The letters of the word 'GAUSS' and the digits in the number ' 1998 ' are each cycled separately and then numbered as shown.
 1. AUSSG 9981
 2. USSGA 9819
 3. SSGAU 8199

etc.

If the pattern continues in this way, what number will appear in front of GAUSS 1998?
(A) 4
(B) 5
(C) 9
(D) 16
(E) 20
The letters of the word 'GAUSS' and the digits in the number ' 1998 ' are each cycled separately and then numbered as shown.
 1. AUSSG 9981
 2. USSGA 9819
 3. SSGAU 8199

etc.

If the pattern continues in this way, what number will appear in front of GAUSS 1998 ?
(A) 4
(B) 5
(C) 9
(D) 16
(E) 20

## Solution

Because the word 'GAUSS' has five letters in it, the numbers $5,10,15,20, \ldots$ will appear beside this word. Similarly, the four digits of ' 1998 ' will have the numbers $4,8,12,16,20,24, \ldots$ beside this number.

From this listing, we can see that the correct number is 20 which is the 1.c.m. of 5 and 4.

ANSWER: (E)