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 2 years ago
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
The sum of "z" consecutive integers is 90. Which of the following cannot be the value of "z". 3, 4, 5, 6, 9.

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mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0it seems that the answer given by saurav is very correct

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

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

mukushla
 2 years ago
Best ResponseYou've already chosen the best response.6guys 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...

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

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

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

myko
 2 years ago
Best ResponseYou've already chosen the best response.12nz+z^2z=180 z^2+(2n1)z180=0 and I think just check for possible natural solutions of this

mukushla
 2 years ago
Best ResponseYou've already chosen the best response.6now 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

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

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

myko
 2 years ago
Best ResponseYou've already chosen the best response.1only difference is that i start fomr n and @mukushla from n+1

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

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

mukushla
 2 years ago
Best ResponseYou've already chosen the best response.6let 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

myko
 2 years ago
Best ResponseYou've already chosen the best response.14and 6 would be the answer

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

myko
 2 years ago
Best ResponseYou've already chosen the best response.1i got it by mine first formula using n like a start integer.

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

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

rsadhvika
 2 years ago
Best ResponseYou've already chosen the best response.04 90/4  4+1/2 90/4  10/4 80/4 is an integer

saifoo.khan
 2 years ago
Best ResponseYou've already chosen the best response.04 is incorrect too!

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

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

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

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

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

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

mukushla
 2 years ago
Best ResponseYou've already chosen the best response.6well that means there is not 6 consecutive integers such that their sum is 90

saifoo.khan
 2 years ago
Best 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

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

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