matm wrote:
Hi guys, I'm certainly no math"magician" and just started studying for the GMAT and as such perhaps why I did not take the same approach to solve the question but it seems to be the answer of "E" is wrong, can anyone help figure out if I'm just insane ?
I went with a basic trial & error approach and stated the following:
75 Reps = R
Country A or A # of R cannot be = to B, C, D, E ,F
A must be # 2 in terms of high # of R and need to find out if A is = or greater than 10 ?
Condition 1: One of the six countries sent 41 representatives to the congress
So filling in the blanks by trial & error:
Country # R Ranking
A = 10 2
B = 41 1
which we know must be respected, so 75 - 51 = 24 R left, if we randomly assign countries C, D, E, F, #'s of R that are not the same, lets say like :
C = 9 3
D = 8 4
E = 4 5
F = 3 6
Then the total = 75 which makes condition # 1 work and is true ??
If we sub in condition # 2: Country A sent fewer than 12 representatives to the congress
this still holds true and you could make A = 11 and C = 9, D = 8, E= 4, F = 2 and this would still work and add up to 75 ? as well as many other combination allowing for condition 1 & 2 to hold true so it seems as though each of them alone is enough to satisfy the questions ? Am I missing something ? If someone can help clarify it would be highly appreciated
Matt
Hi Matt
Let me try to see if I can help. Firstly, in DS questions, even if we are unable to calculate a unique value, there should at least be a unique proper answer to the question asked. Eg, if a question asks 'Is XYZ true or no' then the answer needs to be either a clear-cut YES or a clear-cut NO - then only we can say that we have got our answer.
In the given question, 'did Country A send at least 10 representatives', we can be sure that we have our answer in two situations:
Either if we can logically conclude that there were at least 10 representatives - in this case we have our answer as YES to the question asked
Or if we can logically conclude that there were less than 10 representatives for sure - in this case we have our answer as NO to the question asked
But if we cannot conclude any one (and only one) of the above two things then our conclusion would be that 'the data is insufficient to answer the question asked'.
Lets now analyse the statements.
(1) One country sent 41, if country A sent 10, then remaining 75-51 = 24; which can be divided among 4 different countries (say 3, 4, 8, 9 as you depicted).
But if country A sent 9, then remaining 75-50 = 25; this too can be divided among 4 different countries (say 4, 6, 7, 8).
So, the given condition of statement 1 is
possible with country A having 10 R, and it is also possible with country A having 9 R.
Thus, we cannot say with surety whether country A has sent at least 10 R or not. That is why this condition is
not sufficient to give either a clear-cut YES or a clear-cut NO to the question asked.
(2) As you have yourself said, it is possible with country A sending 11 R. But it is also possible with country A sending 4 R or 9 R (you can make various combinations as you have yourself written).
Again, since it is possible for this condition of statement 2 to hold true with both A having >= 10 R, and also possible with A having < 10 R, we cannot answer with a clear-cut YES or a clear-cut NO to the question asked.
Not sufficient.
When we combine the two statements, still we could make a case with country A having 10 R or 11 R, but we could also make a case with country A having 9 R. This data is
still insufficient to give us either a proper YES or a proper NO to the asked question (which was 'did Country A send at least 10 representatives'). That is why answer is
E.