Question: A certain plumber charges $92 for each job completed in 4 hours or less and $23 per hour for each job completed in more than 4 hours. If it took the plumber a total of 7 hours to complete two separate jobs, what was the total amount charged by the plumber for the two jobs?

(1) The plumber charged $92 for one of the two jobs.
(2) The plumber charged $138 for one of the two jobs.

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are NOT sufficient.

Correct Answer: B
Solution and Explanation:
Approach Solution 1:
According to the question, a certain plumber charges $92 for each job completed in 4 hours or less and $23 per hour for each job completed in more than 4 hours.
It is also said that the total time taken by the plumber to complete two separate jobs is 7 hours. Now, we need to calculate the total amount that the plumber has charged.

Statement One Alone: The plumber charged $92 for one of the two jobs.
Therefore, we can assume, that the job for which he took $92, must be of 1 hour, 2 hours, 3 hours, or 4 hours long.
This implies for the other job it must be 6, 5, 4, or 3 hours, respectively.
Therefore, it is not possible to determine the amount charged for the two jobs.
Therefore, statement one alone is insufficient to find the total amount charged by the plumber for the two jobs.

Statement Two Alone: The plumber charged $138 for one of the two jobs.
Now, we can see that the plumber has charged $138 for one of the two jobs. This implies that the job for which he had charged $138 must be of more than 4 hours.

Since he charges $23 per hour for a job that is longer than 4 hours, we have:
138 = 23(number of hours)
6 = number of hours

As we know that the total time duration of the job done by the plumber is 7 hours, and one job has taken 6 hours, so we get that the plumber has taken one hour to complete the other job.
The amount charged by the plumber for a job that takes up to 4 hours, that the job can be 1,2,3, or 4 hours respectively, is $92.
Therefore, the two jobs will cost a total of $138 + $92 = $230.
Thus we can get the total amount charged by the plumber for the two jobs from the second statement alone.
Thus Statement 2 is sufficient.

Approach Solution 2:

According to the question, a certain plumber charges $92 for each job completed in 4 hours or less and $23 per hour for each job completed in more than 4 hours.
It is also said that the total time taken by the plumber to complete two separate jobs is 7 hours. Now, we need to calculate the total amount that the plumber has charged.

Statement 1: The plumber charged $138 for one of the two jobs.
We can see that the plumber charges $92, for any job that takes 4 hours or less than 4 hours, and he charges $23 per hour when the time taken by the plumber is more than 4 hours.
Now, the statement is the plumber charged $92 for one of the two jobs.

As he charges $92 for one job, that means the time taken to complete that job may be 1 hour, 2 hours,3 hours, or 4 hours.
If we assume that the plumber has finished the job in 1 hour that would mean that he took 6 hours for the other job.
Therefore, the total amount charged for the second work = 92 + 2*23= 138

Again if we assume that the plumber has finished the job in 3.5 hours, that would mean that he took 3.5 hours for the other job.
Therefore, the total amount charged for the second work = 92 + 92 = 184$
Hence, statement one alone is insufficient.

Statement 2: The plumber charged $138 for one of the two jobs.
As given, he charges $138 for one job, then we can calculate that he finished the work in 6 hours.

Thus, charges for a work of 6 hours is 92 + 2*23= 138$
This means that the other job is done in 1 hour by the plumber,
Therefore, the total amount charged is 92 + 138 = 230$

Thus, we got the total amount charged by the plumber.
Hence, Statement 2 alone is sufficient.

Approach Solution 3:

According to the question, a certain plumber charges $92 for each job completed in 4 hours or less and $23 per hour for each job completed in more than 4 hours.
It is also said that the total time taken by the plumber to complete two separate jobs is 7 hours. Now, we need to calculate the total amount that the plumber has charged.

Statement One Alone: The plumber charged $92 for one of the two jobs.

We can find several scenarios that satisfy statement 1. Here are two:

Case a: The plumber spent 1 hour on one job (and received $92).
The plumber spent 6 hours on the other job (at $23/hour).
In this case, the TOTAL amount charged = $92 + (6)($23) = $230

Case b: The plumber spent 2 hours on one job (and received $92)
The plumber spent 5 hours on the other job (at $23/hour).
In this case, the TOTAL amount charged = $92 + (5)($23) = $207
Therefore, the target question cannot be answered with certainty.
Statement 1 is NOT SUFFICIENT

Statement Two Alone: The plumber charged $138 for one of the two jobs.
This implies that the plumber must have spent more than 4 hours on this job.
Therefore, the amount charged is $23/hour
Therefore, the plumber spent $138/23 = 6 hours on this job (and received $138), which signifies he spent 1 hour on the other job (and received $92)
Therefore, the total amount charged = $138 + $92 = $230
Thus, the target question can be answered with certainty.
Hence, statement 2 alone is SUFFICIENT

“A certain plumber charges $92 for each job completed in 4 hours”- is a topic of the GMAT Quantitative reasoning section of GMAT. The GMAT Quant section includes a total of 31 questions. GMAT Data Sufficiency questions are characterised by a problem statement and followed by two factual statements. GMAT data sufficiency constitutes 15 questions which are two-fifths of the total 31 GMAT quant questions.

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