TANCET 2011 Data Sufficiency Qn 2 : Ratio Proportion, Counting Methods

Directions

The following problem has a question and two statements which are labeled (1) and (2) in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the problem plus your knowledge on mathematics and every day facts, choose:

(1)    If you can get the answer from (1) ALONE but not from (2) alone
(2)    If you can get the answer from (2) ALONE but not from (1) alone
(3)    If you can get the answer from BOTH (1) and (2) TOGETHER, but not from (1) alone or (2) alone
(4)    If EITHER statement (1) ALONE or statement (2) ALONE suffices
(5)    If you CANNOT get the answer from statements (1) and (2) TOGETHER, but need even more data

Question
A jar is filled with 60 marbles. All the marbles in the jar are either red or green. What is the smallest number of marbles that must be drawn from the jar in order to be certain that a red marble is drawn?
(1)    The  ratio of red marbles to green marbles is 2 : 1
(2)    There are 20 green marbles in the jar

Correct Answer – Choice 4. Each statement is independently sufficient.

Explanatory Answer

Information given in the question stem
1.    Total of 60 marbles.
2.    Only red and green marbles.

Statement 1:  Ratio of red to green marbles is 2 : 1.
There are 40 red marbles and 20 green marbles. The smallest number of marbles that must be drawn from the jar to be certain that a red marble is drawn is when you can be certain that if the all the marbles that you have drawn to that point are green and that there are no more green marbles.

i.e., the 21st marble will certainly be a red marble. Statement 1 provides us the required data.
Statement 1 is SUFFICIENT.

Statement 2: There are 20 green marbles in the jar.
Statement 2 directly gives the number of green marbles. As explained in statement 1 this information is sufficient to answer the least number of marbles required to be certain that a red marble is drawn.

Statement 2 is also SUFFICIENT.

Choice (4) is the correct answer.

TANCET 2011 Data Sufficiency Qn 1 - Speed Distance Time

Directions

The following problem has a question and two statements which are labeled (1) and (2) in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the problem plus your knowledge on mathematics and every day facts, choose:

(1)    If you can get the answer from (1) ALONE but not from (2) alone
(2)    If you can get the answer from (2) ALONE but not from (1) alone
(3)    If you can get the answer from BOTH (1) and (2) TOGETHER, but not from (1) alone or (2) alone
(4)    If EITHER statement (1) ALONE or statement (2) ALONE suffices
(5)    If you CANNOT get the answer from statements (1) and (2) TOGETHER, but need even more data

Question

Plane X files at r miles per hour from A to B. Plane Y files at S miles per hour from B to A. Both planes take off at the same time. Which plane files at a faster rate? Town C is between A and B.
(1)    C is closer to A than it is to B
(2)    Plane X flies over C before plane Y

Correct Answer – Choice 5. Data is INSUFFICIENT

Explanatory answer

Information given in the question stem
1.    Plane X and Plane Y take off at the same time.
2.    Town C is between A and B.

Statement 1: C is closer to A than it is to B

This statement is not helpful in determining which of the two planes is faster unless we know that the two planes met at C. That is not stated in the statement or the question stem.

Statement 1 is INSUFFICIENT. 

Statement 2: Plane X flies over C before Plane Y

This statement alone is not sufficient to determine which of the planes is faster unless we know where C is located.

Statement 2 is INSUFFICIENT.

Combining the two statements, we know that C closer to A. X flies over C before Y.

Because C is closer to A, even if X is as fast as Y or even if it is slower than Y, X could have flown over C earlier than Y.

On the contrary if the statement had mentioned that Y flew over C before X and C is closer to A than to B, we could have inferred that Y was faster than X.

Even after using the two statements we cannot infer which plane is faster.

Choice 5 is the correct answer.

TANCET 2012 Quant - Qn 43

This question tests your ability to express one variable in terms of the other. Level of difficutly easy.

