# Question & Answer of Analytical Skills

Seven machines take 7 minutes to make 7 identical toys. At the same rate, how many minutes would it take for 100 machines to make 100 toys?

A rectangle becomes a square when its length and breadth are reduced by 10 m and 5 m, respectively. During this process, the rectangle loses 650 m2 of area. What is the area of the original rectangle in square meters?

A number consists of two digits. The sum of the digits is 9. If 45 is subtracted from the number, its digits are interchanged. What is the number?

For integers $a,\;b$ and $c$ what would be the minimum and maximum values respectively of $a+\;b+\;c$ if $\log\left|a\right|+\log\left|b\right|+\log\left|c\right|=0?$

Given that $a\;$and $\;b$ are integers and  $a\;+a^2\;b^3$ is odd, which one of the following statements is correct ?

From the time the front of a train enters a platform, it takes 25 seconds for the back of the train to leave the platform, while travelling at a constant speed of 54 km/h. At the same speed, it takes 14 seconds to pass a man running at 9 km/h in the same direction as the train. What is the length of the train and that of the platform in meters, respectively?

Which of the following functions describe the graph shown in the below figure?

Consider the following three statements:
(i) Some roses are red.
(ii) All red flowers fade quickly.

Which of the following statements can be logically inferred from the above statements?

Find the missing group of letters in the following series: BC, FGH, LMNO, _____

The perimeters of a circle, a square and an equilateral triangle are equal. Which one of the following statements is true?

The value of the expression$\frac1{1+\log_uvw}+\frac1{1+\log_vwu}+\frac1{1+\log_wuv}$ is _________.

Forty students watched films A, B and C over a week. Each student watched either only one film or all three. Thirteen students watched film A, sixteen students watched film B and nineteen students watched film C. How many students watched all three films?

A wire would enclose an area of 1936 m2, if it is bent into a square. The wire is cut into two pieces. The longer piece is thrice as long as the shorter piece. The long and the short pieces are bent into a square and a circle, respectively. Which of the following choices is closest to the sum of the areas enclosed by the two pieces in square meters?

A contract is to be completed in 52 days and 125 identical robots were employed, each operational for 7 hours a day. After 39 days, five-seventh of the work was completed. How many additional robots would be required to complete the work on time, if each robot is now operational for 8 hours a day?

A house has a number which needs to be identified. The following three statements are given that can help in identifying the house number.

i. If the house number is a multiple of 3, then it is a number from 50 to 59.

ii. If the house number is NOT a multiple of 4, then it is a number from 60 to 69.

iii. If the house number is NOT a multiple of 6, then it is a number from 70 to 79.

What is the house number?

An unbiased coin is tossed six times in a row and four different such trials are conducted. One trial implies six tosses of the coin. If H stands for head and T stands for tail, the following are the observations from the four trials:

(1) HTHTHT (2) TTHHHT (3) HTTHHT (4) HHHT__ __.

Which statement describing the last two coin tosses of the fourth trial has the highest probability of being correct?

A right-angled cone (with base radius 5 cm and height 12 cm), as shown in figure below, is rolled on the ground keeping the point P fixed until the point Q (at the base of the cone, as shown) touches the ground again.

In a company with 100 employees, 45 earn Rs. 20,000 per month, 25 earn Rs. 30,000, 20 earn Rs. 40,000, 8 earn Rs. 60,000, and 2 earn Rs. 150,000. The median of the salaries is

P,Q, and R talk about S’s car collection. P states that S has at least 3 cars. Q believes that S has less than 3 cars. R indicates that to his knowledge, S has at least one car. Only one of P,Q and R is right. The number of cars owned by S is

What is the sum of the missing digits in the subtraction problem below?

 5 _ _ _ _ - 4 8 _ 8 9 1 1 1 1

Let $S_1$ be the plane figure consisting  of the points $(x,y)$ given by the inequalities $\left|x-1\right|\le 2$ and  $\left|y+2\right|\le 3$. Let $S_2$ be the plane figure given by the inequalities $x-y\geq-2,y\geq1,$ and $x\leq3$. Let $S$ be the union of $S_1$ and $S_2$ The area of $S$ is

Two very famous sportsmen Mark and Steve happened to be brothers, and played for country K. Mark teased James, an opponent from country E, “There is no way you are good enough to play for your country.” James replied, “Maybe not, but at least I am the best player in my own family.”

