CTS - Analytical Reasoning

CTS – Analytical Reasoning

1. Out of forty students, there are 14 who are taking Physics and 29 who are taking Calculus. What is the probability that a randomly chosen student from this group is taking only the Calculus class?

Ans: 0.65 = 65%.

The total number of students is 40. Number of students taking Physics and Calculus are 14+29=43.

Thus 3 students are taking both Physics and Calculus. Hence, the number of students taking only Calculus is 26 and the probability is 26C1 / 40C1 = 0.65 or 65%

2. In town of 500 people, 285 read Hindu and 212 read Indian express and 127read Times of India 20 read Hindu and times of India and 29 read Hindu and Indian express and 35 read Times of India and Indian express. 50 read no newspaper. Then how many read only one paper?

Ans: 450

People reading only Hindu   =    285 – (20+29) = 236.   (Through Venn diagram these figures can be

People reading only Express =    212 – (29+35) = 148    arrived at)

People reading only Times    =    127 – (35+20) =   72

Total                                                                              456 (less 6 who read all the three papers) = 450.

3. In a group of persons traveling in a bus, 6 persons can speak Tamil, 15 can speak Hindi and 6 can speak Gujarati. In that group, none can speak any other language. If 2 persons in the group can speak two languages and one person can speak all the three languages, then how many persons are there in the group?

A) 21      B) 23      C) 22      D)24

Ans: B

Let us assume the two persons who can speak two languages speak Hindi and Tamil. The third person then speaks all the three languages.

Tamil – Number of persons who can speak is 6. Only Tamil 6 – 2 – 1 = 3

Hindi -  Number of persons who can speak is 15. Only Hindi 15 – 2 – 1 12

Gujarati – Number of persons who can speak is 6. Only Gujarati 6 – 1 = 5

Thus the number of persons who can speak only one language is 3 + 12 + 5 = 20

Number of persons who can speak two languages                                            =  2

Number of person who an speak all the languages                                            =   1

Total number of persons                                                                               = 23.

4. Out of a total of 120 musicians in a club, 5% can play all the three instruments- Guitar, violin and Flute. It so happens that the number of musicians who can play any two and only two of the above instruments is 30. The number of musicians who can play the guitar alone is 40. What is the total number of those who can play violin alone or flute alone?

A) 30      B) 38      C) 44      D) 45

Ans: C

Out of total 120 musicians 40 can play only Guitar. That leaves remaining 80 persons of which 30 can play only two or any two instruments. Excluding this we now have 50 persons of which 6 persons (5% of 120) can play all the three instruments. Excluding this we now have 44 persons who can now either play Violin or flute alone.  

5. In a town 65% people watched the news on television, 40% read a newspaper and 25% read a newspaper and watched the news on television also. What percent of the people neither watched the news on television nor read a newspaper?

A) 5        B) 10      C) 15      D) 20

Ans: D

People watching Television is 65%. People watching only Television is 65% - 25% = 40%

People reading newspaper is 40%. People reading only newspaper is 40% - 25% = 15%

Thus percentage of people watching TV, reading newspaper and

Both TV and newspaper is   40% + 15% + 25% = 80%

Hence percentage of people neither watching TV nor reading newspaper is  100% - 80% = 20%                

Directions for Questions 6-10:

Each question given below has a problem and two statements numbered I and II giving certain information. You have to decide if the information given in the statements is sufficient for answering the problem. Indicate your answer as

(a) If the data in statement I alone are sufficient to answer the question;

(b) If the data in statement II alone are sufficient to answer the question;

(c) If the data in either in I or II alone are sufficient to answer the question;

(d) If the data even in both the statements together are not sufficient to answer the question;

(e) If the data in both the statements together are needed;

6. How many visitors saw the exhibition yesterday?

I. Each entry pass holder can take up to three persons with him / her.

II. In all, 243 passes were sold yesterday.

Ans:D

7. How much was the total sale of the company?

I. The company sold 8000 units of product A each costing Rs. 25.

II. The company has no other product line

Ans: E

8. In what proportion would Raj, Karan and Altaf distribute profit among them

I. Raj gets two-fifth of the profit.

II. Karan and Althaf have made 75% of the total investment.

Ans: D

9. What time did the train leave today.

I. The train normally leaves on time

II. The scheduled departure is at 14.30.

Ans: D

10. On which day in January, Subhas left for Germany

I. Subhas has so far spent 10 years in Germany.

II. Subhas’ friend Anil left for Germany on 15th February and joined Subhas 20 days after Subhas’ arrival.

Ans: D.

Directions(11-15): A cube is colored orange on one face , pink on the opposite face, brown on one face and silver on a face adjacent to the brown face. The other two faces are left un-colored. It is then cut into 125 smaller cubes of equal size. Now, answer the following questions based on the above statements:

11. How many cubes have at least one face colored pink?

A) 1        B)9         C) 16      D) 25

Ans: D

12. How many cubes have all the faces un-colored?

A) 24      B)36       C) 48      D) 64

Ans:C

13. How many cubes have at least two faces colored?

A) 19      B)20       C) 21      D) 23

Ans: C

14 How many cubes are colored orange on one face and have the remaining faces uncolored ?

A) 8        B) 12      C) 14      D) 16

Ans: D

15 How many cubes are colored silver on one face , orange or pink on another face and have four uncolored faces?

A) 8        B) 10     C) 12      D) 16

Ans: A

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