If x = 2k – 2 and y = 4k^2, then what is y in terms of x?
1. x + 2
2. ((x + 2)^2)/2
3. (x + 2)^2
4.  x^2 + 4
5. (x + 4)^2

TANCET 2012 Quant - Percents - Q42

This question appeared in the Quant section of the TANCET 2012 Paper. An easy percents question.

Question

If S is 150 percent of T, then T is what percent of S + T?
1. 33.33%
2. 40%
3. 75%
4. 80%
5. 85%

Correct Answer: Choice 2. 40%

Explanatory Answer

The easiest way to solve this question is by assuming a value of T.

Take T to be 100.

Therefore, S = 150% of T = 150% of 100 = 150.

So, S + T = 150 + 100 = 250.

We need to find out T as a percent of S + T

i.e., (100 / 250)* 100 = 40%

For additional TANCET Percentage practice questions, click here

TANCET 2008 Quant Qn 9 - Geometry, Mensuration

Question 9 : Geometry - Right Triangles : If the shaded area is one half the area of triangle ABC and angle ABC is right angle, then the length of line segment AD is

1. 
2. c
3. 
4. 
5. 

TANCET Previous Year Question Papers

I am putting together answers for previous year TANCET MBA question papers. I have started with the quant section of the TANCET 2008 paper.

Here is the set of links to all the questions with explanatory answers.

Quant Section of TANCET 2008

1. Question 1 : Linear Equation : An owner of a pizza stand sold small slices of pizza for Rs. 150 each and large slices for Rs. 250 each. One night he sold 5000 slices, for a total of Rs. 10.50 lakh. How many small slices were sold?
   Answer and Explanation »
2. Question 2 : Framing Equations : Jack has three more cards than Bill. Together they have 47 cards. If x represents the number of cards Bill has, then an equation that can be used to determine the number of cards each one has is
   Answer and Explanation »
3. Question 3 : Number Properties - Fractions : If two fractions, each of which has a value between 0 and 1, are multiplied together, the product will be:
   Answer and Explanation »
4. Question 4 : Work Time : A father can do a certain job in x hours. His son takes twice as long to do the job. Working together, they can do the job in 6 hours. How many hours does the father take to do the job?
   Answer and Explanation »
5. Question 5 : Mensuration : If x units are added to the length of the radius of a circle, what is the number of units by which the circumference of the circle is increased?
   Answer and Explanation »
6. Question 6 : Percents, Comparison : John weighs twice as much as Maria. Marcia's weight is 60% of Bob's weight. Dave weighs 50% of Lee's weight. Lee weighs 190% of John's weight. Which of these 5 persons weighs the least?
   Answer and Explanation »
7. Question 7 : Mathematical Expressions : There were P people in a room when a meeting started. Q people left the room during the first hour, while R people entered the room during the same time. What expression gives the number of people in the room after the first hour as a percentage of the number of people in the room who have been there since the meeting started?
   Answer and Explanations »
8. Question 8 : Mathematical Expressions : It costs Rs. x each to make the first thousand copies of a compact disk and Rs. y to make each subsequent copy. If z is greater than 1,000, how many Rupees will it cost to make z copies of the compact disk?
   Answer and Explanation »
9. Question 9 : Geometry - Right Triangles : If the shaded area is one half the area of triangle ABC and angle ABC is right angle, then the length of line segment AD is
   
   Answer and Explanation »
10. Question 10 : Speed, Distance & Time : A plane flying north at 500 kmph passes over a city at 12 noon. A plane flying east at the same attitude passes over the same city at 12.30 pm. The plane is flying east at 400 kmph. To the nearest hundred km, how far apart are the two planes at 2 pm?
    Answer and Explanation »
11. Question 11 : Framing Expressions : Profits : A clothing manufacturer has determined that she can sell 100 suits a week at a selling price of Rs. 200 each. For each rise of Rs. 4 in the selling price she will sell 2 less suits a week. If she sells the suits for Rs. x each, how many rupees a week will she receive from the sales of the suits?
    Answer and Explanations »
    
