Test: Tree Structure - Super TET MCQ

70% of all the staff members in a college are administrators and the remaining are teachers. If the total number of teachers is 60, then what is the total number of staff members in the college?

30% of staff members are teachers = 60
=> total number of staff members in the college = 60/0.3 = 200.

Given Fresher + Work ex = 500
Also 70% of 500 = Fresher
Then 30% of 500 = work ex= 150

Now 20% of 150 have atleast 2 year or more work ex

So 80% of 150 will have less than 2 year work ex= 80/100 x 150 = 120

Ratio = a:b:c=4:3:1
but c =2 million
Thus multiplying the ratio with 2 we get = 8:6:2
thus total = 16 million
As 16 million is 20% decreased value of total X(let) voters
16 = X(1-20/100)
Thus X= 20 million
Thus number of people not voted = 20-16 million =4 million

Total Books = 100
Fiction = 60, Books less than 350 pages are = 48
Non Fiction = 40, Books less than 30 pages are = 32

Total books less than 350 pages = 48 + 32 = 80

Men who older than 25 years is 40%
No. of men who are at-most 25 years is 72000 i.e. left 60%. So total are = 120000
Men older than 25 = 120000 x 0.4 = 48000
50% married = 48000 x 0.5 = 24000
40% do not have kids = 24000 x 0.4 = 9600
 

Step 1: Question statement and Inferences

We are given that a broker booked 1200 apartments for sale. There are only two types of apartments in these 1200: either 2-bedroom apartments or 3-bedroom apartments.

Let’s say:

The number of 2-bedroom apartments = x

And the number of 3-bedroom apartments = y  

Thus,

x + y = 1200     ………….. (1) 

Next the question says, 20% of the 2-bedroom apartments have terrace gardens, and 80% of the 3-bedroom apartments have terrace gardens. So,

The number of 2-bedroom apartments with terrace gardens = 20% of x = 0.2x

And the number of 3-bedroom apartments with terrace gardens = 80% of y = 0.8y  

It is also given that there are 600 apartments with terrace gardens. So,

0.2x + 0.8y = 600

2x + 8y = 6000          ……………… (2)

We have to find the number of 3-bedroom apartments booked i.e. the value of y.

Step 2: Finding required values

Now, we have two equations and two variables. So, let’s solve them to get the value of y. 

 x + y = 1200         ……………… (1)    

 2x + 8y = 6000      ……………… (2)    

Multiplying equation (1) by 2, and then subtracting it from equation (2), we get:

 6y = 3600

 Thus,y = 600  

Step 3: Calculating the final answer

So, the number of 3-bedroom apartments = 600   

Answer: Option (B)

Step 1: Question statement and Inferences

Let the total number of kids at the day care be N

So, number of American kids = 80% of N = 0.8N

Number of non-American kids = N-0.8N = 0.2N

It is given that 0.2N = 40

From here, we calculate that N = 200

Step 2: Finding required values

Number of kids who speak = 60% of N = 60% of 200 = 120

Of these, 20% are under 2 years of age.

Remaining 80% are not under 2 years of age

Step 3: Calculating the final answer

Number of kids who are not under 2 years of age = 80% of 120

= 96

Looking at the answer options, we see that option C is correct.

Steps 1&2: Understand question and draw inferences

This question involves the creation of two trees.

In the first tree, the node ‘Total Students’ is branched on the basis of gender. So, we get two branches: Girls and Boys.

Let the number of Girls in the class be g, and the number of boys in the class be b.

Let the total number of students in the class be T.

So, we can write:

g+b=T

  . . . Equation 1

In the second tree, the node ‘Total Students’ is branched out on the basis of grades.

So, we get three branches: Grade A, Grade B and Grade C.

Let the number of students who got grades A, B and C be a, b and c respectively.

So, we can write:

a+b+c=T. . . Equation 2

We need to find the value of a.

Step 3: Analyze Statement 1

As per Statement 1,

20% of the class got grade B and 50% of the class got grade C

b = 20% of T  and c = 50% of T 

⇒ b = 0.2T and c = 0.5T 

Substituting these values of b and c in Equation 2:

a + 0.2T + 0.5T = T     

a=0.3 T   

Since we don’t know the value of T, we will not be able to find the value of a.

Therefore, Statement 1 is not sufficient.

Step 4: Analyze Statement 2

As per Statement 2,

The 12 girls in the class make up 40% of the class

⇒ g=12 

and g=40% of T 

⇒  12 = 40100T 

⇒ T = 30 

However, this statement gives us no clue about the value of a. Therefore, this statement is clearly not sufficient.

Step 5: Analyze Statement 1 and Statement 2 together (if needed)

From Statement 1,

a=0.3 T   

From Statement 2,

T = 30   

Thus, by combining the two statements,

We get a = 9 

Thus, we are able to get a unique value by combining the two statements.

