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In a college, 300 graduates sit for the recruitment drive of three companies-A, B, and C. 120 graduates are placed in A, 180 are placed in B and 80 are placed in C. 5 students are placed in all the three companies. How many of them are not placed in any of the three companies?
(1) Out of the graduates who got placed in A, 75 and 45 are also placed in B and C respectively.
(2) Out of the graduates who got placed in C, 35 are also placed in B.
- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- d)EACH statement ALONE is sufficient.
- e)Statements (1) and (2) TOGETHER are NOT sufficient.
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
In a college, 300 graduates sit for the recruitment drive of three com...
Steps 1 & 2: Understand Question and Draw Inferences
We are given that 300 graduates from a college participate in recruitment process conducted by companies A, B, and C. The results of the process are as follows:
Let’s say:
X = the number of students who got placed in A
Y = the number of students who got placed in B
Z = the number of students who got placed in C
P = the number of students who got placed in B and C
Q = the number of students who got placed in A and C
R = the number of students who got placed in A and B
S = the number of students who got placed in all three companies
T = the number of students who were not placed in any of the companies
Now, per the question:
X + Y + Z + P + Q + R + S + T = 300 ………… (1)
X + P + Q + S = 80 …………. (2)
Y + P + S + R = 180 …………. (3)
Z + Q + S + R = 120 …………. (4)
S = 5 …………. (5)
We need to find the value of T. However, we have 8 variables and only 5 equations. So, we need three more equations in these variables to find the value of T.
Step 3: Analyze Statement 1
Statement 1 says: Out of the number of graduates who got placed in A, 75 and 45 are also placed in B and C respectively.
Per this statement,
The number of students placed in A and B = 75
We know from the diagram that the students placed in A and B consist of R and S. So,
R + S = 75
So, R = 70 ………….. (6)
Note that, since S represents the number of students who were placed in all the three companies, it includes the number of students who were placed in A and B.
The number of students placed in A and C = 45
We know from the diagram that the students placed in A and B consist of Q and S. So,
Q + S = 45
So, Q = 40 ………….. (7)
Thus, we get a total of 7 equations, but we have 8 variables. So, we still can’t find the value of T.
Hence, statement I alone is not sufficient to answer the question: What is the value of T?
Step 4: Analyze Statement 2
Statement 2 says: Out of the number of graduates who got placed in C, 35 are also placed in B.
The number of students placed in B and C = 35
We know from the diagram that the students placed in B and C consist of P and S. So,
P + S = 35
So, P = 30 ………….. (8)
Thus, we get a total of 6 equations (5 from Steps 1 and 2, and another one in this step, from Statement 2), but we have 8 variables. So, we still can’t find the value of T.
Hence, statement II alone is not sufficient to answer the question: What is the value of T?
Step 5: Analyze Both Statements Together (if needed)
Since statement I and II alone are not sufficient to answer the question, let’s analyse both the statements together:
Now, the combination of both the statements gives us 8 equations in 8 variables, we can easily find the value of T. By plugging in the values of P, Q, and R, we get:
Now, by plugging in the values of P, Q, R, and S in the following equations, we get:
X + Y + Z + P + Q + R + S + T = 300 ………… (1)
X + P + Q + S = 80 …………. (2)
Y + P + S + R = 180 …………. (3)
Z + Q + S + R = 120 …………. (4)
X = 5
Y = 75
Z = 5
Thus, from equation (1):
5 + 75 + 5 + 40 + 30 + 70 + 5 + T = 300
230 + T = 300
So, T = 70
So, there are total 70 students who were not placed in any of the companies.
Both statements together are sufficient to answer the question.
Answer: Option (C)
(Note: We have solved for the value of T only to illustrate how such an answer could be calculated if one wanted to solve for T. The given question is a Data Sufficiency question, and therefore, you as a student need not solve for the value of T. Once you determine in Step 5 that you have 8 equations and 8 variables, and therefore the two statements together are sufficiency to find a unique value of T, you can-you should! – stop there and confidently mark the answer as C)
Most Upvoted Answer
In a college, 300 graduates sit for the recruitment drive of three com...
Given Information:
- Total number of graduates sitting for recruitment drive = 300
- Number of graduates placed in Company A = 120
- Number of graduates placed in Company B = 180
- Number of graduates placed in Company C = 80
- Number of graduates placed in all three companies = 5
To Find:
The number of graduates not placed in any of the three companies.
Statement 1:
Out of the graduates who got placed in Company A, 75 and 45 are also placed in Company B and C respectively.
