Question & Answer of Analytical Skills

The three roots of the equation $ f(x)=0 $ are x = {-2, 0, 3}. What are the three values of $ x $ for which $ f\;(x-3)=0\;? $

For what values of $ k $ given below is $ \textstyle\frac{(k+2)^2}{k-3} $ an integer?

Functions $ F(a,b) $ and $ G(a,b) $ are defined as follows:

$ F(a,b)=(a,b)^2 $ and $ G(a,b)=\left|a-b\right| $ , where $ \left|x\right| $ represents the absolute value of $ x $ What would be the value of $ \style{font-family:'Times New Roman'}{G(F(1,3),G(1,3))?} $ 

An e-mail password must contain three characters. The password has to contain one numeral from 0 to 9, one upper case and one lower case character from the English alphabet. How many distinct passwords are possible?

In a certain code, AMCF is written as EQGJ and NKUF is written as ROYJ. How will DHLP be written in that code?

A class of twelve children has two more boys than girls. A group of three children are randomly picked from this class to accompany the teacher on a field trip. What is the probability that the group accompanying the teacher contains more girls than boys?

A designer uses marbles of four different colours for his designs. The cost of each marble is the same, irrespective of the colour. The table below shows the percentage of marbles of each colour used in the current design. The cost of each marble increased by 25%. Therefore, the designer decided to reduce equal numbers of marbles of each colour to keep the total cost unchanged. What is the percentage of blue marbles in the new design?

Blue Black Red Yellow
40% 25% 20% 15%

P, Q, R and S crossed a lake in a boat that can hold a maximum of two persons, with only one set of oars. The following additional facts are available.

(i) The boat held two persons on each of the three forward trips across the lake and one person on each of the two return trips.

(ii) P is unable to row when someone else is in the boat.

(iii) Q is unable to row with anyone else except R.

(iv) Each person rowed for at least one trip. (v) Only one person can row during a trip.

Who rowed twice?

Rahul, Murali, Srinivas and Arul are seated around a square table. Rahul is sitting to the left of Murali, Srinivas is sitting to the right of Arul. Which of the following pairs are seated opposite each other?

Find the smallest number y such that y × 162 is a perfect cube.

The probability that a k-digit number does NOT contain the digits 0, 5, or 9 is

Six people are seated around a circular table. There are at least two men and two women there are at least three right-handed persons. Every woman has a left-landed person to her immediate right. None of the women are right-handed. The number of women at the table is

The expression (x+y)-x-y2 is equal to

Arun, Gulab, Neel and Shweta must choose one shirt each from a pile of four shirts colored red, pink, blue and white respectively. Arun dislikes the color red and Shweta dislikes the colour white. Gulab and Neel like all the colors. In how many different ways can they choose the shirts so that no one has a shirt with a color he or she dislikes?

A contour line joins location having the same height above the mean sea level. The following is a contour plot of a geographical region. Contour lines are shown at 25m intervals in this plot. If in a flood, the water level rises to 525 m. which of the villages P, Q, R, S, T get submerged?


There are five buildings called V, W, X, Y and Z in arrow (not necessarily in that order). V is to the West of W. Z is to East of X and the West of V. W is to the West of Y. Which is the building in the middle?

A test has twenty questions worth 100 marks in total. There are two types of questions. Multiple choice questions are worth 3 marks each and essay questions are worth 11 marks each. How many multiple choice questions does the exam have?

There are 3 red socks, 4 green socks and 3 blue socks. You choose 2 socks. The probability that they are of the same colour is

There are three boxes. One contains apples, another contains orange and the last one contains both apples and oranges. All three are known to be incorrectly labeled. If you are permitted to open just one box and then pull out and inspect only one fruit, which box would you open to determine the contents of all three boxes?

X is a 30 digit number starting with the digit 4 followed by the digit 7. Then the number X3 will have

The number of roots of $e^x+0.5x^2-2=0$ in the range [-5,5] is

An air pressure contour line joins location in a region having the same atmospheric pressure. The following is an air pressure contour plot of a geographical region. Contour lines are shown at 0.05 bas intervals in this plot.



If the possibility of a thunderstorm is given by how fast air pressure rises or drops over a region, which of the following regions is most likely to have a thunderstorm?

Pick the odd one from the following options.

In a quadratic function, the value of the product of the roots $ (\alpha,\beta) $ is 4. Find the value of


Among 150 faculty members in an institute, 55 are connected with each other through Facebook® and 85 are connected through WhatsApp®. 30 faculty members do not have Facebook® or WhatsApp® accounts. The number of faculty members connected only through Facebook® accounts is ______________.

In a 2 × 4 rectangle grid shown below, each cell is a rectangle. How many rectangles can be observed in the grid?


Choose the correct expression for f(x) given in the graph.

Pick the odd one out in the following:

13, 23, 33, 43, 53

If |9y−6| =3, then y2 −4y/3 is ___________.

