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1000 PS section 24- Q-8

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by ash_maverick » Mon Jun 01, 2009 3:54 am
The pages of a report are numbered consecutively from 1 to 10. If the sum of the page numbers up to and including page number x of the report is equal to one more than the sum of the page numbers following page number x, then x =?

(A) 4 (B) 5 (C) 6 (D) 7 (E) 8


Expalnation will be appreciated.ThnX
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here is my solution, but it seems to be wrong

by ash_maverick » Mon Jun 01, 2009 4:07 am
x[(x+1)]/2 = (11-x)(x+10)/2 +1

=>(x^2+x)/2 =[ (11x+110-x^2-10x)/2 ] +1

=>x^2+x = x+108-x^2

=>2x^2-108=0

=>x^2= 54

=> x=sqrt 54

what mistake i am doing here???
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by pathaniaus » Mon Jun 01, 2009 4:18 am
ok i jus did lit like this:
1 2 3 4 5 6 7 8 9 10
I started at wat if x = 5? i could readily see that it couldnt equal to 5 because 6+7+8+9+10 is far more than 1 when subracted by 1+2+3+4+5
I went up to x =6, still it wasnt one more
I went up to x=7, 1+2+3+4+5+6+7 = 28 then 8+9+10=27. this is the answer. x =7
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by ash_maverick » Mon Jun 01, 2009 4:30 am
pathaniaus wrote:ok i jus did lit like this:
1 2 3 4 5 6 7 8 9 10
I started at wat if x = 5? i could readily see that it couldnt equal to 5 because 6+7+8+9+10 is far more than 1 when subracted by 1+2+3+4+5
I went up to x =6, still it wasnt one more
I went up to x=7, 1+2+3+4+5+6+7 = 28 then 8+9+10=27. this is the answer. x =7
thanks for the answer..

But is there a way we can make algebraic equation out of it?
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I got it

by vineetbatra » Mon Jun 01, 2009 4:36 pm
Well this can be solved using Arithmetic Progression

Formula for AP is n(a1+an)/2

n = numbers in a sequence

Given the question we can come up with the following equation

n(1+x)/2 = (10-n)((X+1) + 10)/2 +1

We can replace n with x because we have consecutive numbers. Once we solve this we will get the quadratic equation

X^2 +x -56 = 0, the answer is -8, 7. So x is 7

Hope it helps.

Vineet
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I got it

by vineetbatra » Mon Jun 01, 2009 4:36 pm
Well this can be solved using Arithmetic Progression

Formula for AP is n(a1+an)/2

n = numbers in a sequence

Given the question we can come up with the following equation

n(1+x)/2 = (10-n)((X+1) + 10)/2 +1

We can replace n with x because we have consecutive numbers. Once we solve this we will get the quadratic equation

X^2 +x -56 = 0, the answer is -8, 7. So x is 7

Hope it helps.

Vineet
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I got it

by vineetbatra » Mon Jun 01, 2009 4:37 pm
Well this can be solved using Arithmetic Progression

Formula for AP is n(a1+an)/2

n = numbers in a sequence

Given the question we can come up with the following equation

n(1+x)/2 = (10-n)((X+1) + 10)/2 +1

We can replace n with x because we have consecutive numbers. Once we solve this we will get the quadratic equation

X^2 +x -56 = 0, the answer is -8, 7. So x is 7

Hope it helps.

Vineet
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Apologies

by vineetbatra » Mon Jun 01, 2009 4:39 pm
Apologies for the same post 3 times, I had a problem with my browser.
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