## Data Sufficiency

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## Data Sufficiency Introductions

CAT test writers use data sufficiency questions to test your ability to “reason quantitatively.” This stands in sharp contrast to the problem solving section, which is designed to test how well you manipulate numbers. If you find yourself doing a lot of number crunching on the data sufficiency questions, you are doing something wrong.

## Math Concepts You Should Know

The data sufficiency questions cover math that nearly any college-bound high school student will know. In addition to basic arithmetic, you can expect questions testing your knowledge of averages, fractions, decimals, algebra, factoring, and basic principles of geometry such as triangles, circles, and how to determine the areas and volumes of simple geometric shapes.

## The Answer Choices

The options for answers can take two or three forms. See one of the forms below for a question where you are given two statements 1 and 2 are asked to make a judgment call based on the same. Your task is to decide if

1. Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked.
2. Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked.
3. Both statements 1 and 2 together are sufficient to answer the question but neither statement is sufficient alone.
4. Each statement alone is sufficient to answer the question.
5. Statements 1 and 2 are not sufficient to answer the question asked and additional data is needed to answer the statements.

## Use Process of Elimination

If statement 1 is insufficient, then choices A and D can immediately be eliminated.

Similarly, if statement 2 is insufficient, then choices B and D can immediately be eliminated.

If either statement 1 or 2 is sufficient on its own, then choices C and E can be eliminated.

## Data Sufficiency Tips and Strategies

The following 11 strategies should help you become a master of the Data Sufficiency section.

1. Study the questions carefully. The questions generally ask for one of three things: a) a specific value, b) a range of numbers, or c) a true/false value. Make sure you know what the question is asking. If a question asks for a numerical value (as opposed to a quantitative expression that includes variables), the question is answerable only if a numbered statement (1 or 2) yields one and only one possible numerical answer–not a range of values

1. Determine what information is needed to solve the problem. This will, obviously, vary depending on what type of question is being asked. For example, to determine the area of a circle, you need to know the circle’s diameter, radius, or circumference. Whether or not statements 1 and/or 2 provide that information will determine which answer you choose for a data sufficiency question about the area of a circle.

1. Look at each of the two statements independently of the other. Follow the process of elimination rules covered above to consider each statement individually.

1. If step 3 did not produce an answer, then combine the two statements. If the two statements combined can answer the question, then the answer choice is C. Otherwise, E

1. Use only the information given in the questions. CAT seeks to measure your ability to distinguish facts from careless assumptions. Do not rely on a visual assessment of a diagram accompanying a geometry question to determine angle sizes, parallel lines, etc. In addition, do not carry any information over from one question to the next. Each question in the data sufficiency section stands on its own. You can count on seeing at least a few questions where a wrong answer choice tries to capitalize on this common fallacy.

1. Do not get bogged down with complicated or lengthy calculations. As we stated before, these questions are designed to test your ability to think conceptually, not to solve math problems.

1. Use process of elimination. This section lends itself perfectly to using the process of elimination. If time becomes an issue, you can always look at the 2 statements in either order. Remember, the order you analyze the two statements in doesn’t matter, so long as you begin by looking at them individually. If you find statement 1 confusing, you can save time by skipping to statement 2 and seeing whether it can help you eliminate incorrect answer choices.

1. Be on the lookout for statements that tell you the same thing in different words. When the 2 statements convey the same exact information, you will know, through process of elimination, that the correct answer choice is either D or E. A favorite ploy of  testers is to mix ratios and percentages. Here is an example where Statement 2 simply states backwards the exact same information provided by Statement 1.
1. x is 50% of y
2. the ratio of y:x is 2:1

1. Make real-world assumptions where necessary. Just as in Problem Solving questions, in Data Sufficiency questions cast in a real-world setting you should make reasonable real-world assumptions. Don’t split hairs by looking for subtle meanings or ambiguous language. The test-makers are not out to trick you in this way. You must assume that, in certain abstract questions such as “What is the value of x?”, that x might be a fraction and/or a negative number.