This statement tells us about the number of graduates who are placed in both Company A and either Company B or Company C. However, it does not provide any information about the total number of graduates not placed in any of the three companies. Therefore, statement 1 alone is not sufficient to answer the question.
Statement 2:
Out of the graduates who got placed in Company C, 35 are also placed in Company B.
This statement tells us about the number of graduates who are placed in both Company B and Company C. However, it does not provide any information about the number of graduates placed in Company A or the graduates not placed in any of the three companies. Therefore, statement 2 alone is not sufficient to answer the question.
Statements 1 and 2 together:
Combining both statements, we can deduce the following information:
- Number of graduates placed in Company A and Company B = 75
- Number of graduates placed in Company A and Company C = 45
- Number of graduates placed in Company B and Company C = 35
Using this information, we can create the following Venn diagram to represent the placements:
```
A
/ \
/ \
75 45
/ \
/ \
B-----35----C
/ \ / \
/ \ / \
/ \ / \
5
```
From the Venn diagram, we can calculate the number of graduates placed in only Company A, only Company B, only Company C, and in none of the three companies:
- Number of graduates placed only in Company A = 120 - 75 - 45 - 5 = 120 - 125 = -5 (negative value is not possible)
- Number of graduates placed only in Company B = 180 - 75 - 35 - 5 = 180 - 115 = 65
- Number of graduates placed only in Company C = 80 - 45 - 35 - 5 = 80 - 85 = -5 (negative value is not possible)
- Number of graduates placed in none of the three companies = Total number of graduates - (Number of graduates placed in A + Number of graduates placed in B + Number of graduates placed in C + Number of graduates placed in all three companies)
= 300 - (120 + 180 + 80 + 5)
= 300 - 385
= -85 (negative value is not possible)
From the calculations, we can see that the number of graduates placed in only Company B is 65, but the number of graduates not placed in any of the three companies is not possible to determine. Therefore, even when the two statements are used together, they are not sufficient
- Total number of graduates sitting for recruitment drive = 300
- Number of graduates placed in Company A = 120
- Number of graduates placed in Company B = 180
- Number of graduates placed in Company C = 80
- Number of graduates placed in all three companies = 5
To Find:
The number of graduates not placed in any of the three companies.
Statement 1:
Out of the graduates who got placed in Company A, 75 and 45 are also placed in Company B and C respectively.
This statement tells us about the number of graduates who are placed in both Company A and either Company B or Company C. However, it does not provide any information about the total number of graduates not placed in any of the three companies. Therefore, statement 1 alone is not sufficient to answer the question.
Statement 2:
Out of the graduates who got placed in Company C, 35 are also placed in Company B.
This statement tells us about the number of graduates who are placed in both Company B and Company C. However, it does not provide any information about the number of graduates placed in Company A or the graduates not placed in any of the three companies. Therefore, statement 2 alone is not sufficient to answer the question.
Statements 1 and 2 together:
Combining both statements, we can deduce the following information:
- Number of graduates placed in Company A and Company B = 75
- Number of graduates placed in Company A and Company C = 45
- Number of graduates placed in Company B and Company C = 35
Using this information, we can create the following Venn diagram to represent the placements:
```
A
/ \
/ \
75 45
/ \
/ \
B-----35----C
/ \ / \
/ \ / \
/ \ / \
5
```
From the Venn diagram, we can calculate the number of graduates placed in only Company A, only Company B, only Company C, and in none of the three companies:
- Number of graduates placed only in Company A = 120 - 75 - 45 - 5 = 120 - 125 = -5 (negative value is not possible)
- Number of graduates placed only in Company B = 180 - 75 - 35 - 5 = 180 - 115 = 65
- Number of graduates placed only in Company C = 80 - 45 - 35 - 5 = 80 - 85 = -5 (negative value is not possible)
- Number of graduates placed in none of the three companies = Total number of graduates - (Number of graduates placed in A + Number of graduates placed in B + Number of graduates placed in C + Number of graduates placed in all three companies)
= 300 - (120 + 180 + 80 + 5)
= 300 - 385
= -85 (negative value is not possible)
From the calculations, we can see that the number of graduates placed in only Company B is 65, but the number of graduates not placed in any of the three companies is not possible to determine. Therefore, even when the two statements are used together, they are not sufficient
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In a college, 300 graduates sit for the recruitment drive of three companies-A, B, and C. 120 graduates are placed in A, 180 are placed in B and 80 are placed in C. 5 students are placed in all the three companies. How many of them are not placed in any of the three companies?(1) Out of the graduates who got placed in A, 75 and 45 are also placed in B and C respectively.(2) Out of the graduates who got placed in C, 35 are also placed in B. a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about In a college, 300 graduates sit for the recruitment drive of three companies-A, B, and C. 120 graduates are placed in A, 180 are placed in B and 80 are placed in C. 5 students are placed in all the three companies. How many of them are not placed in any of the three companies?(1) Out of the graduates who got placed in A, 75 and 45 are also placed in B and C respectively.(2) Out of the graduates who got placed in C, 35 are also placed in B. a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a college, 300 graduates sit for the recruitment drive of three companies-A, B, and C. 120 graduates are placed in A, 180 are placed in B and 80 are placed in C. 5 students are placed in all the three companies. How many of them are not placed in any of the three companies?(1) Out of the graduates who got placed in A, 75 and 45 are also placed in B and C respectively.(2) Out of the graduates who got placed in C, 35 are also placed in B. a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer?.
