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In a certain quiz that consists of 10 questions, each questi

This topic has 3 expert replies and 1 member reply

In a certain quiz that consists of 10 questions, each questi

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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?

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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!

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Quote:
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.

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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
The first question is worth x, the 2nd worth x + 4, the 3rd worth x + 2(4) = x + 8, ..., the 10th is worth x + 9(4) = x + 36.

Since we have a set of evenly-spaced numbers, the average is (x + x + 36)/2 = (2x + 36)/2 = x + 18.

Since sum = average * quantity we have:

360 = (x + 18) * 10

36 = x + 18

18 = x

The first question is worth x = 18 points. So the third question is worth x + 8 = 18 + 8 = 26 points.

Answer: C

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scott@targettestprep.com



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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.

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