Minesh wrote:

1 What is the 100th letter in this endless string of letters?

abbcccddddeeeeeaaaaaabb..

options - a,b,c,d,e

Let's count up the letters:

first, 1 a, makes 1

add 2 bs, makes 3

add 3 cs, makes 6

add 4 ds, makes 10

add 5 es, makes 15

add 6 as, makes 21

add 7 bs, makes 28

add 8 cs, makes 36

add 9 ds, makes 45

add 10 es, makes 55

add 11 as, makes 66

add 12 bs, makes 78

add 13 cs, makes 91

add 14 ds, makes 105

so we were adding ds when we went past 100. A more sophisticated answer would be that the numbers on the right are triangular numbers, with number n being n*(n+1)/2, so the 14th one takes us past 100. We're cycling through 5 letters, so at the 14th step we have the 4th letter, i.e. d (4 is the remainder from dividing 14 by 5).

Minesh wrote:

2. Each of the letters in the row of boxes represents a number. The sum of any three consecutive numbers in the row is 19. What is the value of I + o + U?

I8WORK4FUN

options - 4, 7, 8, 15, 19

First, we notice that for any consecutive four letters, like WORK, we have

W + O + R = 19 = O + R + K

so we have W = K. Applying similar reasoning all along the row, we see that each letter is the same as the one 3 places further on:

I = O = 4 = N

8 = R = F

W = K = U

Because any three consecutive numbers must add to 19, the letters in the last group must equal 7. Thus

I + O + U = 4 + 4 + 7 = 15