is shorter than R/ S

P>Q; R,S>P ; R,T>Q; S>R,T ;

So option (4) suits the best. We don’t know the relation between R and T.

**33. In a group of Army Officers, 02% of Officers neither take Coffee nor Tea, while rest of them take either Tea or Coffee or both. If 60% of Officers take Tea, while 58% take Coffee, what percentage of Officers take Tea but do not take Coffee? **

- 02%
- 20%
- 40%
- 60%

Total officers = People who take tea + who take coffee + don’t take anything – intersection/double count/who take both tea and coffee.

100 = 60 + 58 + 2 – x => x =20.

So people who take tea but no coffee = take tea – intersection = 60 – 20 =40.

Option(3)

**Approach#2**

T+B=60

C+B=58

Therefore (T+C)+2B=118…eq1

Next, we know that total number of officers are 100

T+B+C+N=100; but N=2

(T+C)+B=98….eq2

eq1 minus eq2

118-98=(T+C)+2B –((T+C)+B)

20=B.

Officers who only drink tea: T=60-B=60-20=40. Option #3.

## English

Total 10 questions asked

**91. Which of the following is the wrongly matched word-meaning pair? **

- Indict: Accuse
- Onset: Beginning
- Recite: Propose
- Temerity: Boldness

Since option 1, 2 and 4 are right as per wordweb software hence answer is (3).

**92. Which of the following sentences is grammatically correct? **

- Either he or I am mistaken. (correct because of the rule “when subjects joined by or, the verb agrees with the nearer.”)
- He gave me an advice. (Advice is an uncountable noun. “An advice” is wrong. As per Longman dictionary.
- The sceneries here are very good. (wrong because Scenery doesn’t have plural form)
- Let you and I do it. (it should be either “let’s do it”)

Therefore, Answer #1.

**93.Which of the following word is closest in meaning to the idiom, “cast down”? **

- Humiliated
- Defeated
- Depressed
- Discouraged

Merriam Webster says Depressed is one of its synonym. Hence answer (3)

**94. The letter, ‘0’, in the word, ‘about’, is pronounced like letter, ‘o’, in the word : **

- Go
- Boy
- Got
- Now

Answer is “4”.

**95. Khali was sitting on the fence, means Khali was : **

- Living dangerously
- Undecided
- Stubborn
- Annoying

It means a state of indecision to conflicting positions. Says Webster. So answer is #2.

**96. In the sentence, ‘Don’t talk so loud’, the word ‘loud’ is used as an : **

- Adverb
- Adjective
- Idiom
- Active verb

loud is adjective, says Webster So answer is #2.

**97. In the sentence, ‘None but the brave deserves the fair’, the word ‘but’ is used as : **

- An adverb
- A preposition
- A conjunction
- A pronoun

“But” is a conjunction – as per Webster Hence answer #3

**98. Which of the following is a correctly matched adjective-noun pair?**

- Restless – Restlessly
- Restless – Restlessness
- Restless – Restive
- Restless – Restivity

restlessness is noun as per Oxford Dictionary Hence answer #2

**99. His bad eyesight exempted him ……… military service. Fill in the blank with : **

- in
- of
- from
- At

Statement lifted verbatim from Oxford dictionary hence answer is #3 “From”. as per Oxford Dictionary

**100. Which of the following is an incorrectly matched word-meaning pair? **

- Excursion – Short journey
- Homage – Tribute
- Sidekick – Close companion
- Intact – Tactful

Since first three are correctly matched so answer is #4.

## Essay List

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

- Right to freedom of expression should be an absolute right
- Inclusive Growth: A pipedream
- Intelligence is an important aspect of statecraft
- “It is often safer to be in chains than to be free”

## 76 Comments on “[ACIO Answerkey] Part 4/4: Aptitude- Maths, English and Reasoning MCQs solved with Explanation”

bhai koi batayega ki ACIO notification kab aata hai last year t was Nov 2014 and exam on “22 Feb 2015”

next exam kab hogi ???

ACIO exams are held every year or alternate years ??

PLEASE ANSWER