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List S consists of 10 consecutive odd integers, and list T

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List S consists of 10 consecutive odd integers, and list T [#permalink] New post 16 Feb 2011, 08:42
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List S consists of 10 consecutive odd integers, and list T consists of 5 consecutive even integers. If the least integer in S is 7 more than the least integer in T, how much greater is the average (arithmetic mean) of the integers in S than the average of the integers in T?

A. 2
B. 7
C. 8
D. 12
E. 22
[Reveal] Spoiler: OA

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Re: Arithmetic Statistics [#permalink] New post 16 Feb 2011, 08:56
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Sum of evenly spaced progression:
\frac{n}{2}(2a+(n-1)d)

Average = \frac{Sum}{n}
or
Average =\frac{1}{2}(2a+(n-1)d)


\frac{1}{2}(2a+(10-1)*2) - \frac{1}{2}(2(a-7)+(5-1)*2)

\frac{1}{2}(2a+(10-1)*2) - \frac{1}{2}(2(a-7)+(5-1)*2)

a+9-(a-7+4)

a+9-a+7-4

12

Ans: "D"
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Re: Arithmetic Statistics [#permalink] New post 16 Feb 2011, 08:59
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Baten80 wrote:
List S consists of 10 consecutive odd integers, and list T consists of 5 consecutive even integers. If the least integer in S is 7 more than the least integer in T, how much greater is the average (arithmetic mean) of the integers in S than the average of the integers in T?

a) 2
b) 7
c) 8
d) 12
e) 22


For any evenly spaced set median=mean=the average of the first and the last terms.

So the mean of S will be the average of the first and the last terms: mean=(x+x+9*2)/2=x+9, where x is the first term;
The mean of T will simply be the median or the third term: mean=(x-7)+2*2=x-3;

The difference will be (x+9)-(x-3)=12.

Answer: D.
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Re: Arithmetic Statistics [#permalink] New post 17 Feb 2011, 04:51
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If you didnt know the formula for evenly spaced sets, you can pick numbers and solve this question very easily.

Pick first number of set T=2. Since number of elements = 5, the mean will be the middle term ie the 3rd term, which will be 6.

From the question, you can infer that first number of the set T, will be 2+7= 9. Since this set consists of even number of terms,ie 10, the mean will be the average of the middle 2 terms, ie 5th and 6th term, which are 17 and 19 respectively and their average will be 18= mean of the set.

Therefore, the difference between the mean of two sets= 18-6= 12.

Answer D.
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Re: Arithmetic Statistics [#permalink] New post 17 Feb 2011, 12:01
Fluke - when u say 2a - what do u mean?
shouldnt it be A1 (the first number in the series)?

thanks.
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Re: Arithmetic Statistics [#permalink] New post 17 Feb 2011, 17:24
Easy by picking numbers, but I didn't know that formula. Thanks.
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Re: Arithmetic Statistics [#permalink] New post 17 Feb 2011, 23:46
144144 wrote:
Fluke - when u say 2a - what do u mean?
shouldnt it be A1 (the first number in the series)?

thanks.


You are half right;

It should be 2*a_1 i.e. twice of the first term. "a" is another way of depicting a_1

The formula for Sum of n numbers in an evenly spaced progression is denoted by:
\frac{n}{2}(2*a_1+(n-1)d)

If the progression is: 2,4,6. Sum=12

Using formula:
a_1=2. First term of the series
n=3 Number of elements in the progression(series)
d=a_2-a_1=4-2=2

Sum=\frac{n}{2}(2a_1+(n-1)d)
Sum=\frac{3}{2}(2*2+(3-1)2)
Sum=\frac{3}{2}*8
Sum=12
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Re: Arithmetic Statistics [#permalink] New post 18 Feb 2011, 05:55
ye, i mixed with N formula. thanks.
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Re: Arithmetic Statistics [#permalink] New post 18 May 2011, 22:43
(2a + 2a + 8) /2

(2a+7 + 2a + 25)/2

leaves 12 after subtracting.
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Re: Arithmetic Statistics [#permalink] New post 19 May 2011, 18:57
I got 12 by solving but i think Bunuel's method is brilliant ( as always )
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Re: List S consists of 10 consecutive odd integers, and list T [#permalink] New post 23 Jun 2014, 00:53
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Re: List S consists of 10 consecutive odd integers, and list T [#permalink] New post 23 Jun 2014, 01:53
Picked up numbers:

T = 2 , 4 , 6, 8 , 10 (Mean = 6)

S = 9, 11, 13, 15, 17, 19, 21, 23, 25, 27 (Mean = \frac{17+19}{2} = 18)

Difference = 18-6 = 12

Answer = D
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Re: List S consists of 10 consecutive odd integers, and list T [#permalink] New post 29 Jun 2014, 21:14
PareshGmat wrote:
Picked up numbers:

T = 2 , 4 , 6, 8 , 10 (Mean = 6)

S = 9, 11, 13, 15, 17, 19, 21, 23, 25, 27 (Mean = \frac{17+19}{2} = 18)

Difference = 18-6 = 12

Answer = D


PareshGmat's solution is the quickest way. Anyway, here is mine:
T=(t1+t2+t3+t4+t5)/5
=[t1+(t1+1*2)+(t1+2*2)+(t1+3*2)+(t1+4*2)]/5
=[5t1+2*(1+2+3+4)]/5
=[5t1+2*(4*(4+1)/2)]/5
=[5t1+20]/5=t1+4
S=(s1+...+s10)/10
=[s1+(s1+1*2)+...+(s1+9*2)]/10
=[10s1+2*(1+...+9)]/10
=[10s1+2*(9*(9+1)/2)]/10
=[10s1+90]/10=s1+9
We have s1=t1+7
S-T=s1+9-t1-4=t1+7+9-t1-4=12 =>D
P/S: Sum of n consecutive integers:
n(n+1)/2
Re: List S consists of 10 consecutive odd integers, and list T   [#permalink] 29 Jun 2014, 21:14
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