1. Do not assume figures are drawn to the scale

Data Sufficiency figures are not necessarily drawn proportionately–unless a figure indicates explicitly that it is drawn to scale. Do NOT rely on your eye to measure angle sizes, line segment lengths, or areas. Instead, handle any Data Sufficiency question using your knowledge of mathematics along with the numbers provided.

1. Practice, practice, practice. The more time you spend practicing data sufficiency questions, the better able you will be to internalize the tips and strategies given above. You will also become very comfortable with the type of questions from this portion of the test, and will quickly realize if there are any math areas, such as geometry or algebra where you need to brush up your skills. When it comes time to sit for the MBA exam, you will want to know key math formulas and data relationships off the top of your head.

Let us try a few questions. For questions 1-5, use the following answer choices. Mark your answer as:

(a) If statement (A) alone is sufficient to solve the question; but statement (B) alone is not

(b) If statement (B) alone is sufficient to solve the question but statement (A) alone is not

© If neither (A) or (B) is individually sufficient to solve the question but a combination of these is sufficient to solve the question

(d) If both the statements taken together are not sufficient and more information is required to solve the question.

Q1) Is X greater than Y?

(A) X + Y = 6

(B) X + 2K = 15, Y + K = 10

Statement (A) and (B) both are needed. As we need two equations to solve and get the values of the two variables. And hence, determine whether X > Y or not.

Q2) What is the distance of the point (X, Y) from the origin?

(A) x2 + y2 = 9

(B) X = 3

A2) Correct answer is (a).

Statement (A) is an equation of a circle having the centre at its origin. Thus, the radius of the circle is the distance of the point from the origin.

Q3) What is the value of X + Y + Z?

(A) X, Y, Z are either 1 or 0 or -1

(B) X2 + y2 + Z2 = 2

A3) Correct answer is (d).

In spite of using the information available in both the statements we cannot arrive at a definite value of X + Y + Z.

Q4) The average weight of students in class 50 kg. What is the number of students in the class?

(A) The heaviest and the lightest members of the class weigh 60 kg and 40 kg respectively.

(B) Exclusion of the heaviest and the lightest members from the class does not change the average weight of the students.

A4) Correct answer is (d).
Statement (A) gives highest and lowest weight of members of the class. This does not give anything. Statement (B) gives that by eliminating the highest and lowest members. the average weight does not change. This is also not sufficient to answer anything. On combining also nothing can be found.

Q5) A small storage tank is spherical in shape. What is the storage volume of the tank?

(A) The wall thickness of the tank is 1 cm.

(B) When the empty spherical tank is immersed in a large tank filled the water, 20 litres of water overflow from the large tank.

Statement (A) does not give us any information .Statement (B) says 20 lts. of water are displaced when the tank is fully immersed. This should be the outer volume of the spherical tank. Now with this the outer radius of the tank can be found. But this is not sufficient to get an answer. On combining we can find the inner radius because the wall is 1 cm thick. And hence the storage volume.

Let us try a few questions with different options for answers. For questions 6-10, use the following answer choices

• Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked.
• Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked.
• Both statements 1 and 2 together are sufficient to answer the question but neither statement is sufficient alone.
• Each statement alone is sufficient to answer the question.
• Statements 1 and 2 are not sufficient to answer the question asked and additional data is needed to answer the statements.

Q6) If the average size of 3 accounts is Rs 1 crore, is the smallest account less than Rs 50 lakh ?

1. The largest account is \$1.3 crore.
2. One of the accounts is \$0.7 crore.

A6) Correct answer is ©.  Recall that the sum of the 3 accounts is Rs 3 crore. If the largest is Rs 1.3 crore, then the sum of the other two accounts must be Rs 1.7 crore. Since the second-largest account could be Rs 1.29 crore, then the smallest account could be Rs 41 lakh, which is less than Rs 50 lakh. Hence, Statement 1 by itself is insufficient.

