The first row in a puzzle has one block, the second row has three blocks, the third row has five blocks, and so on. If there are 60 rows in the puzzle, the number of blocks in the entire puzzle is closest to
Answer Choices
Correct answer marked belowSee the full step-by-step explanation
You can see the correct answer above. Sign in for free to unlock the complete worked solution.
Track your performance and improve
Get detailed analytics, unlock full explanations, and move up difficulty tiers as you practice.
Unlock the full explanation
Create a free account to reveal the correct answer, see the step-by-step explanation, and start tracking your GMAT progress.
This is a classic arithmetic sequence. The number of blocks in row n is 2n-1. For 60 rows, sum = 60^2 = 3600. So the answer is E. Easy one.
Yep, sum of first n odd numbers is n^2. Nice and quick.
I almost went with 1830 because I thought it was 60*61/2. Good thing I double-checked.
Wait, how do we know it's 60^2? I get that the rows are 1,3,5,... but I'm not seeing why the sum is n squared. Can someone explain that?
The sum of the first n odd numbers is always n^2. You can also use the average term times number of terms: average of first and last term (1+119)/2 = 60, times 60 = 3600.
Or just list small cases: 1=1^2, 1+3=4=2^2, 1+3+5=9=3^2, so it holds.
I thought it was asking for the 60th row only. Then I reread and saw 'entire puzzle'. That would be 119, but 119 isn't an option. So it's definitely the sum. Answer E.
For these sequence sum problems, I like to use the formula S = n/2 * (first + last). First term 1, last term 2(60)-1 = 119. So S = 60/2 * 120 = 3600. Closest is 3600. E.
What it tests
Your ability to spot and extend arithmetic and geometric sequences and work with recursive definitions.
Common trap
Off-by-one errors in indexing (a₀ vs a₁) or confusing an arithmetic difference with a geometric ratio.