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30 Aug 2024, 01:30
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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Question Stats:
71% (02:14) correct
29%
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Out of the 60 employees of a startup, only 10 are non-engineers. How many employees of the startup are engineers with a MBA degree?
(1) Only 1 out of every 12 employees with a MBA degree is a non-engineer
(2) More than 55 percent of all employees have a MBA degree
(1) Only 1 out of every 12 employees with a MBA degree is a non-engineer
(2) More than 55 percent of all employees have a MBA degree
30 Aug 2024, 02:16
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Using a 3x3 matrix and filling in the info provided in the stem
\begin{tabular}{|l|l|l|l|}
\hline
~ & E & nE & Total \\ \hline
MBA & ~ & ~ & ~ \\ \hline
nMBA & ~ & ~ & ~ \\ \hline
Total & 50 & 10 & 60 \\ \hline
\end{tabular}
(1) Only 1 out of every 12 employees with a MBA degree is a non-engineer
Let the number of employees who have an MBA = x
\begin{tabular}{|l|l|l|l|}
\hline
~ & E & nE & Total \\ \hline
MBA & \(\frac{11}{12}\)x & \(\frac{1}{12}\)x & x \\ \hline
nMBA & ~ & ~ & ~ \\ \hline
Total & 50 & 10 & 60 \\ \hline
\end{tabular}
With the info provided it is impossible to solve for a value for x and thus know the number of employees who are engineers and have an MBA.
INSUFFICIENT
(2) More than 55 percent of all employees have a MBA degree
\begin{tabular}{|l|l|l|l|}
\hline
~ & E & nE & Total \\ \hline
MBA & ~ & ~ & ~ \\ \hline
nMBA & ~ & ~ & ~ \\ \hline
Total & 50 & 10 & 60 \\ \hline
\end{tabular}
Without an exact value it is impossible to plot or use the info provided in the statement to solve the question.
INSUFFICIENT
(1+2)
Putting the two statements together does not provide enough with which to solve this question.
INSUFFICIENT
ANSWER E
\begin{tabular}{|l|l|l|l|}
\hline
~ & E & nE & Total \\ \hline
MBA & ~ & ~ & ~ \\ \hline
nMBA & ~ & ~ & ~ \\ \hline
Total & 50 & 10 & 60 \\ \hline
\end{tabular}
(1) Only 1 out of every 12 employees with a MBA degree is a non-engineer
Let the number of employees who have an MBA = x
\begin{tabular}{|l|l|l|l|}
\hline
~ & E & nE & Total \\ \hline
MBA & \(\frac{11}{12}\)x & \(\frac{1}{12}\)x & x \\ \hline
nMBA & ~ & ~ & ~ \\ \hline
Total & 50 & 10 & 60 \\ \hline
\end{tabular}
With the info provided it is impossible to solve for a value for x and thus know the number of employees who are engineers and have an MBA.
INSUFFICIENT
(2) More than 55 percent of all employees have a MBA degree
\begin{tabular}{|l|l|l|l|}
\hline
~ & E & nE & Total \\ \hline
MBA & ~ & ~ & ~ \\ \hline
nMBA & ~ & ~ & ~ \\ \hline
Total & 50 & 10 & 60 \\ \hline
\end{tabular}
Without an exact value it is impossible to plot or use the info provided in the statement to solve the question.
INSUFFICIENT
(1+2)
Putting the two statements together does not provide enough with which to solve this question.
INSUFFICIENT
ANSWER E
07 Jul 2026, 20:21
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This overlapping sets question illustrates an important DS principle: for a statement or statements to be insufficient, you must get (or at least be able to get) two distinct answers.
Let's use a table to organize the information from the prompt:
We want to know if we can solve for the upper left box (with the ?).
Statement 1:
Let's set m as the total number of employees with an MBA. Then we can represent this info as:
With no concrete numbers, this statement may not seem to give you much; however, your possibilities are restricted because a number that represents people must be an integer. So, in order to take 1/12 or 11/12 of a number of people, that number must be a positive multiple of 12. If m = 12, then there are 11 MBAs who are engineers (and 1 who is not). If m = 24, then there are 22 MBAs who are engineers (and 2 who are not). Both possibilities are consistent with the rest of the table. Two or more possible answers means the statement is insufficient.
Statement 2:
By itself this statement gives you a range for the number of MBAs at the startup, but no indication as to the split between MBAs who are engineers and those who are not. There are many possible answers. The statement is insufficient.
Together:
Again, you need to be careful and make sure that, for the statements together to be insufficient, at least two answers are possible.
If m represents over 55% of the employees, m cannot be 12 or 24 (which we used in Statement 1). 36 could work, however, since 36/60 = 6/10 = 60%. If m = 36, then there are 33 MBAs who are engineers and 3 who are not. If m = 48, then there are 44 MBAs who are engineers and 4 who are not. Both possibilities are consistent with the rest of the table. Two possible answers means the statements together are insufficient and the answer is E.
Note that m can't be 60. If m = 60, then there are 55 MBAs who are engineers, but this contradicts the existing table, which has 50 total engineers. So, the statements together are insufficient, but "barely", with exactly two possible answers. If the question were slightly different, the answer could have been C.
Remember: insufficient doesn't mean "I can't get an answer." It means "I can get at least two answers". Make sure this is true before selecting choice E.
Let's use a table to organize the information from the prompt:
| Engineer | Non-Engineer | Total | |
| MBA | ? | ||
| no MBA | |||
| Total | 50 | 10 | 60 |
We want to know if we can solve for the upper left box (with the ?).
Statement 1:
Let's set m as the total number of employees with an MBA. Then we can represent this info as:
| Engineer | Non-Engineer | Total | |
| MBA | \(\frac{11}{12}m\) | \(\frac{1}{12}m\) | m |
| no MBA | |||
| Total | 50 | 10 | 60 |
With no concrete numbers, this statement may not seem to give you much; however, your possibilities are restricted because a number that represents people must be an integer. So, in order to take 1/12 or 11/12 of a number of people, that number must be a positive multiple of 12. If m = 12, then there are 11 MBAs who are engineers (and 1 who is not). If m = 24, then there are 22 MBAs who are engineers (and 2 who are not). Both possibilities are consistent with the rest of the table. Two or more possible answers means the statement is insufficient.
Statement 2:
By itself this statement gives you a range for the number of MBAs at the startup, but no indication as to the split between MBAs who are engineers and those who are not. There are many possible answers. The statement is insufficient.
Together:
Again, you need to be careful and make sure that, for the statements together to be insufficient, at least two answers are possible.
If m represents over 55% of the employees, m cannot be 12 or 24 (which we used in Statement 1). 36 could work, however, since 36/60 = 6/10 = 60%. If m = 36, then there are 33 MBAs who are engineers and 3 who are not. If m = 48, then there are 44 MBAs who are engineers and 4 who are not. Both possibilities are consistent with the rest of the table. Two possible answers means the statements together are insufficient and the answer is E.
Note that m can't be 60. If m = 60, then there are 55 MBAs who are engineers, but this contradicts the existing table, which has 50 total engineers. So, the statements together are insufficient, but "barely", with exactly two possible answers. If the question were slightly different, the answer could have been C.
Remember: insufficient doesn't mean "I can't get an answer." It means "I can get at least two answers". Make sure this is true before selecting choice E.