However, if we know the value of 2 of the variables (as we do if we read statements 1 and 2 together), and the average value of all three variables (as we do from reading the question), then we can determine the value of the third variable. If the largest account is worth Rs 1.3 crore and the smallest is worth Rs 0.7 crore, then the third variable must be \$1.0 crore. With the value of all 3 variables, we can quickly determine the value of the smallest variable. Statements 1 and 2 together give us the information needed to answer the question.

Q7) Is the product of x and y greater than 60?

1. The sum of x and y is greater than 60.
2. Each of the variables is greater than 2.

Statement 1 by itself is not sufficient. One of the two variables could be a small fraction. (Think of 500 and 0.01.) Statement 2 by itself could yield the product of 3 and 4. However, the information from both statements is taken together, we can definitively state that the answer to this question is “true.”

Q8) What is the value of y?

1. y – 3 = 2
2. y2 = 25

A8) Correct answer is (a).  Statement 1 is sufficient to determine that y equals 5. Statement 2 only tells us that y could be +5 or -5.

Q9) Which company reported the larger increase in earnings?

1. Company A reported that its earnings increased by 5%.
2. Company B reported that its earnings increased by 7%.

A9) Correct answer is (e).  The question can not be answered with the statements provided. The question asks which company’s earnings increased by more rupees, not which company’s earnings increased by a greater percentage. The different percentage rates of increase tell us nothing about either company’s actual (rupee) increase in sales unless we know each firm’s starting baseline.

Q10) Is x a prime number?

1. x is an even number.
2. x can not be divided evenly by an odd number other than 1.

A10)  Correct answer is (e)

The question can not be answered with the statements provided. Because x can be an even number and still be prime (2 is a prime number), statement 1 is insufficient. Additionally, x might be divisible by even numbers, so statement 2 is also insufficient.

Let us try a new format for different options for answers. Slight tricky in the choices so be careful. Remember, Option (a) stands true if either of the two statements (not necessarily first statement) can answer the question.

For questions 11-12, use the following answer choices

1. a)  If the question can be answered by using one of the statements alone, but cannot be answered using the other statement alone.
2. b) If the question can be answered by using either statement alone.
3. c)  If the question can be answered by using both statements together, but cannot be answered by using either statement alone.
4. d)  If the question cannot be answered based on the information provided

Toyota motor company’s teams A, B, C, D, E and F are racing new concept cars competing in a season of 6 races. Points awarded for rank 1, 2, 3, 4, 5 and 6 are 10, 8, 5, 3, 1 and 0 respectively. Points scored by five teams in the first 4 races are given in the table below.

 Race Team A Team B Team C Team D Team E Team F 1 1 10 0 3 8 5 2 0 1 3 10 8 5 3 10 3 5 0 1 8 4 10 5 8 1 0 3

The Championship is won by the team which scores the highest points

Q11) If Team C wins the next two races, who wins the championship?

(1) Team F finishes second in the fifth race.

(2) Team F does not finish second in the sixth race.

Team C has 36 points after the 6 races:

Statement I and II are individually insufficient as the positions of the other players in the last two races are not known.

Combining I and II: Maximum number of points Team F can get = 8 + 5 = 13. His maximum possible score at the end of 6 races = 21 + 13 = 34.

Team A cannot finish second in the fifth race as Team F is second. Maximum possible score of Team A is 21 + 13 = 34.

No other player can score more than this, as their scores in the first four races are less than Team F and Team A. Therefore Team C wins the championship with 36 points.

Q12) If Team E wins the next race and finishes second in the last race, who wins the championship?

(1) Team D finishes second in one of the races.

(2) Team F does not win any race.

A12) Correct answer is (d).

End score of Team E = 17 + 10 + 8 = 35.

From statement I, Team D’s maximum possible score = 14 + 8 + 10 = 32.

Team F maximum possible score = 21 + 8 + 5 = 34.

Team A’s maximum possible score = 21 + 5 + 10 = 36.

Thus, nothing can be said about the winner.

## Practice Test 1 – Data Sufficiency

For questions 1-10, use the following answer choices

• Statement A alone is sufficient but statement B alone is not sufficient to answer the question asked.
• Statement B alone is sufficient but statement A alone is not sufficient to answer the question asked.
• Both statements A and B together are sufficient to answer the question but neither statement is sufficient alone.
• Each statement alone is sufficient to answer the question.
• Statements A and B are not sufficient to answer the question asked and additional data is needed to answer the statements.

