Hi, there. I'm happy to help out with this one.
Prompt:
If a herd of cows is split in three unequal parts, how many there would be in the largest group?
This prompt gives astonishingly little information.
Statement #1:
The number of cows in the two larger groups is 57.
This leaves a lot of possibilities. If the smallest group has, say, 7 cows, then each of the two other groups has to have more than seven, and their sum has to be 57. That could be 8 & 49, 10 & 37, etc. etc.
Let's say that the two smallest groups have the minimum --- 1 in the smallest, and 2 in the second smallest. That would mean the largest group had 55 cows. That's the maximum.
What's the smallest the largest group could be? Well, it must be the bigger of two numbers adding up to 57. The closest the two numbers could be would be 28 and 29 (28 + 29 = 57). So the smallest the max group could be is equal to 29. Thus
29 <= max group <= 55
That's the range we have from statement #1. Obviously, at this point, we don't have enough info to answer the question. Statement #1, by itself, is
insufficient.
Statement #2:
The number of cows in the two smaller groups is 43.
If the two smaller groups are as far apart as possible, that's 1 + 42, and the largest group must be bigger than 42.
If the two smaller group are as close as possible, that's 21+22, and the largest group must be bigger than 21.
This statement doesn't place many limits on the max group. It tells that, at rock bottom, the largest group must be more than 21. It places no upper limit at all. Statement #2, by itself, is
insufficient.
Combined statements #1 & #2:
Statement #1 tells us:
29 <= max group <= 55
Statement #2 gives the absolute minimum:
max group > 21
but that would already be true with the conditions of statement #1.
We have no more information, so we can't determine anything.
Answer =
E
Does all this make sense? Let me know if you have any further questions.
Mike
