# UPSC IAS Exam: IAS Prelims CSAT Basic Numeracy Set 8

In the Civil Services IAS Prelim Examination, the CSAT paper has been made qualifying in nature from 2015 onwards. The candidates have to score at least qualifying marks in the paper but in case, if a candidate could not be able to score the required qualifying marks in CSAT Paper then his/her other papers will not be evaluated. So, it is important for the candidates to do preparation in such a manner that there must not lay them in any suspicion of underscoring.**Category: Number system**

**1.An auto-manufacturing company has three machines producing the same auto part. If machine A produces 1/6th as many of the item as machine B produces in the same time and machine B produces twice as many of the item as machine C in the same time, then during a fixed period machine C produces what fraction of the total number of items produced? **

**Answer (b) **

**Explanation:**

Assuming, Machine A produces 100 units in a certain time period.

Machine B would produce 6 times of X or 600 units.

Machine C would produce half of that = 300 units

The three machines together would produce 1000 units, of which 300 are produced by machine C.

Required Fraction = 300/1000= 3/10**2. If the sum of three numbers is 272 and the ratio between first and second be 2: 3 and that between second and third is 5: 3, then the second number is**

a) 130

b) 140

c) 150

d) 120

**Answer (d)**

** Explanation:**

**Category: Probability**

**3. What is the probability that there are 53 Mondays if a leap year is chosen at random?**

a) 1/7

b) 1/14

c) 2/7

d) 3/7

**Answer (c) **

**Explanation:**

There are 52 weeks (364 days) and 2 extra days in a leap year.

The probability that the first of the two extra days is a Monday is (1/7)

The probability that the second of the two extra days is a Monday is (1/7)

Thus the probability is 1/7+1/7=2/7**Category: Permutation and combination****4.Find out the number of ways in which a mixed doubles game of tennis can be arranged of 5 married couples, if no husband and wife play in the same game?**

a) 46

b) 54

c) 60

d) 80

**Answer (c)**

** Explanation:**

Let the sides of the game be A and B.

Given 5 married couples,

i.e., 5 husbands and 5 wives.

Now, 2 husbands for two sides A and B can be selected out of 5 = 5C2 = 10 ways.

After choosing the two husbands their wives are to be excluded (since no husband and wife lay in the same game).

So we are to choose 2 wives out of remaining 5 – 2 = 3 wives, i.e., 3C2 = 3 ways.

Again two wives can interchange their sides A and B in 2! = 2 ways.

Therefore, the required number of ways = 10 × 3 × 2 = 60.**Category: Mensuration**

**5.One of the diagonal of a rhombus is 20% less than the other diagonal. A semi-circle is described taking the smaller diagonal as diameter. What is the ratio of area of the rhombus to the area of semi-circle? **

a) 5 : π

b) 2 : 5π

c) 1 : 5π

d) None of these** **

**Answer (a)**

** Explanation:**

**Category: Data interpretation**

**
**

The bar graph provided below gives the sales of Music CD’s (in thousand numbers) from six stores of a Music company during two consecutive years 2012 and 2013. Answer the questions based on the graph.

**6. Total sales of stores A, C and E together for both the years (in thousands) is: **

a) 586

b) 560

c) 480

d) Data Inadequate

**Answer (b)**

** Explanation: **

Total sales of stores A, C and E for both years = (80+105)+(95+110)+(75+95)

= 185+205+170

= 560.**7.Total sales of store F for both the years are what percent of the total sales of the store C for both the years? **

a) 64.04%

b) 81.12%

c) 73.17%

d) 71.71%**Answer (c) **

**Explanation:**

**8.Find the average sales (in thousands) of all the stores in the year 2012.**

a) 76

b) 85

c) 92

d) None of these

**Answer (d)**

** Explanation:**

**9.What percent of average sales of stores A, B and C in 2013 is the average sales of the stores A, C and F in 2012? **

a) 91.1%

b) 82.6%

c) 114.2%

d) 87.5%

**Answer (C) **

**Explanation: **

Category: Data Sufficiency

Directions for questions (20 -21) In each question there are two statements A and B, you have to select the correct answer from 1 to 4 depending upon the sufficiency of data given in the statements to answer the question.

a) If statement A alone is sufficient and statement B alone is not sufficient to answer the question.

b) If statement B alone is sufficient and statement A alone is not sufficient to answer the question

c) If statements A and B together are sufficient but neither statements alone is sufficient to answer the question.

d) I both the statements A and B together are not sufficient to answer the question.**10.Find the profit obtained by the Ramesh at the end of the year .if the profit is Rs 60,000.**

A: Ramesh has invested 60,000 and Vishwas 25,000.

B: Ramesh has invested the money for 10 months and Vishwas for 12 months.

**Answer (c) **

**Explanation:**

**11.There are two varieties of tea available in the market names as Sugandha and Suvarna the average price of Sugandha is Rs 60 per kg and that of Suvarna is 180 Rs per kg. Find the Selling price of the mixture?**

A: If the Shopkeeper mixes these two varieties in the ratio of 2:3

B: If the Shopkeeper decides to sell the mixture at a profit of 25 %.

**Answer (c) **

**Explanation:**

Both the statements are needed to solve as the A gives the ratio in which they are mixed and B gives the information about percentage he needs in terms of profit.

**Click here for the CSAT Basic Numeracy Study Material**