    
12. Question 12 : Framing Expressions : Set Theory : The schedule of G first year students was inspected. It was found that M were taking a Mathematics course, L were taking a Language course and B were taking both a Mathematics course and a Language course. Which of the following expression gives the percentage of the students whose schedule was inspected who were taking neither a mathematics course nor a language course?
    Answer and Explanations »
    
    
13. Question 13 : Speed, Distance & Time : A plane flying north at 500 kmph passes over a city at 12 noon. A plane flying east at the same attitude passes over the same city at 12.30 pm. The plane is flying east at 400 kmph. To the nearest hundred km, how far apart are the two planes at 2 pm?
    Answer and Explanations »
    
    
14. Question 14 : Percents » Joan started work 2 years ago. Her starting salary was half of Mike's salary at that time. Each year since then Joan and Mike have received a rise of 10% in their respective salary. What percentage (to the nearest percent) of Mike's current salary is Joan's current salary?
    Answer and Explanation »
    
    
15. Question 15 : Mensuration - Solid Geometry » ABCD has area equal to 28. BC is parallel to AD. BA is perpendicular to AD. If BC is 6 and AD is 8, then what is CD?
    
    Answer and Explanation »
    
    
16. Question 16 : Mensuration - Solid Geometry » Which of the following figures has the largest area?
    
    1. A circle of radius
    2. An equilateral triangle whose sides each have length 4
    3. A triangle whose sides have lengths 3, 4 and 5
    Answer and Explanation »
    
    
17. Question 17 : Mathematical Expressions - equations » A charity solicited P persons over the phone who agreed to an average pledge of Rs.R each. Q of these people who had pledged an average of Rs. S each never sent in the pledged amount. Which of the following expressions represents the percentage of pledged money that the charity received?
    Answer and Explanation »
    
    
18. Question 18 : Number Theory » If x, y, z are chosen from the three numbers, -3, and 2, what is the largest possible value of the expression z²?
    Answer and Explanation »
    
    
19. Question 19 : Mensuration - Solid Geometry » The hexagon ABCDEF is regular. That means all its sides are of the same length and all its interior angles are of the same size. Each side of the hexagon is 2m. What is the area of the rectangle BCEF?
    Answer and Explanation »
    
    
20. Question 20 : Permutation » 36 identical chairs must be arranged in rows with the same number of chairs in each row. Each row must contain at least three chairs and there must be at least three rows. A row is parallel to the front of the room. How many different arrangements are possible?
    Answer and Explanation »

Profit Loss Question

Profit Loss is a relatively easy topic and quite often gets tested in these kinds of entrance tests.

Question

If the cost price of 12 articles is the same as the selling price of 10 of those articles, what percent profit does the trader make?
1. 16.66%
2. 20%
3. 25%
4. 16.66% loss
5. 20% loss

Correct Answer: Choice (2) - 20% profit.

Explanatory Answer

Let the cost of 12 articles = Rs.x

Hence, the cost of 1 article = x/12

So, the selling price of 10 articles = Rs.x

Hence, the selling price of 1 article = x/10

The quickest way to solve this question is to assume some value for x. Assume x to be a number that is divisible by 12 and 10.

So, x should be a multiple of 12 and 10. Take x to be 120.

So, the cost of 12 articles = 120. Therefore, the cost of 1 article = Rs.10

The selling price of 10 articles = 120. Therefore, the selling price of 1 article = Rs.12.

The profit on 1 article = Selling price - Cost price = 12 - 10 = Rs.2

Percent Profit = (Profit / CP) * 100 = (2/10)*100 = 20%

Speed Distance Time : TANCET Quant

Speed Distance Time is one of the topics from which you should expect a question either in the quantitative reasoning section or in the data sufficiency section of the TANCET MBA.