1). If digit h is the hundredths’ digit in the decimal d = 0.2h6, what is the value of d, rounded to the nearest tenth?

1. d < ¼
2. h < 5

A1) Correct answer is (d).

Both options indicate the same thing that the value of d is 0.2

2). If * represents one of the operations +, -, and x, is k * (Q + m) = (k * m) for all numbers k, Q, and m?

1. k * 1 is not equal to 1 * k for some numbers k.
2. * represent subtraction.

A2) Correct answer is (d)

Q3). If x + y > 0, is x > |y|?

A x > y

B y < 0

A3) Correct answer is (d)

Q4). If x is an integer, is (x + p)(x + q) an even integer?

1. q is an even integer.
2. p is an even integer.

A4) Correct answer is (e). The answer will also depend on if x is an even or odd integer

5) The figure above shows the dimensions of square picture frame that was constructed using four pieces of frame as shown. If w is the width of each piece of the frame, what is the area of each piece? 1. w = 3 inches
2. PQ = √18 inches

A5) Correct answer is (d)

6) Of the 230 homes built in City X last year, how many were occupied at the end of the year?

A Of all homes in City X, 90% were occupied at the end of the last year?

B A total of 7,200 single-family homes in City X were occupied at the end of last year.

A6) Correct answer is (e).

The information tells us about all the homes, not just those built in last year

7) If m and n are consecutive positive integers, is m greater than n?

1. m –1 and n +1 are consecutive positive integers.
2. m is an even integer.

A7) Correct answer is (a)

The first information in (A) tell is that m > n

8) What is the value of the sum of a list of n odd integers?

1. n = 8
2. The square of the number of integers on the list is 64

A8) Correct answer is (e).

Don’t get information re what the numbers actually are, only get to know about the quantity

9) What is the ratio of x to y?

1. x is 4 more than twice y?
2. The ratio of 0.5x to 2y is 3 to 5.

A9) Correct answer is (b). (B) clearly shows the ratio between x and y

10) The area of a triangle with base of X and one side of Y  is

1. Altitude is Z1
2. The distance between the median and the base is Z2

A10) Correct answer is (b)

At first glance (a) may seem to be the right answer since Area of a triangle is ½ (base) (altitude). But we don’t know the altitude given is for base X or not, so A is not sufficient. B helps us since median with divide the base into two equal parts and we can calculate the area of the half triangle which is sqrt[s(s-a)(s-b)(s-c)]; where s = ½ (a+b+c).

Thus B alone is sufficient

11) If the average height of three people if 68 inches, is the shortest person more than 60 inches tall ?

1. The height of the tallest person is 72 inches
2. One of the persons is 70 inches tall

A11) Correct answer is (a)

Only the first statement is needed. If x, y and z are the heights,

X + y + z = 68 x 3 = 204

If z = 72, x + y = 132

Since x and y are less than 72 (z is the tallest person), the shortest person has to be as tall as 132 – 72 = 60 inches.

12) Is triangle ABC a right angled triangle ?

1. The square of sum of two sides of the triangle equals the square of the third side
2. One of the angles is equal to the sum of the other two angles of the triangle

A12) Correct answer is (d)

Both statements by themselves lead to the fact that ABC is a right angles triangle

13) If a, b, c and d are not all zero, the value of  (a+b) / (c+d) is

1. Ratio between a to c is same as ratio between b and d
2. b – d = 2

A13) Correct answer is (e)

Both statements do not lead to any answer

14) In the 2007 world cap match between India and Bermuda, the partnership between Sehwag and Ganguly was 207 runs. How much did Sehwag contribute to that partnership, assuming there were 12 extras?

1. Sehwag made a century in the game while Ganguly did not
2. Ganguly batted at a slower pace than Sehwag and his contribution to the partnership was 45 lesser than Sehwag

A14) Correct answer is (b).