The following graph represents the installed capacity for cement production (in tonnes) and the actual production (in tonnes) of nine cement plants of a cement company. Capacity utilization of a plant is defined as ratio of actual production of cement to installed capacity. A plant with installed capacity of at least 200 tonnes is called a large plant and a plant with lesser capacity is called a small plant. The difference between total production of large plants and small plants, in tonnes is ____.


Shaquille O’ Neal is a 60% career free throw shooter, meaning that he successfully makes 60 free throws out of 100 attempts on average. What is the probability that he will successfully make exactly 6 free throws in 10 attempts?

The numeral in the units position of 211870 + 146127 × 3424 is _____.

Based on the given statements, select the most appropriate option to solve the given question.

If two floors in a certain building are 9 feet apart, how many steps are there in a set of stairs that extends from the first floor to the second floor of the building?


(I) Each step is ¾ foot high.
(II) Each step is 1 foot wide.

Given set A = {2, 3, 4, 5} and Set B = {11, 12, 13, 14, 15}, two numbers are randomly selected, one from each set. What is probability that the sum of the two numbers equals 16?

The pie chart below has the breakup of the number of students from different departments in an engineering college for the year 2012. The proportion of male to female students in each department is 5:4. There are 40 males in Electrical Engineering. What is the difference between numbers of female students in the Civil department and the female students in the Mechanical department?

The probabilities that a student passes in Mathmatics, Physics and Chemistry are m,p, and c respectively. Of these subjects, the student has 75% chance of passing in at least one, a 50% chance of passing in at least two and a 40% chance of passing in exactly two. Following relations are drawn in m, p, c:

(I)   p + m + c = 27/20
(II)  p + m + c = 13/20
(III) (p)×(m)×(c) = 1/10

The number of students in a class who have answered correctly, wrongly, or not attempted each question in an exam, are listed in the table below. The marks for each question are also listed. There is no negative or partial marking.

Q No. Marks Answered Correctly Answered Wrongly Not  Attemted
1 2 21 17 6
2 3 15 27 2
3 1 11 29 4
4 2 23 18 3
5 5 31 12 1

What is the average of the marks obtained by the class in the examination?

Based on the given statements, select the most appropriate option to solve the given question.

What will be the total weight of 10 poles each of same weight?


(I) One fourth of the weight of a pole is 5 kg

(II) The total weight of these poles is 160 kg more than the total weight of two poles.

Consider a function f(x) = 1-x on -1 x 1. The value of x at which the function attains a maximum, and the maximum value of the function are:

In a triangle PQR, PS is the angle bisector of QPR and QPS = 60° . What is the length of PS?

If p, q, r, s are distinct integers such that:
f (p, q, r, s) = max (p, q, r, s)
g (p, q, r, s) = min (p, q, r, s)
h (p, q, r, s) = remainder of (p × q)/(r × s) if (p × q) > (r × s) or remainder of (r × s)/(p × q) if (r × s) > (p × q)
Also a function fgh (p, q, r, s) = f(p, q, r, s) × g(p, q, r, s) × h(p, q, r, s)
Also the same operations are valid with two variable function of the form f(p, q).
What is the value of fg (h(2, 5, 7, 3), 4, 6, 8)?

If the list of letters, P, R, S, T, U is an arithmetic sequence, which of the following are also in arithmetic sequence?

I   2P, 2R, 2S, 2T, 2U
II  P-3, R-3, S-3, T-3, U-3
III P2, R2, S2, T2, U2

Four branches of a company are located at M,N,O, and P. M is north of N at a distance of 4 km; P is south of O at a distance of 2 km; N is southeast of O by 1 km. What is the distance between M and P in km?

If (z + 1/z)2 = 98, compute (z2 + 1/z2).

The roots of ax2 + b+ c= 0 are real and positive. a, b and c are real. Then ax2 + b|x| + c = 0 has

Round-trip tickets to a tourist destination are eligible for a discount of 10% on the total fare. In addition, groups of 4 or more get a discount of 5% on the total fare. If the one way single person fare is Rs 100, a group of 5 tourists purchasing round-trip tickets will be charged Rs _________.

In a survey, 300 respondents were asked whether they own a vehicle or not. If yes, they were further asked to mention whether they own a car or scooter or both. Their responses are tabulated below. What percent of respondents do not own a scooter?

When a point inside of a tetrahedron (a solid with four triangular surfaces) is connected by straight lines to its corners, how many (new) internal planes are created with these lines? _____________

What is the average of all multiples of 10 from 2 to 198?

The value of 12+12+12+... is

If x is real and x2-2x+3=11 then possible values of -x3+x2-x=11 include

The ratio of male to female students in a college for five years is plotted in the following line graph. If the number of female students doubled in 2009, by what percent did the number of male students increase in 2009?

At what time between 6 a.m. and 7 a.m. will the minute hand and hour hand of a clock make an angle closest to 60°?

Which number does not belong in the series below?

