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saifoo.khan
Group Title
The sum of "z" consecutive integers is 90.
Which of the following cannot be the value of "z".
3, 4, 5, 6, 9.
 one year ago
 one year ago
saifoo.khan Group Title
The sum of "z" consecutive integers is 90. Which of the following cannot be the value of "z". 3, 4, 5, 6, 9.
 one year ago
 one year ago

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mathslover Group TitleBest ResponseYou've already chosen the best response.0
it seems that the answer given by saurav is very correct
 one year ago

saifoo.khan Group TitleBest ResponseYou've already chosen the best response.0
i still don't get it. lol.
 one year ago

myko Group TitleBest ResponseYou've already chosen the best response.1
maybe first put it like this: \[n+(n+1)+(n+2)+...+(n+(z1))=90\] and find it from here
 one year ago

saifoo.khan Group TitleBest ResponseYou've already chosen the best response.0
How? Why? @myko
 one year ago

mukushla Group TitleBest ResponseYou've already chosen the best response.6
guys lets work it step by step \[n+1+n+2+...+n+z=90\]\[nz+\frac{z(z+1)}{2}=90\]\[z^2+(2n+1)z=180\]\[z(z+2n+1)=180\] we can find all integers \(z\) that satisfies the last equality...but here we have options and we can plug them into equation and see what happens...
 one year ago

myko Group TitleBest ResponseYou've already chosen the best response.1
the expretion would be equal to: n*z+ sum of first (z1) integers = 90
 one year ago

myko Group TitleBest ResponseYou've already chosen the best response.1
@mukushla your sum is of z+1 consecutive integers
 one year ago

mukushla Group TitleBest ResponseYou've already chosen the best response.6
no its z n+1 n+2 ... n+z
 one year ago

myko Group TitleBest ResponseYou've already chosen the best response.1
should be nz+z(z1)/2=90
 one year ago

myko Group TitleBest ResponseYou've already chosen the best response.1
2nz+z^2z=180 z^2+(2n1)z180=0 and I think just check for possible natural solutions of this
 one year ago

mukushla Group TitleBest ResponseYou've already chosen the best response.6
now u have \[n=\frac{90}{z}\frac{z+1}{2}\] now plug the values of \(z\) and if the value of \(n\) becomes an integer then that \(z\) is your answer
 one year ago

saifoo.khan Group TitleBest ResponseYou've already chosen the best response.0
@mukushla : Your's and @myko 's methods are same right?
 one year ago

mukushla Group TitleBest ResponseYou've already chosen the best response.6
for example \(z=3\) gives \[n=\frac{90}{3}\frac{3+1}{2}=302=28\]
 one year ago

mukushla Group TitleBest ResponseYou've already chosen the best response.6
yes they are same
 one year ago

myko Group TitleBest ResponseYou've already chosen the best response.1
only difference is that i start fomr n and @mukushla from n+1
 one year ago

saifoo.khan Group TitleBest ResponseYou've already chosen the best response.0
So answer is 3?
 one year ago

myko Group TitleBest ResponseYou've already chosen the best response.1
it asks: Which of the following cannot be the value of "z". and 3 aparently , is.
 one year ago

saifoo.khan Group TitleBest ResponseYou've already chosen the best response.0
But it's incorrect. :S
 one year ago

mukushla Group TitleBest ResponseYou've already chosen the best response.6
let me complete the solution \[z=3 > n=\frac{90}{3}\frac{3+1}{2}=28\] \[z=4 > n=\frac{90}{4}\frac{4+1}{2}=20\] \[z=5 > n=\frac{90}{5}\frac{5+1}{2}=15\] \[z=6 > n=\frac{90}{6}\frac{6+1}{2}=11.5\] \[z=9 > n=\frac{90}{9}\frac{9+1}{2}=5\] so the answer is only z=6
 one year ago

myko Group TitleBest ResponseYou've already chosen the best response.1
4and 6 would be the answer
 one year ago

saifoo.khan Group TitleBest ResponseYou've already chosen the best response.0
Myko's thinking is going the correct way!
 one year ago

myko Group TitleBest ResponseYou've already chosen the best response.1
i got it by mine first formula using n like a start integer.
 one year ago

myko Group TitleBest ResponseYou've already chosen the best response.1
but aparently there should be no difference in starting from n+1 or n+2 or n+whatever
 one year ago

mukushla Group TitleBest ResponseYou've already chosen the best response.6
for \(z=4\) \[21+22+23+24=90\]
 one year ago

rsadhvika Group TitleBest ResponseYou've already chosen the best response.0
4 90/4  4+1/2 90/4  10/4 80/4 is an integer
 one year ago

saifoo.khan Group TitleBest ResponseYou've already chosen the best response.0
4 is incorrect too!
 one year ago

mukushla Group TitleBest ResponseYou've already chosen the best response.6
its impossible ... see my last reply
 one year ago

saifoo.khan Group TitleBest ResponseYou've already chosen the best response.0
The answer is 6. :S
 one year ago

saifoo.khan Group TitleBest ResponseYou've already chosen the best response.0
I'm going to type the solution.. just a sec.
 one year ago

mukushla Group TitleBest ResponseYou've already chosen the best response.6
@saifoo.khan thats right answer is 6...
 one year ago

saifoo.khan Group TitleBest ResponseYou've already chosen the best response.0
How? Why? :D
 one year ago

mukushla Group TitleBest ResponseYou've already chosen the best response.6
man... we already solved it...
 one year ago

saifoo.khan Group TitleBest ResponseYou've already chosen the best response.0
But you were getting 11.5 when we inserted 6.
 one year ago

mukushla Group TitleBest ResponseYou've already chosen the best response.6
well that means there is not 6 consecutive integers such that their sum is 90
 one year ago

saifoo.khan Group TitleBest ResponseYou've already chosen the best response.0
(behind the book) Solution: Plug in numbers! This may take some time, but we will eventually find the answer. Three numbers 20+30+31=90,eliminate A, four numbers 21+22+23+24=90,eliminate b,five numbers 16+17+18+19+20=90,elimnate c.nine numbers 6+7+8+9+10+11+12+13+14=90 elimate e.no six consecutive numbers add up to 90
 one year ago

saifoo.khan Group TitleBest ResponseYou've already chosen the best response.0
@mukushla , got it right!
 one year ago

saifoo.khan Group TitleBest ResponseYou've already chosen the best response.0
I totally get it. Thanks a ton! @mukushla & @myko
 one year ago
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