Correct Answer - Choice C

Step 1: Question statement and Inferences

We are given that in a certain school, there are a total of 770 students. Let’s say the number of male students is x and the number of female students is y. So,

x + y = 770            …………… (1) 

The number of male students in acting courses = 2x/3

The number of male students in other courses = x/3

The number of female students in acting courses = 3y/4

The number of female students in other courses = y/4

Thus,

The total number of students in acting courses =

And, the total number of students in other courses=

It is also given that, If there were 55 less female students who opted for other courses, then the number of male students who opted for other courses will be twice that of the female students who opted for other courses. So,

Step 2: Finding required values

Adding equations (1) and (4), we get y = 440 from which we can calculate x = 330.

Step 3: Calculating the final answer

Now, from equation (2),

The total number of students in acting courses

Correct choice : D

Step 1: Question statement and Inferences

The first step will be to draw the tree structure that depicts the question statement.

The next step will be to find the value at each node and branch of the tree.

Step 2: Finding required values

Let the money donated by The Goodwill Foundation be $x

It is given that

Amount donated by Goodwill Foundation =25% of Total Donation

Total Donation=4x

So, Donations by others=4x–x=3x

We need to find the value of 

We are also given that

Funding received by P = Funding Received by Q = $40,000

Also,

Funding received by P= Funding received by R+100 of Funding received by R

Thus,x=40,000 + 40,000 + 20,000 = $100,000

Step 3: Calculating the final answer

Donation that is not received by the university from The Goodwill Foundation = 3x = $300,000

 (D) is the correct answer.

Step 1: Question statement and Inferences

Let the number of students in the Class of 2012 be x.

So, number of students who chose consultancy in the first survey = x/3.

Two-third out of the students who chose consultancy as their first career choice, changed their mind by the completion of the course.

So, the number of students who changed their mind

Step 2: Finding required values 

Out of the students who chose consulting in the second survey as well, three-fifth started their careers as entrepreneurs and 12 as employee to firms. 

The number of students who still chose consulting in the second survey = 

The number of student who became entrepreneurs = 3/5 x The number of students who stayed with their first choice  

The number of student who joined firms = 12

That is, 

Step 3: Calculating the final answer

Thus, the total number of students in the class = 270.

Answer: Option (D) 

Steps 1&2: Understand question and draw inferences

Let the number of candidates who gave 0 correct answers, 1 correct answer and 2 correct answers = A, B and C respectively

A + B + C = 120 -----(1)

We have to find the value of A.

To do so, we need to find:

(i)    Either the value of B and C

(ii)   Or the value of (B + C)

Step 3: Analyze Statement 1

Number of students who answered at least one question correctly = B + C

We derive a relation between B and C, but we cannot find the value of B or C or (B + C) from equation (1) and (2).

INSUFFICIENT.

Step 4: Analyze Statement 2

Number of students who answered none or all questions correctly = A + C

We derive a relation between A and C, but we cannot find the value of B or C or (B + C) from equation (1) and (3).

Step 5: Analyze Statement 1 and Statement 2 together (if needed)

We have equations (1), (2) and (3) when we combine the two statements.

Substituting A and B from equation (2) and (3) in equation (1),

3C + 4C + C = 120

We can find the value of C from this equation and substitute the value in equation (3) the find the required value of A.

SUFFICIENT.

(C) is the correct answer.

Steps 1 & 2: Understand Question and Draw Inferences

We are given that 80% employees of a company play soccer. We have to find the percentage of the employees who play golf.

Since this question only talks about the percentage, not the absolute numbers, let’s say the number of employees in the company is 100.

80% of these employees play soccer. Now, these 80% employees include the employees who play only soccer and the employees who play soccer and golf both.

So, the employees who play soccer = 80% of 100 = 80

Let’s say the number of employees who play both soccer and golf = x

Thus, the number of employees who play only soccer = 80 – x

Also, let the number of employees who play only golf = y

If there are any employees who play neither soccer nor golf = 20 – y

The total number of employees who play golf = x + y 

We have to find the value of (x + y).

Step 3: Analyze Statement 1

Statement (1) says: 25% of the employees who play soccer also play golf.     

The number of employees who play soccer and golf is x.

Per this statement:

 x = 25% of 80

x = 20   ………….. (1)

However, since we do not know the value of y, we cannot get the value of (x + y). 

Hence, statement (1) is not sufficient to answer the question: What is the value of (x + y)?     

Step 4: Analyze Statement 2

Statement (2) says:  50% of the employees who play golf also play soccer.         

The employees who play golf and soccer are (x + y). 50% of these employees also play soccer. Out of these (x + y) employees, the employees who play soccer = x

50% of (x + y) = x

x + y = 2x

y = x             …… (2)

However, we don’t know the value of x and y. so, we can’t determine the value of (x + y).

Hence, statement II is not sufficient to answer the question: What is the value of (x + y)?  

Step 5: Analyze Both Statements Together (if needed)

Since step 3 and step 4 were not able to provide the answer to the question, let’s analyse both the statements together:

Statement (1):

x = 20   ………….. (1)      

Statement (2):

y = x          ………… (2)      

Thus,

y = 20

Hence,

x + y = 20 + 20 = 40 

So, statement (1) and (2) combined are sufficient to answer the question.   

Answer: Option (C)