Statement B provides the required answer

15) Inflation is India is currently at 6%. Upto what percentage does a middle class family need to reduce their consumption ?

1. Expenditure can be increased by 3%
2. The family was spending Rs 40,000 per month before

A15) Correct answer is (a)

Statement A is sufficient. Expenditure (E) = Consumption© x Price (P). In the new situation, we have 1.03E, 1.06P leading to new C

## Practice Test 2 – Data Sufficiency

For questions in this test, use the following answer choices

1. a)  If the question can be answered by using one of the statements alone, but cannot be answered using the other statement alone.
2. b) If the question can be answered by using either statement alone.
3. c)  If the question can be answered by using both statements together, but cannot be answered by using either statement alone.
4. d)  If the question cannot be answered based on the information provided

1). A car originally sold for Rs 3,00,000. After a month the car was discounted x%, and a month later the car’s price was discounted y%. is the  car’s price after the discounts less than \$2,60,000?

1. y = 10
2. x = 15

A1) Correct answer is (a)

The second statement answers the question by itself, so answer is (a)

2). Is the integer k odd of even?

1. k2  is odd
2. 2k is even

A2) Correct answer is (a)

The first statement answers the question by itself, so answer is (a)

3). Is a number divisible by 9?

1. The number is divisible by 3
2. The number is divisible by 27

A3) Correct answer is (a)

Only the second statement answers the questions, so answer is (a)

4). Mr. Purohit made Rs 2,000,000 in 2003. What is Mr. Parker average yearly income for the three years 2003 to 2005?

1. He made 10% more in each year than he did in the previous year.
2. His total combined income for 2004 and 2005 was Rs 4,620,000

A4) Correct answer is (b)

Either of the two statements can provide the answer

5). A car drives around a circular track once. A second car dives from point A to point B in a straight line. Which car travels further?

1. The car driving around the circular track takes longer time to complete its trip than the car travelling in a straight line.
2. The straight line from A to B is 1 ½ times as long as the diameter of the circular track.

A5) Correct answer is (d)

Focus only on the information provided in the question, car speeds are not given so you can’t determine the distance traveled

6). 3.2 X Y 6 If X and Y each represent single digits in the decimal above, what digit does Y represent?

1. When the decimal is rounded to the nearest tenth, 3.2 is the result.
2. When the decimal is rounded to the nearest hundredth, 3.24 is the result.

A6) Correct answer is (d)

While it may be tempting to choose (b) as an answer, remember there are many choices for Y which would lead to the same result. If X is 3, Y can be anywhere from 0 to 9.

7). A certain company currently has how many employees?

1. If 3 additional employees are hired by the company and all of the present employees remain, there will be at least 20 employees in the company
2. If no additional employees are hired by the company and 3 of the present employees resign, there will be fewer than 15 employees in the company.

Both statements together provide the correct answer

8) If n is an integer, is n/15 an integer?

1 3n/15 is an integer.

1. 8n/15 is an integer.

A8) Correct answer is (d)

Neither of the two statements lead to an answer

9) If R  is an integer, is R evenly divisible by 3?

1 2R is evenly divisible by 3

2 3R is evenly divisible by 3

A9) Correct answer is (a)

The first statement provides the correct answer

10) If a certain movie clip consist of a total of 17280 frames on film how many minutes will it take to run the clip?

1. The clip runs without interruption at the rate of 24 frames per second.

2 It takes 6 times as long to run the clip as it takes to rewind the film and it takes a total of 14 minutes to do both.

A10) Correct answer is (b)

Either of the two statements can answer the question.

1. If a, b and c are integers, is a – b + c greater than a + b – c?
2. b is negative.
3. c is positive.

Only by using both statements can we arrive at an answer

1. The total number of employees on the payroll of a company was what percent greater at the end of the year than at the beginning of the year

1. During the year, 160 employees were dropped from the payroll
2. During the year, 265 employees were added to the payroll

A12) Correct answer is (e)

Both statements together are not sufficient. The two statements together show that net of 265-160 – 105 employees were added to the payroll. But since we don’t know how many employees did the company have at the beginning / end of the year, the percentage amount can not be determined

1. If n = p + r, where n, p, and r are positive integers and n is odd, does p equal 2?
2. p and r are prime numbers.
3. r 2

Both statements taken together provide the answer

1. If Q is an integer between 10 and 100, what is the value of Q?
2. One of Q’s digit is 3 more than the other, and the sum of its digits is 9.
3. Q < 50.

