Data Sufficency

Based on the information given above, the minimum number of volunteers involved in both FR and TR projects, but not in the ER project is

Which of the following additional information would enable to find the exact number of volunteers involved in various projects?

After some time, the volunteers who were involved in all the three projects were asked to withdraw from one project. As a result, one of the volunteers opted out of the TR project, and one opted out of the ER project, while the remaining ones involved in all the three projects opted out of the FR project. Which of the following statements, then, necessarily follows?

After the withdrawal of volunteers, as indicated in Question 89, some new volunteers joined the NGO. Each one of them was allotted only one project in a manner such that, the number of volunteers working in one project alone for each of the three projects became identical. At that point, it was also found that the number of volunteers involved in FR and ER projects was the same as the number of volunteers involved in TR and ER projects. Which of the projects now has the highest number of volunteers?

Is it more profitable for Company M to produce Q?
I. Product R is sold at a price four times that of Q.
II. One unit of Q requires 2 units of labour, while one unit of R requires 5 units of labour. There is no other constraint on production.

A train started from Station A, developed engine trouble and reached Station B, 40 minutes late. What is the distance between Stations A and B?
I. The engine trouble developed after travelling 40 km from Station A and the speed reduced to of the original speed.
II. The engine trouble developed after travelling 40 km from station A in two hours and the speed reduced to of the original speed.

What is the value of prime number x?
I. x² + x is a two digit number greater than 50.
II. x³ is a three digit number.

The average of three unequal quotations for a particular share is Rs.110. If all are quoted in integral values of rupee, does the highest quotation exceed Rs.129?
I. The lowest quotation is Rs.100.
II. One of the quotations is Rs.115.

How many people (from the group surveyed) read both Indian Express and Times of India?
I. Out of total of 200 readers, 100 read Indian Express, 120 read Times of India and 50 read Hindu.
II. Out of a total of 200 readers, 100 read Indian Express, 120 read Times of India and 50 read neither.

X says to Y, “I am 3 times as old as you were 3 years ago”. How old is X?
I. Y’s age 17 years from now will be same as X’s present age.
II. X’s age nine years from now is 3 times Y’s present age.

What is the area under the line GHI − JKL in the given quadrilateral OPQR, knowing that all the small spaces are squares of the same area?

What is the radius of the circle?
I. Ratio of its area to circumference is > 7.
II. Diameter of the circle is ≤ 32

What is the time difference between New York and London?
I. The departure time at New York is exactly 9.00 a.m. local time and the arrival time at London is at 10.00 a.m. local time.
II. The flight time is 5 hours.

Mr. Murthy takes the morning train to his office from station A to station B, and his colleague Mr.Rahman joins him on the way. There are three stations C, D and E on the way not necessarily in that sequence. What is the sequence of stations?
I. Mr. Rahman boards the train at D.
II. Mr. Thomas, who travels between C & D has two segments of journey in common with

Given that X and Y are non-negative. What is the value of X?
I. 2X + 2 Y ≤ 40
II. X – 2Y ≥ 20

What are the values of 3 integers a, b and c?
I. ab = 8
II. bc = 9

Is the average of the largest and the smallest of four given numbers greater than the average of the four numbers?
I. The difference between the largest and the second largest numbers is greater than the difference between the second smallest and the smallest numbers.
II. The difference between the largest and the second largest numbers is less than the difference between the second largest and the second smallest numbers.

What are the ages of the three brothers?
I. The product of their ages is 21.
II. The sum of their ages is not divisible by 3.

Two types of widgets, namely type A and type B, are produced on a machine. The number of machine hours available per week is 80. How many widgets of type A must be produced?
I. One unit of type A widget requires 2 machine hours and one unit of type B widget requires 4 machine hours.
II. The widget dealer wants supply of at least 10 units of type A widget per week and he would not accept less than 15 units of type B widget.

What is the area of a regular hexagon?
I. The length of the boundary line of the hexagon is 36 cm.
II. The area of the hexagon is 6 times the area of an equilateral triangle formed on one of the sides.

