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 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.

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

TANCET Prep Qn: Ratio Proportion

Ratio proportion is a fundamental topic from which you should expect anything from 2 to 3 questions out of the 20 questions in the Math section of TANCET MBA test.

The following question is a ratio question and tests your ability to express one term in terms of another, given the ratio between the two terms.

Question
Sum of the ages of three friends is 98 years. If the ratio of the ages of the oldest to the middle is 5 : 3 and that of the middle to the youngest is 5 : 3, how old is the oldest?
1. 49 years
2. 50 years
3. 30 years
4. 32 years
5. 42 years

The correct answer is 50 years. i.e., Choice (2).

Explanatory Answer
One of the easiest approach to solve this question is outlined below

Let A be the oldest, B the middle one and C the youngest amongst the three friends.
Ratio of the ages of A and B, A : B :: 5 : 3
i.e., A/B = 5/3
Therefore, A = (5/3) B

Ratio of the ages of B and C, B : C :: 5 : 3
i.e, B/C = 5/3.
Hence, C = (3/5)B

We also know that A + B + C = 98

Rewriting the equation in terms of B, we get (5/3)B + B + (3/5)B = 98.
Taking 15 as the common denominator and adding we get (25B + 15B + 9B)/15 = 98
Or (49/15)B = 98
Or B = (98*15)/49 = 30.

Hence, age of A = (5/3)B = (5/3)*30 = 50 years.

Various alternative formats of the same question exist. Some oft repeated questions are given at the Ratio Proportion Practice Question Set.