# Question & Answer of Analytical Skills

If the number $715\blacksquare423$ is divisible by 3 ($\blacksquare$ denotes the missing digit in the thousandths place), then the smallest whole number in the place of $\blacksquare$ is _________.

What is the value of $1+\frac14+\frac1{16}+\frac1{64}+\frac1{256}+........$ ?

A 1.5 m tall person is standing at a distance of 3 m from a lamp post. The light from the lamp at the top of the post casts her shadow. The length of the shadow is twice her height. What is the height of the lamp post in meters?

Leila aspires to buy a car worth Rs. 10,00,000 after 5 years. What is the minimum amount in Rupees that she should deposit now in a bank which offers 10% annual rate of interest, if the interest was compounded annually?

Two alloys A and B contain gold and copper in the ratios of 2:3 and 3:7 by mass, respectively. Equal masses of alloys A and B are melted to make an alloy C. The ratio of gold to copper in alloy C is ______.

The Cricket Board has long recognized John’s potential as a leader of the team. However, his on-field temper has always been a matter of concern for them since his junior days. While this aggression has filled stadia with die-hard fans, it has taken a toll on his own batting. Until recently, it appeared that he found it difficult to convert his aggression into big scores. Over the past three seasons though, that picture of John has been replaced by a cerebral, calculative and successful batsman-captain. After many years, it appears that the team has finally found a complete captain. Which of the following statements can be logically inferred from the above paragraph?

(i) Even as a junior cricketer, John was considered a good captain.

(ii) Finding a complete captain is a challenge.

(iii) Fans and the Cricket Board have differing views on what they want in a captain.

(iv) Over the past three seasons John has accumulated big scores.

A cab was involved in a hit and run accident at night. You are given the following data about the cabs in the city and the accident.

(i) 85% of cabs in the city are green and the remaining cabs are blue.

(ii) A witness identified the cab involved in the accident as blue.

(iii) It is known that a witness can correctly identify the cab colour only 80% of the time. Which of the following options is closest to the probability that the accident was caused by a blue cab?

A coastal region with unparalleled beauty is home to many species of animals. It is dotted with coral reefs and unspoilt white sandy beaches. It has remained inaccessible to tourists due to poor connectivity and lack of accommodation. A company has spotted the opportunity and is planning to develop a luxury resort with helicopter service to the nearest major city airport. Environmentalists are upset that this would lead to the region becoming crowded and polluted like any other major beach resorts.

Which one of the following statements can be logically inferred from the information given in the above paragraph?

In the summer, water consumption is known to decrease overall by 25%. A Water Board official states that in the summer household consumption decrease by 20%, while other consumption increase by 70%.

Which of the following statements is correct?

40% of deaths on city roads may be attributed to drunken driving. The number of degrees needed to represents this as a slice of a pie chart is

Some tables are shelves. Some shelves are chairs. All chairs are benches. Which of the following conclusion can be deduced from the preceding sentence?

i.                     At least one bench is a table

ii.                   At least one shelf is a bench

iii.                  At least one chair is a table

iv.                 All benches are chairs

S, T, U, V, W, X, Y, and Z are seated around a circular table. T’s neighbour are Y and V. Z is seated third to the left of T and second to the right of S. U’s neighbor are S and Y; and T and W are not seated opposite each other. Who is third to the left of V?

Trucks (10 m long) and cars (5 m long) go on a single lane bridge. There must be a gap of at least 20 m after each truck and a gap of at least 15 m after each car. Trucks and cars travel at a speed of 36 km/h. If cars and trucks go alternately, what is the maximum number of vehicles that can use the bridge in one hour?

There are 3 Indians and 3 Chinese in a group of 6 people. How many subgroups of this group can we choose so that every subgroup has at least one Indian?

A contour line joins locations having the same height above the mean sea level. The following is a contour plot of a geographical region. Contour lines are shown at 25 m intervals in this plot.

The path from P to Q is best description by

A rule states that in order to drink beer, one must be over 18 years old. In a bar, there are 4 people. P is 16 years old, Q is 25 years old, R is drinking milkshake and S is drinking a beer. What must be checked to ensure that the rule is being followed?

Fatima starts from P, goes North for 3 km, and then East for 4 km to reach point Q, She then turns to face point P and goes 15 km in that direction. She then goes North for 6 km. How far is she from point P, and which direction should she go to reach point P?

