pacifist85 wrote:
Hi, I see that no one responded to this one. I cannot figure it out muself, but will share my thoughts.
[1] a+b+c+4 / 4 > a+b+c/3
I tested the means for these numbers: 2-4-6-4 (if a,b,c did have a common difference). It turns out that the means are the same.
I tested the means for these numbers: 2-5-6-4 (if a,b,c did not have a common difference). It turns out that the first means is greater than the second.
However, I have no idea what this means, or if, in the condition when they d have a common difference, they should also have a common difference with 4 (the extra number).
[2] Let's say that these are the numbers in increasing order:
a-b-c-4 or 4-a-b-c (and I am not sure here is 4 is supposed to be greatersmaller than the rest or could even be in between).
Then bc (or ab) > b.
If the numbers are: 1,2,3,4, then the median is 2.5. For 1,2,3 the median is 3. So, the second median is greater, which should not happen.
If the numbers are: 1,3,4,4, then the median is 3.5. For 1,3,4 the median is 3. The first median is greater, which is what should happen.
But again, I have no idea what this means...
We need to find out whether is a,b,c - progression
1.s (a+b+c+4)/4>(a+b+c)/3 , thus a+b+c<12 or in other words a+b+c<=11 as a,b,c - integers. Let's test it 2,3,4=9 ok 2,3,5=10 also satisfy. Thus s1 is unsuf.
2. median of a,b,c is b as a<b<c. Median in a,b,c,4 could be 4 versions (4,a,b,c) , (a,4,b,c), (a,b,4,c), (a,b,c,4)
(4,a,b,c) means b>(a+b)/2 if a>4 . b>a>4
(a,4,b,c) means b>(4+b)2 if a<4<b . b>4 -
(a,b,4,c) means b>(b+4)/2 if b<4<c. b>4 - doesn't work as 4>b condition
(a,b,c,4) means b>(b+c)/2 if b<c<4. b>c - doesn't work as c>b condition
Conclusion:
b>a>4 for sure
Clearly statement 2 is not suf, as a,b,c could be progression or could be not. Simply input numbers
Let's combine 1 and 2 statements.
We know that a+b+c<12, and b>a>4. Let's input numbers a=5, b=6,c=7 total>12. the answer is no, thus sufficient.
Answer C.