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In a certain quiz that consists of 10 questions, each question after

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Re: In a certain quiz that consists of 10 questions, each question after [#permalink]
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Aves wrote:
Equation is like this:

$$10x + ( 4 + 8 + 12 + ... + 32) = 360$$

to find sum of the evenly spaced sequence, use average * number of the members in the sequence

$$10x + (20*9) = 360$$

$$10x + 180 = 360$$
$$x = 18$$

So, $$x + 8 = 26$$

Good shortcut - will use this in the future.

I did it the long way but still got the question right in about 90 seconds

x
x+4
x+8
x+12
x+16
x+20
x+24
x+28
x+32
x+36

10x+180=360
10x=180
x=18

3rd question = x+8 = 18+8 = 26

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Re: In a certain quiz that consists of 10 questions, each question after [#permalink]
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I found a shortcut for the same. Since we know that there are 10 questions on the quiz and all questions are evenly placed by 4 points, DO NOT choose the points in the first question as x.

So, the numbers will be:
1) x-16
2) x-12
3) x-8
4) x-4
5) x
6) x+4
7) x+8
8) x+12
9) x+16
10) x+20

Adding all the above 10 will lead to a simple sum of 10x + 20 (-16 & 16 will lead to a sum of 0, same for -12& +12 so on & so forth)

SO, 10x + 20 = 360
10x= 340
x= 34
3rd question = x-8= 34-8 = 26.

Hope it helps.
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Re: In a certain quiz that consists of 10 questions, each question after [#permalink]
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lpetroski 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

This is an Arithmetic Progression (A.P.) with terms => a, a+4, a+8, ...., a + (n-1) *4

a => First Term of Series
n => Number of the term
l => Last Term

So, l = a + (10-1) * 4 = a + 9*4 = a + 36

Sum of an A.P. Series = $$\frac{n*(a+l)}{2}$$ => Standard Formula

Therefore,

$$360 = \frac{n*(a+l)}{2} => 360 = \frac{10*(a+a+36)}{2}$$

=> 360 = 5 * (2a + 36) => 72 = 2a + 36

=> 2a = 36 => a = 18

Therefore, 3rd Term = a + 8 = 26
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Re: In a certain quiz that consists of 10 questions, each question after [#permalink]
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I got this in a similar approach but we can calculate and get answer in 50 Secs.

Since the seq is in AP evenly spaced the sum= Avg* N

Seq is x,x+4, x+2*4,x+3*4, x+4*4,x+5*4,x+6*4,x+7*4,x+8*4,x+9*4 ( don't need to write the entire seq just get the idea how seq is going to form )

and so on the average of evenly spaced set of 10 numbers is average of 5th and 6th value.

Since each term is increment of 4 the mid value between 5 and 6 will be increment of 2 from 5th value
so fifth value is x+4*4= x+16
so average is x+18 so
(x+18)*10=360
x+18=36
or x=18
and third value is x+2*4=18+8= 26

The trick in above question is identifying the evenly spaced seq, then its average or median value and finding x.
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Re: In a certain quiz that consists of 10 questions, each question after [#permalink]
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This is an Arithmetic progression question.

n/2 * [2a + (n - 1) *d] = 360
10/2 * [2a + (10 - 1)* 4)] = 360
a = 18

So, first question is 18 marks.

So, third question = 26
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Re: In a certain quiz that consists of 10 questions, each question after [#permalink]
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lpetroski 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.

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Re: In a certain quiz that consists of 10 questions, each question after [#permalink]
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lpetroski 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

10x + 4 (1 + 2 + 3 + ....9) = 360

=) 10x + 4 * [n(n+1)]/2 = 360

=) 10x + 4 * [(9 * 10)] / 2 = 360

=) x = 18

third question = (18 +8) =26 = C the answer

thakns
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Re: In a certain quiz that consists of 10 questions, each question after [#permalink]
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There is no need for any formulas here. Sum of 10 consecutive integers = 360. Average = 36. Average of a set of consecutive integers = Median of the set. Median is the number between 5 and 6, and its equals 36.

Since the difference between terms is 4, therefore, 5th term is 34 and 6th term is 38.
5th term = 34
4th term = 30
3th term = 26
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Re: In a certain quiz that consists of 10 questions, each question after [#permalink]
Aves wrote:
Equation is like this:

$$10x + ( 4 + 8 + 12 + ... + 32) = 360$$

Hi why is the last term 32 and not 36? should it be the 9th term which is x+36? thanks
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Re: In a certain quiz that consists of 10 questions, each question after [#permalink]
jack_tay wrote:
Aves wrote:
Equation is like this:

$$10x + ( 4 + 8 + 12 + ... + 32) = 360$$

Hi why is the last term 32 and not 36? should it be the 9th term which is x+36? thanks

_______________________
Yes. Edited the typo. Thanks!
Re: In a certain quiz that consists of 10 questions, each question after [#permalink]
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