Lee, Dimitra, and Jan, each had to pay a fine for accidental property

Question

Lee, Dimitra, and Jan, each had to pay a fine for accidental property damage. If the total amount paid by the 3 was $900, what was the median amount?

(1) Jan was fined $300.
(2) Lee and Dimitra were fined a total of $600.

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shivani1351 · Accepted Answer

Lee, Dimitra, and Jan, each had to pay a fine for accidental property damage. If the total amount paid by the 3 was $900, what was the median amount?

(1) Jan was fined $300.
(2) Lee and Dimitra were fined a total of $600.

Let the amounts spent by Lee, Dimitra and Jan be L,D and J respectively.
Given: L+D+J = 900
Now, let's look at each statement individually and then at both of them together (if required):

Statement 1: Jan was fined $300.
L+D+J = 900
J = 300
Thus, D+J = 600
Now, think about any way two numbers add up to 600:
Way 1 - If one is greater than 300, the other must be less than 300.
Way 2 - Each of the two numbers = 300

Hence, the three amounts would look like:
Way 1 - (<300), 300, (>300)
Way 2 - 300, 300, 300

In either of the two ways, Jan's amount, i.e 300 is the median. Hence, we can determine the answer using Statement 1 alone.

Now, let's take a look at Statement 2 closely:
Statement 2: Lee and Dimitra were fined a total of $600.
If you look at this statement, you will realise that this statement gives us the same information that is provided by Statement 1. L+D = 600 => J = 300. By using the same logic that we used in Statement 1, we can clearly conclude that Jan's amount must be the median.

Hence, the correct answer is Option D - EACH statement alone is sufficient.

Hope this helps!

Xdsa · Answer

option d is correct

statement 1: j=300$
others should pay 600$ in the form 0,600 or 1,599 ,..., 300,300
so clearly median is 300 irrespective of the amount paid by the other 2
so sufficient
statement 2:
L+D=600
J=300 
clearly similar to statement 1 we can find median
Hence sufficient

Dereno · Answer

Lee, Dmitria and Jan were asked to pay a fine totalling $900.

We need to find : Median value

Statement 1:

Jan was fined $300.

if Jan was fined $300. Then the amount paid by Lee and Dmitria equals 900-300 = $600.

The split up between Lee and Dmitiria can be of many values. (1,599);(2,598),.........(598,2);(599,1).

With any value across the spectrum. Jan occupies the middle value.

(1,300,599)
.
....
(599,300,1).

Hence,  Sufficient .

Statement 2:

Lee and Dimitra were fined a total of $600.

If Lee and Dimitra were fined a total of $600, then Jan = $300.

This is same as the statement 1.

Hence,  Sufficient

Option D

nemoexplicabo · Answer

This is a great median problem that tests whether you can recognize when you have enough information about a set of numbers to determine their median — a classic Data Sufficiency concept!

The question asks: If Lee, Dimitra, and Jan each paid a fine and the total was $900, what was the median fine?

Since we have 3 values, the median will be the middle value when the three fines are arranged in order.

Statement (1): Jan was fined $300

From this, we know:
- Jan = $300
- Lee + Dimitra = $900 - $300 = $600

Now here's the key insight: No matter how we split $600 between Lee and Dimitra, when we arrange all three values in order, $300 will ALWAYS be the median.

Let me show you why with a few examples:
- If Lee = $200 and Dimitra = $400: Ordered = {$200, $300, $400} → Median = $300
- If Lee = $100 and Dimitra = $500: Ordered = {$100, $300, $500} → Median = $300
- If Lee = $300 and Dimitra = $300: Ordered = {$300, $300, $300} → Median = $300
- If Lee = $450 and Dimitra = $150: Ordered = {$150, $300, $450} → Median = $300

Since $300 is exactly one-third of the total ($900), and the other two values must sum to twice that amount ($600), $300 will always fall in the middle position.

Statement (1) is SUFFICIENT.

Statement (2): Lee and Dimitra were fined a total of $600

This tells us:
- Lee + Dimitra = $600
- Jan = $900 - $600 = $300

Wait a minute — this gives us exactly the same information as Statement 1! We know Jan = $300, and the analysis is identical. The median must be $300.

Statement (2) is SUFFICIENT.

Answer: D

Common traps to avoid:

A common mistake is thinking that Statement 1 is insufficient because "we don't know how $600 is split between Lee and Dimitra." But in Data Sufficiency, we don't need to find all individual values — we only need to determine if we can find the median. The beautiful thing about this problem is that the median doesn't depend on how the remaining money is distributed. Another trap is not recognizing that Statements 1 and 2 are actually giving the same information in different forms — if you know Jan's fine, you know the sum of the other two, and vice versa.

Key takeaway: For median problems with an odd number of values, you don't always need to know every individual value. If you know enough about the structure of the data set, you can sometimes determine the median even with some unknowns. In this case, knowing one value that equals exactly one-third of the total locks in the median position. This is a powerful concept that applies whenever you have constraints that force certain values into fixed positions in the ordered list!

ExpertsGlobal5 · Answer

Explanation:  
 
The total amount paid by Lee, Dimitra, and Jan = $900. Hence, the average amount paid by them was $300.
  We need to find whether the median amount paid by Lee, Dimitra, and Jan can be determined.  
 
 Statement (1) 
 
Jan was fined $300.
 
Since the average amount paid was $300,   maintaining this average requires that both of the other two values are either equal to $300, or one of them is greater than $300 while the other is less than $300  . In either case, the median will be $300.
 
It is possible to determine the median amount paid by Lee, Dimitra, and Jan.   Hence, Statement (1) is sufficient.  
 
 Statement (2) 
 
 Since  the  total fine paid  = 3 x 300 =  $900 , and Lee and Dimitra paid a total of $600,  it follows that Jan must have paid 900 – 600 = $300 .
 
After that, similar reasoning as above can be used to show that it is possible to determine the median amount paid by Lee, Dimitra, and Jan.   Hence, Statement (2) is sufficient.  
 
  D is the correct answer choice.

Lee, Dimitra, and Jan, each had to pay a fine for accidental property

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GMAT Data Sufficiency (DS) Questions

Lee, Dimitra, and Jan, each had to pay a fine for accidental property

Prep Toolkit

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