Both statements taken together lead to the answer

1. What are the values of X, Y and Z?
2. 2X – 11Y + 3Z = 113.
3. 24X – 132Y + 36Z = 1356

A15) Correct answer is (d).

You need 3 linear equations to solve for 3 variables, here we only have 2 equations.

Practice Test 3 – Data Sufficiency

For questions in this test, use the following answer choices

1. a)  If the question can be answered by using one of the statements alone, but cannot be answered using the other statement alone.
2. b) If the question can be answered by using either statement alone.
3. c)  If the question can be answered by using both statements together, but cannot be answered by using either statement alone.
4. d)  If the question cannot be answered based on the information provided

1) Radhesh is a class X student and is practicing for his board exam. He draws a circle of radius 9.6 cm. He also draws a chord, whose length is

1. If you measure the perpendicular distance from the centre of the centre of the circle to the chord, you get 6 cm
2. If you draw a triangle with two end points being the end points of the chord and the third point touching the circle, the 3rd angle is 80 degrees

A1) Correct answer is (a).

Statement I allows you get the answer since the perpendicular from the centre of the circle to the chord is going to bisect the chord. Then using Pythagoras theorem, you can calculate the length of the ½ chord

Statement II doesn’t provide you any concrete information to be useful

2) Sita and Geeta are twin sisters. When Geeta wears green dress, Sita wears green dress on the next day. Did Sita wear green dress on Thursday ?

1. Sita wore green dress on 2 days of the week
2. On Tuesday, Geeta wore a red dress

A2) Correct answer is (d)

For Sita to wear green dress on Thursday, Geeta has to wear green on Wednesday. The information from both statements is not sufficient to answer the question

3) Are the two lines, drawn in the picture parallel ?

1. The two lines are coplanar
2. The perpendicular distance between the two lines is same for all the points on the lines A3) Correct answer is (a).

Statement I is redundant since the lines are drawn on the same paper, they are co-planar. Statement II tells us that the lines are parallel

4) Is quadrilateral ABCD a parallelogram?

1. All four sides have different dimensions
2. One of the internal angles is 90 degrees, one is obtuse and the other two are acute angles

A4) Correct answer is (a).

Statement I doesn’t tell us anything while statement II shows that ABCD is not a parallelogram

5) Average of ten numbers s 15.34. If the fifth number is incorrect then what would be the average of the remaining nine numbers?

1. In the given ten numbers the average of the first five numbers is 14.35 and the average of the last six numbers is 15.43.
2. In the given ten numbers, the average of the first six numbers is 14.38 and the average of the last six numbers is 15.40.

A5) Correct answer is (a)

Only A alone is sufficient. From B, we can get only the sum of the fifth and the sixth numbers.

6) Consider four real numbers P, Q, R and S. Is R the smallest of these numbers? It is given that S is greater than at least one of Q, P and R.

1. P is greater than at least two of Q, R and S.
2. Q is greater than at least two of P, R and S

From A and B, possible combinations are Q > P > S > R and P > Q > S > R. In both cases R is the lowest. Hence A and B together are sufficient.

7) Is the prime number p equal to 37?

1. p = n2 + 1, where n is an integer
2. p2 is greater than 200

A7) Correct answer is (d)

Since 142 = 196 and 152 = 225, if follows from (B) that p > 14

In (A) the expression n2 + 1 can represent a prime number less than 37, equal to 37, or greater than 37, depending on the value of n. For example, if n = 4, the 42 + 1 = 17; if n = 6, then 62 + 1 = 37; if n = 10, then 102 + 1 = 101; and 17, 37, and 101 are all prime numbers. Thus, (A) alone is not sufficient

Both the statements together are not sufficient

8) Two schools decide to send their students to a picnic on the same day. How many students attend the picnic from the first school?