What is the price of mangoes per kg?
I. Ten kg of mangoes and two dozens of oranges cost Rs.252.
II. Two kg of mangoes could be bought in exchange for one dozen oranges

Is the distance from the office to home less than the distance from the cinema hall to home?
I. The time taken to travel from home to office is as much as the time taken from home to the cinema hall, both distance being covered without stopping.
II. The road from the cinema hall to home is bad and speed reduces, as compared to that on the road from home to the office.

A and B work at digging a ditch alternately for a day each. If A can dig a ditch in ‘a’ days and B can dig that ditch in ‘b’ days, will work get done faster if A begins the work?

I. n is a positive integer such that
II. b > a

If twenty sweets are distributed among some boys and girls such that each girl gets two sweets and each boy gets three sweets, what is the number of boys and girls?
I. The number of girls is not more than five.
II. If each girl gets 3 sweets and each boy gets 2 sweets, the number of sweets required for the children will still be the same.

If the selling price were to be increased by 10%, the sales would reduce by 10%. In what ratio would profits change?
I. The cost price remains constant.
II. The cost price increased 10%.

What is the average weight of the 3 new team members who are recently included into the team?
I. The average weight of the team increases by 20 kg.
II. The 3 new men substitute earlier members whose weights are 64 kg, 75 kg and 66 kg.

Is segment PQ greater than segment RS?
I. PB > RE,BQ = ES.
II. B is a point on PQ, E is a point on RS.

Three boys had a few coffee Bite toffees with them. The number of toffees with the second were four more than those with the first and the number of toffees with the third were four more than those with the second. How many toffees were there in all?
I. The number of toffees with each of them is a multiple of 2.
II. The first boy ate up four toffees from what he had and the second boy ate up six toffees from what had and the third boy gave them two toffees each from what he had and the number of toffees remaining with each of them formed a geometric progression.

Little Beau Peep lost her sheep. She couldn’t remember how many were there. She knew she would have 400 more next year, than the number of sheep she had last year. How many sheep were there?
I. The number of sheep last year was 20% more than the year before that and this rate of increase continues to be the same for the next 10 years.
II. The increase is compounded annually.

What will be the total cost of creating a 1- foot border of tiles along the inside edges of a room?
I. The room is 48 feet in length and 50 fet in breadth.
II. Every tile costs Rs. 10.

Ten boys go to a neighbouring orchard. Each boy steals a few mangoes. What is the total number of mangoes they steal?
I. The first boy steals 4 mangoes and the fourth boy steals 16 mangoes and the eight boy 32 mangoes and the tenth boy steals 40 mangoes.
II. The first boy stole the minimum number of mangoes and the tenth boy stole the maximum number of mangoes.

Direction for questions 92 to 100: Each of these questions is followed by two statements, I and II. Mark the answer as
(a) if the question can be answered with the help of statement I alone.
(b) if the question can be answered with the help of statement II alone.
(c) if both statement I and statement II are needed to answer the question.
(d) if the question cannot be answered even with the help of both the statements.

If x, y and z are real numbers, is z – x even or odd?
I. xyz is odd.
II. xy + yz + zx is even.

Direction for questions 92 to 100: Each of these questions is followed by two statements, I and II. Mark the answer as
(a) if the question can be answered with the help of statement I alone.
(b) if the question can be answered with the help of statement II alone.
(c) if both statement I and statement II are needed to answer the question.
(d) if the question cannot be answered even with the help of both the statements.

What is the value of x, if x and y are consecutive positive even integers?
I. (x – y)² = 4
II. (x + y)² < 100

Direction for questions 92 to 100: Each of these questions is followed by two statements, I and II. Mark the answer as
(a) if the question can be answered with the help of statement I alone.
(b) if the question can be answered with the help of statement II alone.
(c) if both statement I and statement II are needed to answer the question.
(d) if the question cannot be answered even with the help of both the statements.

What is the profit percentage?
I. The cost price is 80% of the selling price.
II. The profit is Rs.50.

Direction for questions 92 to 100: Each of these questions is followed by two statements, I and II. Mark the answer as
(a) if the question can be answered with the help of statement I alone.
(b) if the question can be answered with the help of statement II alone.
(c) if both statement I and statement II are needed to answer the question.
(d) if the question cannot be answered even with the help of both the statements.