2, 5, 10, 17, 26, 37, 50, 64

The table below has question-wise data on the performance of students in an examination. The marks for each question are also listed. There is no negative or partial marking in the examination.

Q No. Marks Answered Correctly Answered Wrongly Not Attempted
1 2 21 17 6
2 3 15 27 2
3 2 23 18 3

What is the average of the marks obtained by the class in the examination?

A dance programme is scheduled for 10.00 a.m. Some students are participating in the programme and they need to come an hour earlier than the start of the event. These students should be accompanied by a parent. Other students and parents should come in time for the programme. The instruction you think that is appropriate for this is

The Gross Domestic Product (GDP) in Rupees grew at 7% during 2012-2013. For international comparison, the GDP is compared in US Dollars (USD) after conversion based on the market exchange rate. During the period 2012-2013 the exchange rate for the USD increased from Rs. 50/ USD to Rs. 60/ USD. India’s GDP in USD during the period 2012-2013

The ratio of male to female students in a college for five years is plotted in the following line graph. If the number of female students in 2011 and 2012 is equal, what is the ratio of male students in 2012 to male students in 2011?

Consider the equation: (7526)8 − (Y)8 = (4364)8 , where (X)N stands for X to the base N. Find Y.

In the summer of 2012, in New Delhi, the mean temperature of Monday to Wednesday was 41°C and of Tuesday to Thursday was 43°C. If the temperature on Thursday was 15% higher than that of Monday, then the temperature in °C on Thursday was

What is the chance that a leap year, selected at random, will contain 53 Saturdays?

The set of values of p for which the roots of the equation 3x2+2x+p(p-1)=0 are of opposite sign is

A car travels 8 km in the first quarter of an hour, 6 km in the second quarter and 16 km in the third quarter. The average speed of the car in km per hour over the entire journey is

Find the sum to n terms of the series 10+84+ 734 + .....

If (1.001)1259 = 3.52 and (1.001)2062 = 7.85, then (1.001)3321 =

A and B are friends. They decide to meet between 1 PM and 2 PM on a given day. There is a condition that whoever arrives first will not wait for the other for more than 15 minutes. The probability that they will meet on that day is

Raju has 14 currency notes in his pocket consisting of only Rs. 20 notes and Rs. 10 notes. The total money value of the notes is Rs. 230. The number of Rs. 10 notes that Raju has is

There are eight bags of rice looking alike, seven of which have equal weight and one is slightly heavier. The weighing balance is of unlimited capacity. Using this balance, the minimum number of weighings required to identify the heavier bag is

The data given in the following table summarizes the monthly budget of an average household.

Category Amount (Rs.)
Food 4000
Clothing 1200
Rent 2000
Savings 1500
Other expenses 1800

The approximate percentage of the monthly budget NOT spent on savings is

There are two candidates P and Q in an election. During the campaign, 40% of the voters promised to vote for P, and rest for Q. However, on the day of election 15% of the voters went back on their promise to vote for P and instead voted for Q. 25% of the voters went back on their promise to vote for Q and instead voted for P. Suppose, P lost by 2 votes, then what was the total number of voters?

The sum of n terms of the series 4+44+444+.... is

The fuel consumed by a motorcycle during a journey while traveling at various speeds is indicated in the graph below.

The distances covered during four laps of the journey are listed in the table below

Lap Distance
Average speed
(kilometers per hour)
P 15 15
Q 75 45
R 40 75
S 10 10

From the given data, we can conclude that the fuel consumed per kilometre was least during the lap

Three friends, R, S and T shared toffee from a bowl. R took 1/3rd of the toffees, but returned four to the bowl. S took 1/4th of what was left but returned three toffees to the bowl. T took half of the remainder but returned two back into the bowl. If the bowl had 17 toffees left, how many toffees-were originally there in the bowl?

Given that f(y) = | y | / y, and q is any non-zero real number, the value of | f(q) - f(-q) | is

25 persons are in a room. 15 of them play hockey, 17 of them play football and 10 of them play both hockey and football. Then the number of persons playing neither hockey nor football is:

Hari (H), Gita (G), Irfan (I) and Saira (S) are siblings (i.e. brothers and sisters). All were born on 1st January. The age difference between any two successive siblings (that is born one after another) is less than 3 years. Given the following facts:

i. Hari’s age + Gita’s age > Irfan’s age + Saira’s age
ii. The age difference between Gita and Saira is 1 year. However Gita is not the oldest and Saira is not the youngest.
iii. There are no twins.

In what order were they born (oldest first)?

5 skilled workers can build a wall in 20days; 8 semi-skilled workers can build a wall in 25 days; 10 unskilled workers can build a wall in 30days. If a team has 2 skilled, 6 semi-skilled and 5 unskilled workers, how long will it take to build the wall?

Given digits 2, 2, 3, 3, 3, 4, 4, 4, 4 how many distinct 4 digit numbers greater than 3000 can be formed?

If 137 + 276 = 435 how much is 731 + 672?