Which one of the following can be inferred from this conversation?

The growth of bacteria (lactobacillus) in milk leads to curd formation. A minimum bacterial population density of 0.8 (in suitable units) is needed to form curd. In the graph below, the population density of lactobacillus in 1 liter of milk is plotted as a function of time, at two different temperatures, 25 ºC and 37 ºC.

Consider the following statements based on the data shown above:

i.           The growth in bacterial population stops earlier at 37 ºC ac compared to 25 ºC

ii.          The time taken for curd formation at 25 ºC is twice the time taken at 37 ºC

Which one of the following options is correct?

If a and b are integers and - b is even, which of the following must always be even?

A couple has 2 children. The probability that both children are boys if the older one is a boy is

P looks at Q while Q looks at R. P is married, R is not. The number of pairs of people in which a married person is looking at an unmarried person is

X bullocks and Y tractors take 8 days to plough a field. If we halve the number of bullocks and double the number of tractors, it takes 5 days to plough the same field. How many days will it take X bullocks alone to plough the field?

There are 4 women P, Q, R, S, and 5 men V, W, X, Y, Z in a group. We are require to form pairs each consisting of women and one man. P is not to be paired with Z, and Y must necessarily be paired with someone. In how many ways can 4 such pairs be formed?

All people in a certain island are either ‘Knights’ or ‘Knaves’ and each person knows every other person’s identity. Knights NEVER lie, and knaves ALWAYS lie.

P says “Both of us are knights”. Q says “None of us are knaves”.

Which one of the following can be logically inferred from the above?

In the graph below, the concentration of a particular pollutant in a lake is plotted over (alternate) days of a month in winter (average temperature 10°C) and a month in summer (average temperature 30°C).

Consider the following statement based on the data shown above:

i.  Over the given month, the difference between the maximum and the minimum pollutant concentrations is the same in both winter and summer.

ii. There are at least four days in the summer month such that the pollutant concentrations on those days are within 1 ppm of the pollutant concentrations on the corresponding days in the winter month.

Which one of the following option is correct?

In a huge pile of apples and oranges, both ripe and unripe mixed together, 15% are unripe fruits. Of the unripe fruits, 45% are apples. Of the ripe ones, 66% are oranges. If the pile contains a total of 5692000 fruits, how many of them are apples?

Michael lives 10 km away from where I live. Ahmed lives 5 km away and Susan lives 7 km away from where I live. Arun is farther away than Ahmed but closer than Susan from where I live. From the information provided here, what is one possible distance (in km) at which I live from Arun’s place?

A person moving through a tuberculosis prone zone has a 50% probability of becoming infected. However, only 30% of infected people develop the disease. What percentage of people moving through a tuberculosis prone zone remains infected but does not show symptoms of disease?

If $\frac12q^{-a}=\frac1r\;$ and $r^{-b}=\frac1s$ and $S^{-C}=\frac1q$ the value of $abc$ is .

P, Q, R and S are working on a project. Q can finish the task in 25 days, working alone for 12 hours a day. R can finish the task in 50 days, working alone for 12 hours per day. Q worked 12 hours a day but took sick leave in the beginning for two days. R worked 18 hours a day on all days.What is the ratio of work done by Q and R after 7 days from the start of the project?

#### SET - 2

The volume of a sphere of diameter 1 unit is ________ than the volume of a cube of side 1 unit.

A window is made up of a square portion and an equilateral triangle portion above it. The base of the triangular portion coincides with the upper side of the square. If the perimeter of the window is 6 m, the area of the window in $\mathrm m^2$ is ___________.

Students taking an exam are divided into two groups, P and Q such that each group has the same number of students. The performance of each of the students in a test was evaluated out of 200 marks. It was observed that the mean of group P was 105, while that of group Q was 85. The standard deviation of group P was 25, while that of group Q was 5. Assuming that the marks were distributed on a normal distribution, which of the following statements will have the highest probability of being TRUE?

Find the missing sequence in the letter series.

B, FH, LNP, _ _ _ _.

The binary operation $\square$ is defined as a $a\;\square\;b\;=\;ab+(a+b)$, where $a$ and $b$ are any two real numbers. The value of the identity element of this operation, defined as the number $x$ such that a $a\;\square\;x=a$, for any $a$, is _________.