What is the area of the triangle?
I. Two sides are 41 cm each.
II. The altitude to the third side is 9 cm long.

Direction for questions 92 to 100: Each of these questions is followed by two statements, I and II. Mark the answer as
(a) if the question can be answered with the help of statement I alone.
(b) if the question can be answered with the help of statement II alone.
(c) if both statement I and statement II are needed to answer the question.
(d) if the question cannot be answered even with the help of both the statements.

What is the price of bananas?
I. With Rs.84, I can buy 14 bananas and 35 oranges.
II. If price of bananas is reduced by 50%, then we can buy 48 bananas in Rs.12.

Direction for questions 92 to 100: Each of these questions is followed by two statements, I and II. Mark the answer as
(a) if the question can be answered with the help of statement I alone.
(b) if the question can be answered with the help of statement II alone.
(c) if both statement I and statement II are needed to answer the question.
(d) if the question cannot be answered even with the help of both the statements.

What is the first term of an arithmetic progression of positive integers?
I. Sum of the squares of the first and the second term is 116.
II. The fifth term is divisible by 7.

Direction for questions 92 to 100: Each of these questions is followed by two statements, I and II. Mark the answer as
(a) if the question can be answered with the help of statement I alone.
(b) if the question can be answered with the help of statement II alone.
(c) if both statement I and statement II are needed to answer the question.
(d) if the question cannot be answered even with the help of both the statements.

What is the length of rectangle ABCD?
I. Area of the rectangle is 48 square units.
II. Length of the diagonal is 10 units.

Direction for questions 92 to 100: Each of these questions is followed by two statements, I and II. Mark the answer as
(a) if the question can be answered with the help of statement I alone.
(b) if the question can be answered with the help of statement II alone.
(c) if both statement I and statement II are needed to answer the question.
(d) if the question cannot be answered even with the help of both the statements.

What is the number x?
I. The LCM of x and 18 is 36.
II. The HCF of x and 18 is 2.

Direction for questions 92 to 100: Each of these questions is followed by two statements, I and II. Mark the answer as
(a) if the question can be answered with the help of statement I alone.
(b) if the question can be answered with the help of statement II alone.
(c) if both statement I and statement II are needed to answer the question.
(d) if the question cannot be answered even with the help of both the statements.

Is x + y – z + t even?
I. x + y + t is even.
II. t and z are odd.

A tractor travelled a distance 5 m. What is the radius of the rear wheel?
I. The front wheel rotates ‘N’ times more than the rear wheel over this distance.
II. The circumference of the rear wheel is ‘t’ times that of the front wheel.

What is the ratio of the two liquids A and B in the mixture finally, if these two liquids kept in three vessels are mixed together? (The containers are of equal volume.)
I. The ratio of liquid A to liquid B in the first and second vessel is 3 : 5, 2 : 3 respectively.
II. The ratio of liquid A to liquid B in vessel 3 is 4 : 3.

If a, b and c are integers, is (a – b + c) > (a + b – c)?
I. b is negative.
II. c is positive.

If α and β are the roots of the equation (ax² + bx + c = 0), then what is the value of (α²+ β²)?

What is the cost price of the article?
I. After selling the article, a loss of 25% on cost price is incurred.
II. The selling price is three-fourths of the cost price.

What is the selling price of the article?
I. The profit on sales is 20%.
II. The profit on each unit is 25% and the cost price is Rs. 250.

How many different triangles can be formed?
I. There are 16 coplanar, straight lines.
II. No two lines are parallel.

What is the total worth of Lakhiram's assets?
I. A compound interest at 10% on his assets, followed by a tax of 4% on the interest, fetches him Rs. 1,500 this year.
II. The interest is compounded once every four months.

How old is Sachin in 1997?
I. Sachin is 11 years younger than Anil whose age will be a prime number in 1998.
II. Anil's age was a prime number in 1996.

What is the number of type-2 widgets produced, if the total number of widgets produced is 20,000?
I. If the production of type-1 widgets increases by 10% and that of type-2 decreases by 6%, the total production remains the same.
II. The ratio in which type-1 and type-2 widgets are produced is 2 : 1.

