Question

In the following series, which letter occupies the 1000${}^{th}$ position? $ABCD......XYZYX....BABCD.....YZYX....CBABC.....YZ.......$

• A. B
• B. A
• C. X
• D. Y
• E. None of these

Answer 1

The correct option is A

B

We have 3 patterns:

I. ABCD . XYZ.Which occurs only once

II. YX BA, which repeats alternately

III. BC .. YZ, which repeats alternately

Now, I has 26 terms

So, number of terms before the desired term = (999 -- 26 ) = 973

Each of the patterns which occurs after I, has 25 letters

Now, 973 $÷$ 25 gives quotient = 38 and remainder = 23

Thus, the 1000${}^{th}$ term of the given series is the 24${}^{th}$ term of the 38${}^{th}$ pattern after I which is B.