Which of the following curves represents the function $y=\mathrm{In}(\;\vert e^{\lbrack\vert\sin(\vert x\vert)\vert\rbrack}\vert)\;\mathrm{for}\;\vert x\vert<2\pi$? Here, $x$ represents the abscissa and $y$ represents the ordinate.

Given $(9\;\mathrm{inches})^½=(0.25\;\mathrm{yards})^½$, which one of the following statements is TRUE?

S, M, E and F are working in shifts in a team to finish a project. M works with twice the efficiency of others but for half as many days as E worked. S and M have 6 hour shifts in a day, whereas E and F have 12 hours shifts. What is the ratio of contribution of M to contribution of E in the project?

The Venn diagram shows the preference of the student population for leisure activities.
From the data given, the number of students who like to read books or play sports is _______.

Two and quarter hours back, when seen in a mirror, the reflecation of a wall clock without number  markings seemed to show 1:30. What is the actual current time shown by the clock?

M and N start from the same location. M travels 10 km East and then 10 km North-East. N travels 5km South and then 4 km South-East. What is the shortest distance (in km) between M and N at the end of their travel?

A wire of length 340 mm is to be cut into two parts. One of the parts is to be made into a square and the other into a rectangle where sides are in the ratio of 1:2. What is the length of the side of the square (in mm) such that the combined area of the square and the rectangle is a MINIMUM?

The statistics of runs scored in a series by four batsmen are provided in the following table. Who is the most consistent batsman of these four?

 Batsman Average Standard deviation K 31.2 5.21 L 46.0 6.35 M 54.4 6.22 N 17.9 5.90

What is the next number in the series?

12 35 81 173 357 ____

Find the odd one from the following group:

W,E,K,O   I,Q,W,A    F,N,T,X    N,V,B,D

For submitting tax returns, all resident males with annual income below Rs 10 lakh should fill up Form P and all resident females with income below Rs 8 lakh should fill up Form Q. All people with incomes above Rs 10 lakh should fill up Form R, except non residents with income above Rs 15 lakhs, who should fill up Form S. All others should fill Form T. An example of a person who should fill Form T is

A train that is 280 metres long, travelling at a uniform speed, crosses a platform in 60 seconds and passes a man standing on the platform in 20 seconds. What is the length of the platform in metres?

The exports and imports (in crores of Rs.) of a country from 2000 to 2007 are given in the following bar chart. If the trade deficit is defined as excess of imports over exports, in which year is the trade deficit 1/5th of the exports?

You are given three coins: one has heads on both faces, the second has tails on both faces, and the third has a head on one face and a tail on the other. You choose a coin at random and toss it, and it comes up heads. The probability that the other face is tails is

A regular die has six sides with numbers 1 to 6 marked on its sides. If a very large number of throws show the following frequencies of occurrence: 1 → 0.167; 2 → 0.167; 3 → 0.152; 4 → 0.166; 5 → 0.168; 6 → 0.180. We call this die

Fill in the missing number in the series

2 3 6 15 ______ 157.5 630

Find the odd one in the following group

Q,W,Z,B     B,H,K,M     W,C,G,J     M,S,V,X

Lights of four colors (red, blue, green, yellow) are hung on a ladder. On every step of the ladder there are two lights. If one of the lights is red, the other light on that step will always be blue. If one of the lights on a step is green, the other light on that step will always be yellow. Which of the following statements is not necessarily correct?

The sum of eight consecutive odd numbers is 656. The average of four consecutive even numbers is 87. What is the sum of the smallest odd number and second largest even number?

The total exports and revenues from the exports of a country are given in the two charts shown below. The pie chart for exports shows the quantity of each item exported as a percentage of the total quantity of exports. The pie chart for the revenues shows the percentage of the total revenue generated through export of each item. The total quantity of exports of all the items is 500 thousand tonnes and the total revenues are 250 crore rupees. Which item among the following has generated the maximum revenue per kg?

It takes 30 minutes to empty a half-full tank by draining it at a constant rate. It is decided to simultaneously pump water into the half-full tank while draining it. What is the rate at which water has to be pumped in so that it gets fully filled in 10 minutes?

The next term in the series 81, 54, 36, 24, … is ________

In which of the following options will the expression P < M be definitely true?