F and M are father and mother of S, respectively. S has four uncles and three aunts. F has two siblings. The siblings of F and M are unmarried. How many brothers does M have?
A. F has two brothers.
B. M has five siblings.

A game consists of tossing a coin successively. There is an entry fee of Rs. 10 and an additional fee of Re. 1 for each toss of coin. The game is considered to have ended normally when the coin turns heads on two consecutive throws. In this case the player is paid Rs. 100. Alternatively, the player can choose to terminate the game prematurely after any of the tosses. Ram has incurred a loss of Rs. 50 by playing this game. How many times did he toss the coin?
A. The game ended normally.
B. The total number of tails obtained in the game was 138.

Each packet of SOAP costs Rs. 10. Inside each packet is a gift coupon labelled with one of the letters S, O, A and P. If a customer submits four such coupons that make up the word SOAP, the customer gets a free SOAP packets. Ms. X kept buying packet after packet of SOAP till she could get one set of coupons that formed the word SOAP. How many coupons with label P did she get in the above process?
A. The last label obtained by her was S and the total amount spent was Rs. 210.
B. The total number of vowels obtained was 18.

If A and B run a race, then A wins by 60 seconds. If B and C run the same race, then B wins by 30 seconds. Assuming that C maintains a uniform speed what is the time taken by C to finish the race?
A. A and C run the same race and A wins by 375 metres.
B. The length of the race is 1 km.

Is a⁴⁴ < b¹¹ , given that a = 2 and b is an integer?
A. b is even
B. b is greater than 16

What are the unique values of b and c in the equation 4x² + bx + c = 0 if one of the roots of the equation is (–1/2)?
A. The second root is 1/2.
B. The ratio of c and b is 1.

AB is a chord of a circle. AB = 5 cm. A tangent parallel to AB touches the minor arc AB at E. What is the radius of the circle?
A. AB is not a diameter of the circle.
B. The distance between AB and the tangent at E is 5 cm.

D, E, F are the mid points of the sides AB, BC and CA of triangle ABC respectively. What is the area of DEF in square centimeters?
A. AD = 1 cm, DF = 1 cm and perimeter of DEF = 3 cm
B. Perimeter of ABC = 6 cm, AB = 2 cm and AC = 2 cm.

At the end of year 1998, Shepard bought nine dozen goats. Henceforth, every year he added p% of the goats at the beginning of the year and sold q% of the goats at the end of the year where p > 0 and q > 0. If Shepard had nine dozen goats at the end of year 2002, after making the sales for that year, which of the following is true?

In a cricket match, the ‘Man of the Match’ award is given to the player scoring the highest number of runs. In case of a tie, the player (out of those locked in the tie) who has taken the higher number of catches is chosen. Even thereafter if there is a tie, the player (out of those locked in the tie) who has dropped fewer catches is selected. Aakash, Biplab, and Chirag who were contenders for the award dropped at least one catch each. Biplab dropped two catches more than Aakash did, scored 50, and took two catches. Chirag got two chances to catch and dropped both. Who was the ‘Man of the Match’?
A. Chirag made 15 runs less than both Aakash and Biplab.
B. The catches dropped less by Biplab are 1 more than the catches taken by Aakash.

Four friends — A, B, C and D got the top four ranks in a competitive examination, but A did not get the first, B did not get the second, C did not get the third, and D did not get the fourth rank. Who secured which rank?
A. Neither A nor D were among the first 2.
B. Neither B nor C was third or fourth.

The members of a local club contributed equally to pay Rs. 600 towards a donation. How much did each one pay?
A. If there had been five fewer members, each one would have paid an additional Rs. 10.
B. There were at least 20 members in the club, and each one paid not more than Rs. 30.

A family has only one kid. The father says, “After ‘n’ years, my age will be 4 times the age of my kid.” The mother says, “After ‘n’ years, my age will be 3 times that of my kid.” What will be the combined ages of the parents after ‘n’ years?
A. The age difference between the parents is 10 years.
B. After ‘n’ years the kid is going to be twice as old as she is now.