ardz24 wrote:In a certain quiz that consists of 10 questions, each question after the first is worth 4 points more than the preceding question. If the 10 questions on the quiz are worth a total of 360 points, how many points is the third question worth?
A. 18
B. 24
C. 26
D. 32
E. 44

Since each question is worth 4 more points than the preceding question, the point values constitute an EVENLY SPACED SET.
For any evenly spaced set:
Average = Median.

Since the 10 point values sum to 360, we get:
Average = median = 360/10 = 36.

We can PLUG IN THE ANSWERS, which represent the 3rd value.
Since there are 10 values, the median = the average of the 5th and 6th values.
When the correct answer is plugged in, the average of the 5th and 6th values = 36.

B: 24
Here, the 3rd through 6th values are as follows:
24, 28, 32, 36.
The values in red will yield an average that is TOO SMALL.
Thus, a greater answer choice is needed.
Eliminate A and B.

D: 32
Here, the 3rd through 6th values are as follows:
32, 36, 40, 44.
The values in red will yield an average that is TOO BIG.
Thus, a smaller answer choice is needed.
Eliminate D and E.

The correct answer is C.

C: 26
Here, the 3rd through 6th values are as follows:
26, 30, 34, 38.
Average of the 5th and 6th values = (34+38)/2 = 72/2 = 36.
Success!

In a certain quiz that consists of 10 questions, each question after the first is worth 4 points more than the preceding question. If the 10 questions on the quiz are worth a total of 360 points, how many points is the third question worth?
A. 18
B. 24
C. 26
D. 32
E. 44

Is there a strategic approach to this question? Any experts help please?

Hi ardz24,
Let's take a look at your question.

Each question after the first is worth 4 points more than the preceding question, so we can write the sequence of points as:
x, x+4, x+8, x+12, ... x+36 (10 questions total)
This seems to be an arithmetic sequence with:
$$n=10,\ d=4$$
The 10 questions on the quiz are worth a total of 360 points, which represents that the sum of 10 terms of the arithmetic sequence is 360, i.e.
$$S=360$$

We know that the sum of the arithmetic sequence can be represented using the formula:
$$S=\frac{n}{2}\left[2a_1+\left(n-1\right)d\right]$$
$$360=\frac{10}{2}\left[2a_1+\left(10-1\right)4\right]$$
$$360=5\left[2a_1+\left(9\right)4\right]$$
$$360=5\left[2a_1+36\right]$$
$$\frac{360}{5}=\left[2a_1+36\right]$$
$$72=\left[2a_1+36\right]$$
$$2a_1=72-36$$
$$2a_1=36$$
$$a_1=\frac{36}{2}=18$$

a1 represents the first term in the sequence, i.e. points of the first question.
Points of second question = 18 + 4 = 22
Points of the third question = 22 + 4 = 26

Therefore Option C is correct.

Hope it helps.
I am available if you'd like any follow up.

Let the first question is worth 'a' points.
Then, Second question is worth a + 4 points, third of worth (a + 4 + 4) = a + 8 points.
So, the sum of the series becomes a + a + 4 + a + 8 + a + 12 ......... upto 10 terms
= 10a + 4 + 8 + 12 + ....... upto 9 terms
Sum = 10a + Sum of A.P with first term 4 and common difference 4.
Sum = 10a + 180 = 360
a = 18
Third question is worth a + 8 points = 18 + 8 = 26 points.