Data Sufficiency

If each of the students in a certain mathematics class is either a junior or a senior, how many students are in the class?

(1) If one student is to be chosen at random from the class to attend a conference, the probability that the student chosen will be a senior is 4/7.

(2) There are 5 more seniors in the class than juniors.

OA: Later.

Please explain how to approach these type of questions.
thanks.

Total number of Students = N
Number of juniors = j
Number of seniors = N - j

What is N?


1. We are choosing one student at random from the class. The total number of ways of doing this is N.
The number of ways that this student is actually a senior is N- j
So, the probability that the student is a senior = 4/7 = (N - j) / N
One equation but 2 variables. Insufficient.


2. We have N - j = j + 5
=> 2j = N - 5
=> j = (N - 5) / 2
One equation but 2 variables. Insufficient.



Both 1 and 2 together:


If we substitute the value of j we found in 2, into the equation for the probability we made in 1, we have the equation only in terms of N, so we can solve for N --> SUFFICIENT

Pick C.



In these kind of DS questions, the first step is word translation. You must look at the details given and the question stem and try to convert into an algebraic formula so you can keep track of the variables. Always remember to include all the information.

When probability comes up, try and express it as number of favourable outcomes / total number of outcomes, so that you can easily solve for the variable.

albatross86 wrote:Total number of Students = N
Number of juniors = j
Number of seniors = N - j

What is N?


1. We are choosing one student at random from the class. The total number of ways of doing this is N.
The number of ways that this student is actually a senior is N- j
So, the probability that the student is a senior = 4/7 = (N - j) / N
One equation but 2 variables. Insufficient.


2. We have N - j = j + 5
=> 2j = N - 5
=> j = (N - 5) / 2
One equation but 2 variables. Insufficient.



Both 1 and 2 together:


If we substitute the value of j we found in 2, into the equation for the probability we made in 1, we have the equation only in terms of N, so we can solve for N --> SUFFICIENT

Pick C.



In these kind of DS questions, the first step is word translation. You must look at the details given and the question stem and try to convert into an algebraic formula so you can keep track of the variables. Always remember to include all the information.

When probability comes up, try and express it as number of favourable outcomes / total number of outcomes, so that you can easily solve for the variable.

Thanks. You are right man.

With DS problems, I always ask myself the following three questions:

What do I want?
What do I have?
What do I need?

With DS problems, the goal is not to solve but to determine whether the statement gives you sufficient information to solve. In other words: Is the statement giving me what I need?

In this case:

What do I want? What is the question asking for? In this case, the number of students in the class.
What do I have? Before I look at the two statements, what information have I been given? In this case, that the class consists of only juniors and seniors: J + S = the total number of students.
What do I need? In this case, more information about the number of juniors and the number of seniors. If I know both values, I'll know how many students are in the class. Since I have two variables, I'm looking for two equations in order to solve for each variable. (When given more than one variable, you generally will need as many equations as you have variables in order to solve.)

Statement 1: If the probability of selecting a senior is 4/7, then for every 7 students, 4 will be seniors and 3 will be juniors. In other words, the ratio of seniors to juniors is 4 to 3. Translated into math, S/J = 4/3. Two variables, one equation, INSUFFICIENT.

Statement 2: If there are 5 more seniors than juniors, then S = J + 5. Two variables, one equation, INSUFFICIENT.

Statements 1 and 2 together: Two variables, two equations, SUFFICIENT.

The correct answer is C.

option1
s=4/7
j=3/7
insuff

option2
s=j+5
insuff


solving both we can get values of s and j

gmat_perfect wrote:If each of the students in a certain mathematics class is either a junior or a senior, how many students are in the class?

(1) If one student is to be chosen at random from the class to attend a conference, the probability that the student chosen will be a senior is 4/7.

(2) There are 5 more seniors in the class than juniors.

OA: Later.

Please explain how to approach these type of questions.
thanks.

outreach wrote:option1
s=4/7
j=3/7
insuff

option2
s=j+5
insuff


solving both we can get values of s and j

I don't see how you can solve these options base on the formulas you have listed.

hre we can see that both the optios talk about probability nd relative difference and what we require is a number so the only way it cn be done is throough combining both the statements...
now,

let us take no. of juniors as X
seniors= X+5

now we know that,

seniors/(juniors+seniors) = 4/7

=> X+5 / (X + (X+5)) = 4/7
=>x+5/(2X+5)= 4/7
=>7X+35=8X+20
=>X=15
=> X+5=20

hence using both the statements we can say that there are 20 seniors in class