500 students are taking one or more courses out of Chemistry, Physics, and Mathematics. Registration records indicate course enrolment as follow: Chemistry (329), Physics (186), Mathematics (295), Chemistry and Physics (83), Chemistry and Mathematics (217), and Physics and Mathematics (63). How many students are taking all 3 subjects?

Each of P, Q, R, S, W, X, Y and Z has been married at most once. X and Y are married and have two children P and Q. Z is the grandfather of the daughter S of P. Further, Z and W are married and are parents of R. Which one of the following must necessary be FALSE?

1200 men and 500 women can build a bridge in 2 weeks, 900 men and 250 women will take 3 weeks to build the same bridge. How many men will be needed to build the bridge in one week?

The number of 3-digit number such that the digit 1 is never to the immediate right of 2 is

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 25 m intervals in this plot.

Which of the following is the steepest path leaving from P?

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 ${q}^{-a}=\frac{1}{r}$ and ${r}^{-b}=\frac{1}{s}$ and ${s}^{-c}=\frac{1}{q}$, 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?

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 quater 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 5 km 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?

#### SET - 3

An apple costs Rs. 10. An onion costs Rs. 8.

Select the most suitable sentence with respect to grammar and usage.

The number that least fits this set: (324, 441, 97 and 64) is ________.

It takes 10 s and 15 s, respectively, for two trains travelling at different constant speeds to completely pass a telegraph post. The length of the first train is 120 m and that of the second train is 150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ____________.

The velocity V of a vehicle along a straight line is measured in m/s and plotted as shown with respect to time in seconds. At the end of the 7 second, how much will the odometer reading increase by (in m)?

Find the area boundeed by the lines 3x+2y=14, 2x-3y=5 in the first quandrant.

A straight line is fit to a data set (ln x, y). This line intercepts the abscissa at ln x = 0.1 and has a slope of −0.02. What is the value of y at x = 5 from the fit?

Operators $\square,\Diamond\;\mathrm{and}\;\rightarrow$ are defined by $\mathrm a\square\mathrm b\;=\;\frac{\mathrm a-\mathrm b}{\mathrm a+\mathrm b};\;\mathrm a\Diamond\mathrm b\;=\frac{\mathrm a+\mathrm b}{\mathrm a-\mathrm b};\;\mathrm a\rightarrow\mathrm b=\mathrm{ab}$

Find the value of $(66\square6\;)\rightarrow(66\;\Diamond6)$

If logx=(5/7)=-1/3,then the value of x is

Find the missing Value:

A cube of side 3 units is formed using a set of smaller cubes of side 1 unit; Find the proportion of the number of faces of the smaller cubes visible to those which are NOT visible.

An electric bus has onboard instruments that report the total electricity consumed since the start of the trip as well as the total distance convered. During a single day of operation the bus travels on stretches M,N, O and P, in that order. The cumulative distances travelled and the corresponding electricity consumption are shown in the Table below:

 Stretch Cumulative distance (km) Electricity used(kWh) M 20 12 N 45 25 O 75 45 P 100 57

The stretch where the electricity consumption per km is minimum is

Ram and Ramesh appeared in an interview for two vacancies in the same department.The probability of Ram’s selection is 1/6 and that of Ramesh is 1/8. What is the probability that only one of them will be selected?

A tiger is 50 leaps of its own behind a deer. The tiger takes 5 leaps per minute to the deer’s 4. If the tiger and the deer cover 8 metre and 5 metre per leap respectively, what distance in metres will the tiger have to run before it catches the deer?

If a2+b2+c2=1, then ab+bc+ac lies in the interval

Find the missing sequence in the letter series below:
A, CD, GHI, ?, UVWXY

If x > y >1, which of the following must be true?

i. ln x > ln y          ii. ex > ey          iii. yx > xy          iv. cos x > cos y

From a circular sheet of paper of radius 30 cm, a sector of 10% area is removed. If the remaining part is used to make a conical surface, then the ratio of the radius and height of the cone is ______.

log tan 1o + log tan 2o + …… + log tan 89o is….

Ms. X will be in Bagdogra from 01/05/2014 to 20/05/2014 and from 22/05/2014 to 31/05/2014. On the morning of 21/05/2014, she will reach Kochi via Mumbai.
Which one of the statements below is logically valid and can be inferred from the above sentences?

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

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 $f\left(x,y\right)={x}^{n}{y}^{m}=P$. 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?

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

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 + .....

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

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

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

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 slightlyheavier. 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