1. 40 students in all attend the picnic
2. If you multiply the number of students from first school with the number of students from the second school, the answer is 300

A8) Correct answer is (d)

While at first glance, you may be tempted to answer ©, since there are two linear equations and two variables, as you try to solve the question you will get two answers 30 and 10. So you can’t say which one of those applies to the first school

9)   On a stretch of water there is no current from P to Q but there is a current from Q to R. In such a circumstance, Vishal takes 3 hours to row downstream from P to R and 3 ½ hours upstream from R to P. Suppose the circumstances change and now the earlier current is there all the way from P to R. How long will Vishal take to row from R to P in the changed circumstances?

1. Ratio of the speed of Vicky in still water and that of the stream is 6 : 1.
2. In the changed circumstances, his downward journey would have taken 2 ¾ hrs.

A9) Correct answer is (b)

Either of the two statement give you the answer

10) A farmer spent three equal sums of money in buying hens, pigeons and parrots. What would be the number of birds of each kind? It is a given that each hen costs Rs 1 more than a pigeon and Rs. 2 more than a parrot.

1. The number of pigeons exceeded that of the hens by as many parrots as he could have bought for Rs. 9
2. Altogether the former bought 47 birds.

A10) Correct answer is (c)

We have the following information given

M = hx, where h is the cost of a hen and x is the number of hens bought by him

M = (n – 1) y,  where (h – 1) is the cost of a pigeon and y is the number of pigeons bought by him

M = (h – 2) z …..3) where (h – 2) is the cost of a parrot and z is the number of parrots bought by him.

From I: M/h – 1 – M/h = 9/h – 2 or, y 0- x = 9z/M

From II:  x + y + z = 47

From all these, we get the answer that ther farmer bought 12 hens, 15 pigeons and 20 parrots.

11) A shopkeeper sells pens of two companies i.e. Reynold and Cello, in two different packs. A pack of Reynold’s pens contains 10 pens while a pack of Cello’s pens contain 5 pens. What is the price of one pack of Reynold’s pens?

1. When a customer came to the shopkeeper’s shop he bought two packs of pens  in rupees by the same two digits.
2. The cost of each Reynold’s pen is 50 paise higher than that of each Cello pen.

A11) Correct answer is (c)

Suppose the number of rupees obtained for the pack of Reynold’s pen is expressed by the digits x and y.

From I: The price of each pen of Reynold’s company 10x + y/10 and, the price of each pen of Cello 10y + x/5

From II : Difference between the price of each pen of the given two companies is Rs 0.5. We get 10x + y/10 – 10y + x/5 = 50 By solving it we get, x = 3 and y = 1 Hence, the price of each pack of Reynold’s pen is Rs. 31.

12) 80 students sit down for lunch in a cafeteria. How many had only Rice ?

1. 60 students had chappatis, rice or both
2. 40 students had chappatis

A12) Correct answer is (c)

You need both statements to get the answer

13) If (888)64 is multiplied by (999)x, the unit digit will be

1. x is even
2. x is 3, 6 or 9

A13) Correct answer is (a)

Only first statement is needed. Last digit for  (888)64   will be 6 (last digit for 8 x 8 x 8 x 8). Last digit for (999)x  will be 1 when x is even and 9 when x is odd. So answer is 6.

14) Mr. Dhingra decides to divide the family company amongst his children. Who gets the majority share ?

1. The older son got 49% of the share
2. The younger son got twice the share of the older son and the difference between their shares was 30%

A14) Correct answer is (a)

Only second statement is needed. Remember, nowhere does it say that Mr. Dhingra has 2 children, he may have more. So A doesn’t mean the other child got majority

15) How fast is the train going ?

1. It takes 1 min 20 sec to go over a bridge that is 1.2 km long
2. It takes 16 sec to pass a pole

A15) Correct answer is (c)

Both statements are needed to get the answer

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