Jay T. answered • 10/20/18
Retired Engineer/Math Tutor
Column B.
One must figure out the pattern of numbers for each column.
Column A: The numbers increase by 7, so from 2 to 1000 is 998. If this is the column, 7 must divide into 998 exactly (no remainder). So, 998/7 = 142 with remainder 2. Column A is eliminated.
Column B: Here, the number increases by 5 or three. Looking closely at the pattern, the increase appears to be 5,3,5,3,5,3,... This requires one or two stages. The first stage is to see if 1000-3=997 divides evenly by 5+3=8. If it does, column B is the correct column. If it does not, then column B could still be the right column if the remainder is either 3 or 5. Thus, 997/8 is 124 rem 5. Column B is still a possibility, but there is one more thing to determine: whether the next number is a three or a five. If it is a 5, Column B is the answer. Look again at the given pattern. When 5 is added, the sum is even. When 3 is added, the sum is odd. The highest number below 997 that is divided evenly by 8 is 997-5 = 992, which is even. That means the last number added was 5. So the next number to be added is 3. 992+3=995. Adding a 5 to this gives 1000 exactly, so column B is the correct answer.
Although the correct answer is column B, it is useful to look at the other columns, because they are ambiguous or indeterminate. Insufficient information is given.
Column C: The pattern here is to add 3 to the first number, 4 to the second, 5 to the third, and so on... This is ambiguous because the pattern could be adding 3,4,5,3,4,5,... or 3,4,5,6,7,8... If it is 3,4,5 then see if 1000-4=996 is evenly divisible by 12. In fact, it is. 996/12=83 exactly, so IF this is the pattern, Column C would be correct. On the other hand, if it is the other pattern, it can be shown that the table does not include 1000. One can write a simple program on a calculator to see that, or manually calculate it. For example note that every three numbers (it could just as well be every 4 or 5, or whatever numbers; the technique is the same) total is 9 more than the previous three numbers. Thus, start with 4, add 12 (3+4+5) + 21 (4+5+6) + 30 + 39,... until you go up to 1000. The last number below it is 987, and the next number to add is over 100.
Column D: There is no obvious pattern, arithmetic or geometric (at least that I can see) with the given numbers. More numbers would be needed to discern one.
Column E: Same as Column D.
