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PostPosted: Thu Oct 07, 2010 12:28 pm 
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Joined: Sun Jul 18, 2010 8:02 pm
Posts: 86
1 What is the 100th letter in this endless string of letters?

abbcccddddeeeeeaaaaaabb..

options - a,b,c,d,e

I can see that there is an increase of 1 each time in first 15 letters
then increase of 5 in next...

what are they testing?

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


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PostPosted: Thu Oct 07, 2010 1:54 pm 
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Joined: Thu Jan 03, 2008 8:26 am
Posts: 1324
Location: Watford, Herts
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


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PostPosted: Thu Oct 07, 2010 2:22 pm 
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Joined: Sun Jul 18, 2010 8:02 pm
Posts: 86
thanks so much - will have to digest this evening :?

there will be more - thanks for taking the trouble and sharing your expertise :roll:


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