Here is a relatively easy quantitative reasoning question from this topic

Question

It takes Kiran 50 minutes lesser to cover a distance if she travels three times as fast as she does now. How long will she take to cover the distance if she travels twice as fast as she does now?
1. 50 minutes
2. 75 minutes
3. 150 minutes
4. 100 minutes
5. 37.5 minutes

Correct Answer : Choice 5. 37.5 minutes

Explanatory Answer

Let Kiran's present speed be S km/min. And let her take t minutes to reach her destination.

If Kiran travels three times as fast as she does now i.e., at 3S, she will cover the same distance in 1/3 of the time i.e., in t/3 minutes.

So, she is saving (t - t/3) minutes = 2t/3 minutes.
The question states that she is saving 50 minutes.
Therefore, 2t/3 = 50
or t = 75 minutes.

If she travels at S km/min, she will reach her destination in 75 minutes.

So, if she travels at 2S km/min, she will take half that time = 75/2 minutes = 37.5 minutes.

TANCET Math - Ratio Proportion

Hi

Ratio proportion is an often tested area in the quant section of the TANCET MBA exam. I have posted a medium level difficulty question on Ratios.

Question

The sum of the ages of 3 friends is 90 years. If 5, 3 and 2 years are subtracted respectively from the ages of the oldest, middle and the youngest the ratio of their ages becomes 8 : 5 : 3. What is the age of the oldest of the 3 friends?
1. 40
2. 48
3. 28
4. 17
5. 45

Correct Answer : 45 years. Choice 5.

Explanatory Answer

Let the age of the 3 friends be a, b and c - a the oldest, b the middle one and c the youngest.

Therefore, a + b + c = 90

The question states that a - 5 : b - 3 : c - 2 :: 8 : 5 : 3
So, a - 5 + b - 3 + c - 2 = 8k + 5k + 3k
Or a + b + c - 10 = 16k ... eqn (1)
Substituting a + b + c = 90 in eqn (1), we get 90 - 10 = 16k
or 16k = 80
Hence, k = 5.

a - 5 = 8k
or a - 5 = 40
Therefore, a = 40 + 5 = 45 years.

Angles in a triangle : TANCET Geometry

Geometry, specifically triangles is an oft tested area in the TANCET quant section.

Here is a relatively easy question on triangles.

If the largest angle in a triangle is 70^o, what is least possible value of the smallest angle of the triangle?

1) 69
2) 1
3) 40
4) 39
5) 41

The correct answer is 40.

Explanatory answer

The sum of the interior angles of a triangle is 180.

The question states that the largest of the angles is 70.

We are interested in finding the least possible value of the smallest of the three angles.

The least value for the smallest angle will be when the other two angles are as large as possible.

The largest value that the other two angles can take is 70 each.

Therefore, the least value of the smallest of the angles = 180 - 70 - 70 = 40

You can access more questions in Geometry by visiting this link

TANCET Quant : Linear Equations, Word Problems

Here is a word problem that requires you to frame a pair of linear equations, solve the equations to arrive at an answer.

Rajesh is 10 years younger to Baskar. 10 years back, Rajesh's age was two-thirds that of Baskar's. How old is Baskar now?
1. 30
2. 40
3. 20
4. 16
5. 28

Correct Answer is Choice (2). 40 years.

Explanatory Answer

Let the present age of Baskar be 'b' and that of Rajesh be 'r'.
So, r = b - 10 .... eqn (1).

10 years back Rajesh was (r - 10) years old. 10 years back Baskar was (b - 10) years old.
The question states that 10 years back Rajesh was two thirds as old as Baskar was.

i.e., (r - 10) = (2/3)*(b - 10) .... eqn (2).
Cross multiplying, we get 3(r - 10) = 2(b - 10)
or 3r - 30 = 2b - 20 .... eqn (2)

From eqn (1) we can substitute r as (b - 10) in eqn (2)
So, 3(b - 10) - 30 = 2b - 20
or 3b - 30 - 30 = 2b - 20
or b = 40.

The present age of Baskar is 40 years.

Word problems : Linear Equations

You should anticipate a question that expects you to convert information presented in words into an equation and solve it.

