Hi All

The posted questions looks rather similar to the following question:

The 288th term of the series a, b , b, c, c, c, d, d, d, d, e, e, e, e, e, .... is

A) u
B) v
C) w
D) x
E) z

D

GMAT assassins aren't born, they're made,
Rich

Hi All,

With this question, you can use the answer choices to your advantage as well as the Arithmetic concept "bunching."

We're given a sequence of increasingly repetitive terms:
A shows up 1 time
B shows up 2 times
C shows up 3 times
Etc.

From the answers, we know that the 288th letter is either U, V, W, X or Z. Working backwards in the alphabet....
Z is the 26th letter
X is the 24th letter
W is the 23rd letter
V is the 22nd letter
U is the 21st letter

This means that the prior 20 letters of the alphabet will ALL show up in the pattern that is described in the prompt, so we can start by figuring out the TOTAL number of letters in that first sequence of 20 different letters. Here, we can use "bunching"

A shows up 1 time
B shows up 2 times
C shows up 3 times
......
T shows up 20 times

1+20 = 21 letters
2+19 = 21 letters
3+18 = 21 letters
Etc.
This means that there will be 10 pairs of letters that fit this pattern. 10(21) = 210 letters. From here, we can just "add" groups of letters until we hit the 288th letter.

U will show up 21 times
210 + 21 = 231

V will show up 22 times
231 + 22 = 253

W will show up 23 times
253 + 23 = 276 .....notice that we're "close" to the 288th letter....

X will show up 24 times....
276 + 24 = 300....this means that the 277th through 300th letters are all X. The letter X is the 288th letter.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

Hi talaangoshtari,

When dealing with large-scale addition, you do NOT have to add the numbers in order.

For example, 1+2+3+4+5+6 is the same as 1+6 + 2+5 + 3+4. Notice in this second example that we have 3 "pairs" of 7, so (3)(7) = 21 (which is the same as 1+2+3+4+5+6).

In this question, we're dealing with a larger amount of 'data', but the concept is the same...

There is 1 "A"
There are 2 "Bs"
There are 3 "Cs",
Etc.

1 "A" and 20 "Ts" = 21 letters
2 "Bs" and 19 "Ss" = 21 letters
Etc.

GMAT assassins aren't born, they're made,
Rich