Find the next term in the sequence: 7G, 11K, 13M, ___

The multi-level hierarchical pie chart shows the population of animals in a reserve forest. The correct conclusions from this information are:

 (i) Butterflies are birds (ii) There are more tigers in this forest than red ants (iii) All reptiles in this forest are either snakes or crocodiles (iv) Elephants are the largest mammals in this forest

A man can row at 8 km per hour in still water. If it takes him thrice as long to row upstream, as to row downstream, then find the stream velocity in km per hour.

A firm producing air purifiers sold 200 units in 2012. The following pie chart presents the share of raw material, labour, energy, plant & machinery, and transportation costs in the total manufacturing cost of the firm in 2012. The expenditure on labour in 2012 is Rs. 4,50,000. In 2013, the raw material expenses increased by 30% and all other expenses increased by 20%. If the company registered a profit of Rs. 10 lakhs in 2012, at what price (in Rs.) was each air purifier sold?

A batch of one hundred bulbs is inspected by testing four randomly chosen bulbs. The batch is rejected if even one of the bulbs is defective. A batch typically has five defective bulbs. The probability that the current batch is accepted is_______

Let f(x,y)=xnym = P If x is doubled and y is halved, the new value of f is

In a sequence of 12 consecutive odd numbers, the sum of the first 5 numbers is 425. What is the sum of the last 5 numbers in the sequence?

Find the next term in the sequence: 13M, 17Q, 19S, ___

If ‘KCLFTSB’ stands for ‘best of luck’ and ‘SHSWDG’ stands for ‘good wishes’, which of the following indicates ‘ace the exam’?

Industrial consumption of power doubled from 2000-2001 to 2010-2011. Find the annual rate of increase in percent assuming it to be uniform over the years

A firm producing air purifiers sold 200 units in 2012. The following pie chart presents the share of raw material, labour, energy, plant & machinery, and transportation costs in the total manufacturing cost of the firm in 2012. The expenditure on labour in 2012 is Rs. 4,50,000. In 2013, the raw material expenses increased by 30% and all other expenses increased by 20%. What is the percentage increase in total cost for the company in 2013?

A five digit number is formed using the digits 1,3,5,7 and 9 without repeating any of them. What is the sum of all such possible five digit numbers?

What will be the maximum sum of 44, 42, 40, ...... ?

Out of all the 2-digit integers between 1 and 100, a 2-digit number has to be selected at random. What is the probability that the selected number is not divisible by 7?

A tourist covers half of his journey by train at 60 km/h, half of the remainder by bus at 30 km/h and the rest by cycle at 10 km/h. The average speed of the tourist in km/h during his entire journey is

Find the sum of the expression

$\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+\dots \dots \dots \dots +\frac{1}{\sqrt{80}+\sqrt{81}}$

The current erection cost of a structure is Rs. 13,200. If the labour wages per day increase by 1/5 of the current wages and the working hours decrease by 1/24 of the current period, then the new cost of erection in Rs. is

The cost function for a product in a firm is given by 5q2, where q is the amount of production. The firm can sell the product at a market price of  50 per unit. The number of units to be produced by the firm such that the profit is maximized is

Given the sequence of terms, AD CG FK JP, the next term is

A political party orders an arch for the entrance to the ground in which the annual convention is being held. The profile of the arch follows the equation y = 2x – 0.1x2 where y is the height of the arch in meters. The maximum possible height of the arch is

An automobile plant contracted to buy shock absorbers from two suppliers X and Y. X supplies 60% and Y supplies 40% of the shock absorbers. All shock absorbers are subjected to a quality test. The ones that pass the quality test are considered reliable. Of X’s shock absorbers, 96% are reliable. Of Y’s shock absorbers, 72% are reliable.

The probability that a randomly chosen shock absorber, which is found to be reliable, is made by Y is

Which of the following assertions are CORRECT?

P: Adding 7 to each entry in a list adds 7 to the mean of the list
Q: Adding 7 to each entry in a list adds 7 to the standard deviation of the list
R: Doubling each entry in a list doubles the mean of the list
S: Doubling each entry in a list leaves the standard deviation of the list unchanged

If Log (P) = (1/2)Log (Q) = (1/3) Log (R), then which of the following options is TRUE?

A container originally contains 10 litres of pure spirit. From this container 1 litre of spirit is replaced with 1 litre of water. Subsequently, 1 litre of the mixture is again replaced with 1 litre of water and this process is repeated one more time. How much spirit is now left in the container?