Quantitative Aptitude

Data Interpretation

290 Questions
All Percentage & Fraction Conversion 77 Sum, Difference & Average 76 Ratio Comparison 37 Pie Chart Angle Mapping 33 Missing Data Derivation 27 Commercial Arithmetic Application 19 Direct Value Extraction 10 Trend & Growth Analysis 9 Compound DI Cross-Referencing 1 Permutations & Arrangements 1

Data Interpretation Questions

Multiple choice

In a Pie chart, the angle for each sector is calculated by using the formula:
  1. $\frac{Component Part}{Total}\times 100$
  2. $\frac{Component Part}{Total}\times 360$
  3. $\frac{Component Part}{Total}\times \pi$
  4. $\frac{Total}{Component Part}\times \pi$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The angle of a sector in a pie chart is proportional to the component part relative to the total, multiplied by the total degrees in a circle (360).

Multiple choice

Choose the correct answer from the alternatives given. Directions for question 71 to 75: Study the following table carefully and answer the questions given below. Number of Students Enrolled With Five Colleges over the Years Year/College A B C D E 2004 450 320 400 480 520 2005 480 350 380 500 540 2006 420 300 410 520 460 2007 460 360 430 470 480 2008 470 340 390 530 530 What is the ratio between the average number of students enrolled with all colleges together in 2007 and 2008, respectively?

  1. 108 : 113

  2. 108 : 117

  3. 110 : 113

  4. 111 : 113
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total students in 2007: 460+360+430+470+480 = 2200. Average = 2200/5 = 440. Total students in 2008: 470+340+390+530+530 = 2260. Average = 2260/5 = 452. Ratio = 440/452 = 110/113.

Multiple choice

The pie chart shows the distribution of grades obtained by a group of students in a test. The number of students who scored grade C is twice the number who scored grade B, and $\displaystyle \frac{3}{5}$ of the students scored grades B and C. Find the angle of sector which represents grade C.
  1. $108^{\circ}$
  2. $144^{\circ}$
  3. $216^{\circ}$
  4. $288^{\circ}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let B and C be the number of students in grades B and C. We know C = 2B and B + C = 3/5 of total students. Thus, 3B = 3/5 total, so B = 1/5 total and C = 2/5 total. The angle for C is (2/5) * 360 = 144 degrees.

Multiple choice

If the number of boys and the number of girls in a class are 45% and 55% respectively and it is represented in a pie chart what will be the central angles of the portions representing boys and girls respectively?
  1. $\displaystyle 160^{\circ},200^{\circ}$
  2. $\displaystyle 162^{\circ},198^{\circ}$
  3. $\displaystyle 150^{\circ},210^{\circ}$
  4. $\displaystyle 180^{\circ},180^{\circ}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Central angle = (Percentage / 100) * 360. Boys: 0.45 * 360 = 162 degrees. Girls: 0.55 * 360 = 198 degrees.

Multiple choice

The following data gives the distribution of monthly expenses under different heads. Type of Commodity Expenditure (in rupees) Food $300$ Rent $200$ Clothes $125$ Education $110$ Miscellaneous $75$ Savings $90$ A pie chart is drawn for the above data, the angle subtended at the centre for the item 'Rent' will be
  1. $20^{\circ}$
  2. $80^{\circ}$
  3. $85^{\circ}$
  4. $120^{\circ}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total expenditure = 300+200+125+110+75+90 = 900. The angle for Rent is (200 / 900) * 360 degrees = (2/9) * 360 = 80 degrees.

Multiple choice

In a class there are 60 students. The following pie diagram shows the number of students according to blood-group. There are 8 students having blood-group A, 18 students having blood-group O. Students having B group are represented by $120^o$, find the number of students having AB blood-group :

  1. 14

  2. 16

  3. 18

  4. 20
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total students = 60. A=8, O=18. B group = 120 degrees out of 360 = 1/3 of total = 20 students. AB group = 60 - (8 + 18 + 20) = 60 - 46 = 14.

Multiple choice

The mean of the followlng frequency table is $53$. But the frequencies $f_1$ and $f_2$ in the classes $20-40 $ and $60-80 $ are missing. Find the missinq frequencies. Age (in years) 0-20 20-40 40-60 60-80 80-100 Total No. of people 15 $f_1$ 21 $f_2$ 17 100
  1. $f_1=20, f_2=28$
  2. $f_1=17, f_2=19$
  3. $f_1=19, f_2=25$
  4. $f_1=18, f_2=29$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total frequency = 15 + f1 + 21 + f2 + 17 = 100, so f1 + f2 = 47. Mean = (sum of f*x)/100 = 53. Using midpoints (10, 30, 50, 70, 90): (150 + 30f1 + 1050 + 70f2 + 1530) / 100 = 53. 30f1 + 70f2 = 2730 - 2700 = 30. This implies 3f1 + 7f2 = 270. Solving the system: f1 = 18, f2 = 29.

Multiple choice

Total number of copies sold End of $1^{st}$ week $3200$ End of $2^{nd}$ week $5500$ End of $3^{rd}$ week $6800$ End of $4^{th}$ week $7400$ End of $5^{th}$ week $7700$ The table above shows the total number of copies of Book B that were sold by the end of each of the first $5$ weeks of its publication. How many copies of the book were sold during the $3^{rd}$ week of its publication?
  1. $1200$
  2. $1250$
  3. $1300$
  4. $1350$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The table shows total copies sold by the end of each week. To find sales during the 3rd week, subtract total sales at the end of the 2nd week from total sales at the end of the 3rd week: 6800 - 5500 = 1300.

Multiple choice

Consider the Rufus School activities-data shown below : Basketball Chess club Jazz Band Not involved Total Males $20$ $2$ $8$ $10$ $40$ Females $20$ $10$ $10$ $20$ $60$ Total $40$ $12$ $18$ $30$ $100$ Prepare bivariate table with relative frequency. Based on bivariate table with relative frequency, what is the relative frequency of students not involved in any activity?
  1. $0.120$
  2. $0.150$
  3. $0.200$
  4. $0.300$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total students = 100. Students not involved = 30. Relative frequency = 30 / 100 = 0.300.

Multiple choice

Each month, the Bureau of Labor Statistics conducts a survey called the Current Population Survey(CPS) to measure unemployment in the United States. Across the country, about $60,000$ households are included in the survey sample. These households are grouped by geographic region. A summary of the January 2014 survey results for male respondents in one geographic region is shown in the table below. Age group Employed Unemployed Not in the Labor Force Total 16 to 19 8 5 10 23 20 to 24 26 7 23 56 25 to 34 142 11 28 157 35 to 44 144 8 32 164 45 to 54 66 6 26 98 Over 54 65 7 36 152 Total 451 44 155 650 According to the data in the table, for which age group did the smallest percentage of men report that they were unemployed in January 2014?

  1. 20 to 24 years

  2. 35 to 44 years

  3. 45 to 54 years

  4. Over 54 years
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Compute unemployed divided by total for each age group. The percentages are approximately 21.7%, 12.5%, 7.0%, 4.9%, 6.1%, and 4.6%, respectively, so the smallest is for men over 54.