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Quantitative Reasoning – Practice – 240th letter is what!

PSA_LEVEL-UP_QNR2) Given the sequence A, B, B, C, C, C, D, D, D, D, … etc., that is one A, two Bs, three Cs, four Ds. five Es and so on, the 240th letter in
the sequence will be:

A) V
B) U
C) T
D) W

Ans:  The alphabets are repeated based upon their position. A is the first alphabet and occurs in the sequence only once, B being the second occurs twice and so on.

Since we are to find the 240th letter we are to find the sum of this arithmetic progression: 1 + 2 + 3 + …..+n where n is currently unknown.

By trial and error,

1 + 2 + 3 +…….+ 20 = 20*21/2= 210 [ From the expression, 1 + 2 + 3 +…….+ N = N * (N + 1)/2 ]

1 + 2 + 3 +…….+ 21 = 21*22/2= 231

1 + 2 + 3 +…….+ 22 = 22*23/2= 253

We see that from the 232nd letter till 253rd, the alphabet ‘V’ ( 22nd alphabet) occurs 22 times. 240th letter is occupied by ‘V’. Option A.

PSA_LEVEL-UP_QNR2

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