They are commonly referred to as "word problems". The key to getting those questions right is to try and decode the information in the sentence and frame equations accordingly.

Here is a question that will give you an idea of how to frame a linear equation from the information given in the question statement.

If the result of seven more than four times a number is tripled, the resultant number is three more than fifteen times the number. What is the number?
1. 6
2. 7
3. 4
4. 15
5. 12

TANCET Math : Averages

Averages is an oft repeated topic in TANCET quant section. You may also get a variant of questions from the arithmetic mean and weighted average concept as Data Sufficiency Questions in TANCET.

Here is a sample averages question. A rather easy one.

Average weight of 25 boys in a class is 48 kgs. The average weight of the class of 40students is 45 kgs. What is the average weight of the 15 girls in the class?
1. 44 kgs
2. 42 kgs
3. 40 kgs
4. 39 kgs
5. 42.5 kgs

Speed Distance Time Question TANCET

Speed, Distance and Time is an important topic from a TANCET quant perspective. You could expect to get one to two questions from this topic.

The core concept in this topic is the relation between these three parameters
Distance = speed * time.

The second point to keep in mind while solving questions from this topic is to check if the units of the three parameters match.
i.e., if distance is measured in kilometres and time in hours, speed should be in km/hr. Alternatively, if speed is in kilometres and time in minute, speed should be in km/min.

Here is an easy to moderate level difficulty question in this topic.

A bus travels at 40 kmph for the first 100 kms, 60 kmph for the next 100 kms and 48 kmph for the final 200 kms, what is the average speed over the total distance?
1. 48 kmph
2. 50 kmph
3. 49 kmph
4. 52 kmph
5. 50.4kmph

The concept tested in this question is that of average speeds.

The answer to this question is 48 kmph.

Explanatory Answer

Average speed for the first 200kms = 2ab/(a + b) = 2 * 40 * 60/(40 + 60) = 48 kmph.

Bus travels equal distances at two different speeds, average speed = 2ab/(a + b)

Now, if we break the overall journey into two stretches of 200 kms each, the bus travels the first 200kms at 48kmph, and the second at 48 kmph. Overall, average speed = 48 kmph.
Correct answer (1)

Alternatively, you could find out the total time taken to cover the entire distance of 400 kms

Time taken for the first 100 kms = 100 / 40 = 10/4 hours

Time taken for the second 100 kms = 100/60 = 10/6 hours

Time taken for the last 200 kms = 200/48 = 50/12.

Adding up all three, we get 10/4 + 10/6 + 50/12 = 100/12 hours.

Average speed = total distance / total time

= 400 /(100/12) = 4800/100 = 48 kmph

For additional questions on Speed, Distance and Time, click here

TANCET Quant : Percents

Here is a relatively easy question from the topic Percents.

Question

If A is 40% more than B and C is 68% more than B, what percent is C more than A?
1. 28%
2. 17%

3. 20%
4. 10.8%
5. 54%

TANCET Quant : Progressions

AP, GP (Arithmetic Progressions and Geometric Progressions) are two topics from which you could expect to get at least one question.

An interesting topic and the kind of questions that you can expect in the TANCET quant section from these two topics will be rather elementary.

The AP topic has two formulae to remember.

The first one is to find the nth or the last term 'l' of an AP : l = a + (n - 1)d, where 'a' is the first term, n is the number of terms and 'd' is the common difference.

The second formula is to find the sum of first 'n' terms of an AP. Sn = (n/2)(2a + (n - 1)d)

Here is a question that tests your understanding of these concepts.

If the first term of an AP is 12 and the 7th term is 36, what is the sum of these 7 terms?

1. 240

2. 168

3. 336

4. 84

5. 121

Explanatory Answer

The first term a = 12

The 7th term l = 36.

We know that l = a + (n - 1)d

or 36 = 12 + (7 - 1)d

or 24 = 6d

or d = 4.

