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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.
 2 years ago
 2 years 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.
 2 years ago
 2 years 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
 2 years ago

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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