Bunuel wrote:
There are 25 necklaces such that the first necklace contains 5 beads, the second contains 7 beads and, in general, the ith necklace contains i beads more than the number of beads in (i-1)th necklace. What is the total number of beads in all 25 necklaces
A. 2690
B. 3025
C. 3380
D. 2392
E. 3762
I think above solution is not correct. I also think it's not GMAT question as it requires way more than 2 minutes to solve this.
We have sequence: \(5, 7, 10, 14, 19, 25...\) \((25 terms)\) and we want to determine the sum.
Let's subtract \(4\) from each term it will total \(4*25=100\), and we''l get:
\(100+1+(3+6)+(10+15)+(21+28)+...\) After 100 we have the same 25 terms.
\(100+1^2+3^2+5^2+7^2...\) after \(100\) we have the sum of the squares of the first n odd numbers. As there are \(25\) terms after \(100\) we'll have \(n=13\) squares.
The sum of the squares of the first \(n\) odd numbers=\(\frac{n*(2n-1)(2n+1)}{3}=\frac{13*25*27}{3}=2925\).
\(100+2925=3025\)
Answer: B (3025)
in the above solution i understood each n every step...
but i have only one concern .....from where it wud enter in our minds during the exam that v got to subtract '4' from each term to get the sequence....
is there any way to observe this thing....i know it wud come only by practice but still i wanted to know that how it wud strike our minds to subtract 4 from each term.....phewwww!!!!!!!!