Sum of these first 7 terms = (n/2)(a + (n - 1)d), where n = 7, a = 12, d = 4

Substituting we get, (7/2)(2*12 + (7 - 1)4)

= (7/2)(24 + 24)

= 7 * 24

= 168

Choice (2) is the correct answer.

Speed Time Distance : TANCET Math

Speed, Time and Distance is an interesting topic from which you could expect to get one question in the math section and probably a question in the data sufficiency section of the TANCET MBA test.

The concept is extremely simple : Distance = Speed * Time
The place where you need to be careful is to make sure that the units that you use for the different quantities have integrity i.e., if the unit for speed used is km/hr, then you should use hour as the unit for time.

Here is a simple question in speed time distance.
Question
Traveling at 4/5ths of her usual speed, Sonal reached office 20 minutes late. How long did she take today?
1. 60 minutes
2. 80 minutes
3. 100 minutes
4. 64 minutes
5. 96 minutes

Explanatory Answer
She travels at 4/5th of her usual speed.
Let her usual speed be 's' km/min. So, today she travels at 4/5s.
Let the usual time she takes be 't' minutes. So, today she will take (t + 20) minutes.
As the distance traveled in both the cases is the same, we can equate them
i.e., st = 4/5s (t + 20)
dividing both sides by 's' we get t = 4/5(t + 20)
or 5t = 4t + 80
or t = 80 minutes.
t is the usual time take.
The time taken today is t + 20 = 100 minutes.

Note: 1. We used km/min as the unit for speed as the unit of time given in the question is in minutes.
2. we did not stop at finding the value of 't'. The question was about finding the time taken today = t + 20.

You can get additional questions on speed time and distance at this link.

TANCET Math : Work Time

Hi

Here is a work time question. You could expect a question on this topic. A topic that gets usually tested in the test.
Question
A works twice as fast as B does and together they complete a task in 8 days, how long will A lone take to complete the task?
1. 16 days
2. 4 days
3. 32 days
4. 12 days
5. 24 days

Correct Answer
Choice (4). 12 days.

Explanatory Answer
A works twice as fast as B does.
So, if B does 'x' units of work in a day, then A does 2x units of work in a day or in a day they do 3x units of work.
Together, they complete the task in 8 days.
i.e., in a day together they complete 1/8th of the total task.
3x = 1/8th of the task.
So, x = 1/24th of the task.
We know A does 2x units of work a day = 2 * (1/24) = 1/12th of the work in a day.
So, A will take 12 days to complete the task.

You could access additional questions on Work Time and Pipes Cisterns here

TANCET Quant Practice Questions

I am providing links to webpages where you can get free practice questions for TANCET Math section.

These links are organized on a chronological order.

August 2003 : You will find a lot of Number Theory, Number Properties and Averages questions in this collection.

Ratio Proportion on Ages

A favorite question that appears more often than not from the Ratio Proportion topic is that of comparing the ages of two people.

Here is an example of such a question.

Question

The ratio of the present ages of Shreyas and Swetha is 3 : 5. Six years back Swetha was twice as old as Shreyas was. How old is Shreyas now?

1. 24
2. 12
3. 30
4. 18
5. 36

Correct Answer is choice (4). 18 years

Explanatory Answer

Let the present age of Shreyas be x years and that of Swetha be y years.
Therefore, x : y :: 3 : 5

Or x/y = 3/5
or x = (3/5)y. --- eqn (1)

6 years back Shreyas was (x - 6) years old.
6 years back Swetha was (y - 6) years old.

We know that Swetha was twice as old as Shreyas was 6 years back.
So, (y - 6) = 2(x - 6) --- eqn (2).

Substituting x = (3/5)y from eqn (1) in eqn (2) we get
(y - 6) = 2((3/5)y - 6)
or 5(y - 6) = 2(3y - 30)
or 5y - 30 = 6y - 60
or y = 30.

x = (3/5)y = (3/5)*30 = 18 years.

You can access more question on TANCET Math Ratio Proportion by clicking here