In a college, 300 graduates sit for the recruitment drive of three companies-A, B, and C. 120 graduates are placed in A, 180 are placed in B and 80 are placed in C. 5 students are placed in all the three companies. How many of them are not placed in any of the three companies?(1) Out of the graduates who got placed in A, 75 and 45 are also placed in B and C respectively.(2) Out of the graduates who got placed in C, 35 are also placed in B. a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about In a college, 300 graduates sit for the recruitment drive of three companies-A, B, and C. 120 graduates are placed in A, 180 are placed in B and 80 are placed in C. 5 students are placed in all the three companies. How many of them are not placed in any of the three companies?(1) Out of the graduates who got placed in A, 75 and 45 are also placed in B and C respectively.(2) Out of the graduates who got placed in C, 35 are also placed in B. a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a college, 300 graduates sit for the recruitment drive of three companies-A, B, and C. 120 graduates are placed in A, 180 are placed in B and 80 are placed in C. 5 students are placed in all the three companies. How many of them are not placed in any of the three companies?(1) Out of the graduates who got placed in A, 75 and 45 are also placed in B and C respectively.(2) Out of the graduates who got placed in C, 35 are also placed in B. a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer?.
Solutions for In a college, 300 graduates sit for the recruitment drive of three companies-A, B, and C. 120 graduates are placed in A, 180 are placed in B and 80 are placed in C. 5 students are placed in all the three companies. How many of them are not placed in any of the three companies?(1) Out of the graduates who got placed in A, 75 and 45 are also placed in B and C respectively.(2) Out of the graduates who got placed in C, 35 are also placed in B. a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
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Here you can find the meaning of In a college, 300 graduates sit for the recruitment drive of three companies-A, B, and C. 120 graduates are placed in A, 180 are placed in B and 80 are placed in C. 5 students are placed in all the three companies. How many of them are not placed in any of the three companies?(1) Out of the graduates who got placed in A, 75 and 45 are also placed in B and C respectively.(2) Out of the graduates who got placed in C, 35 are also placed in B. a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
In a college, 300 graduates sit for the recruitment drive of three companies-A, B, and C. 120 graduates are placed in A, 180 are placed in B and 80 are placed in C. 5 students are placed in all the three companies. How many of them are not placed in any of the three companies?(1) Out of the graduates who got placed in A, 75 and 45 are also placed in B and C respectively.(2) Out of the graduates who got placed in C, 35 are also placed in B. a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer?, a detailed solution for In a college, 300 graduates sit for the recruitment drive of three companies-A, B, and C. 120 graduates are placed in A, 180 are placed in B and 80 are placed in C. 5 students are placed in all the three companies. How many of them are not placed in any of the three companies?(1) Out of the graduates who got placed in A, 75 and 45 are also placed in B and C respectively.(2) Out of the graduates who got placed in C, 35 are also placed in B. a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of In a college, 300 graduates sit for the recruitment drive of three companies-A, B, and C. 120 graduates are placed in A, 180 are placed in B and 80 are placed in C. 5 students are placed in all the three companies. How many of them are not placed in any of the three companies?(1) Out of the graduates who got placed in A, 75 and 45 are also placed in B and C respectively.(2) Out of the graduates who got placed in C, 35 are also placed in B. a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice In a college, 300 graduates sit for the recruitment drive of three companies-A, B, and C. 120 graduates are placed in A, 180 are placed in B and 80 are placed in C. 5 students are placed in all the three companies. How many of them are not placed in any of the three companies?(1) Out of the graduates who got placed in A, 75 and 45 are also placed in B and C respectively.(2) Out of the graduates who got placed in C, 35 are also placed in B. a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice GMAT tests.
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