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# In a set of X consecutive numbers, the first number is 4.

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Senior Manager
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In a set of X consecutive numbers, the first number is 4. [#permalink]  19 Feb 2004, 08:05
In a set of X consecutive numbers, the first number is 4. Which of the following expressions is the average of the set?
a. 4 + x/2
b. (4+x)/2
c. (7+x)/2
d. 4*x/2
e. (3+x)/2
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[#permalink]  19 Feb 2004, 08:15
Rakesh, Is there a formula or did u just work it by plugging in??
Manager
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[#permalink]  19 Feb 2004, 08:19
No I didnt plug it in. I first tried with some numbers and then with another one and then went for the choices. This problem can be done within 1 min or may be less than that.
Director
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[#permalink]  19 Feb 2004, 11:52
Anoter good one
Ans: A
Senior Manager
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[#permalink]  19 Feb 2004, 12:11
Padma.......could u post ur reasoning??Thanks!!
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[#permalink]  19 Feb 2004, 12:16
cbrf3 wrote:
Padma.......could u post ur reasoning??Thanks!!

There is no formula that I've used; I used logic. But I'm not sure of it.
I'll post the logic, if the answer is correct.

This makes others to think independly
Manager
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[#permalink]  19 Feb 2004, 12:59
(7+x)/2

I could not come up with formula. Tried to derive it for about 5 mins then plugged in some values and got the answer. Let us knowwhat is the correct one
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[#permalink]  19 Feb 2004, 15:59
First term = 4

There are total X term and they are consecutive

So Xth term = 4 + (x-1)

The average of consecutive numbers = (the first term + the last term)/2
= [4 + 4 + (x-1)] / 2
= (x + 7)/2
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[#permalink]  19 Feb 2004, 16:12
I think it is B!!Here's my reasoning.......:

Sum of 1st x consecutive integers is= x(x+1)/2
Since 1st integer is 4, therefore sum of x-3 integers is = x(x+1)/2- (1+2+3)
= x(x+1)/2 - 6
Average = {x(x+1)/2 -6}/x-3 = (x+4)/2
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[#permalink]  19 Feb 2004, 16:16
cbrf3 wrote:
I think it is B!!Here's my reasoning.......:

Sum of 1st x consecutive integers is= x(x+1)/2
Since 1st integer is 4, therefore sum of x-3 integers is = x(x+1)/2- (1+2+3)
= x(x+1)/2 - 6
Average = {x(x+1)/2 -6}/x-3 = (x+4)/2

I do no know what you have done here.

But I stand by the answer C
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[#permalink]  19 Feb 2004, 16:35
gmatblast wrote:
cbrf3 wrote:
I think it is B!!Here's my reasoning.......:

Sum of 1st x consecutive integers is= x(x+1)/2
Since 1st integer is 4, therefore sum of x-3 integers is = x(x+1)/2- (1+2+3)
= x(x+1)/2 - 6
Average = {x(x+1)/2 -6}/x-3 = (x+4)/2

I do no know what you have done here.

But I stand by the answer C

yes, the answer is C
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[#permalink]  20 Feb 2004, 04:08
correct ans is C.
Plug in x =3. The resulting set is 4, 5,and 6, adn it has average of 5. plugging x =3 in the ans choices only c is =5.
[#permalink] 20 Feb 2004, 04:08
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# In a set of X consecutive numbers, the first number is 4.

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