M47-137

Question

At a delivery depot, some parcels currently loaded onto Van Cedar are moved to Van Maple before the vans leave for their routes. If no other parcels are added to or removed from either van, then after the transfer, will Van Cedar have more parcels than Van Maple?

(1) After the transfer, Van Cedar will have  33\frac{1}{3}\%  fewer parcels than it had before the transfer.
 
(2) After the transfer, Van Maple will have  100\%  more parcels than it had before the transfer.

Bunuel · Answer

Official Solution:

At a delivery depot, some parcels currently loaded onto Van Cedar are moved to Van Maple before the vans leave for their routes. If no other parcels are added to or removed from either van, then after the transfer, will Van Cedar have more parcels than Van Maple? 
 
(1) After the transfer, Van Cedar will have  33\frac{1}{3}\%  fewer parcels than it had before the transfer.
 
This tells us only that the number of parcels moved from Van Cedar was  \frac{1}{3}  of Van Cedar’s original load. Since no information is given about Van Maple’s original load, this statement is not sufficient.
 
(2) After the transfer, Van Maple will have  100\%  more parcels than it had before the transfer.
 
This tells us only that the number of parcels moved to Van Maple was equal to Van Maple’s original load. Since no information is given about Van Cedar’s original load, this statement is not sufficient.
 
(1)+(2) Let  x  parcels be moved from Van Cedar to Van Maple.
 
From (1),  x  is  \frac{1}{3}  of Van Cedar’s original load, so Van Cedar originally had  3x  parcels.
 
From (2),  x  is equal to Van Maple’s original load, since increasing Van Maple’s load by  100\%  means adding its original number of parcels. So Van Maple originally had  x  parcels.
 
After the transfer:
 
Van Cedar has  3x - x = 2x 
 
Van Maple has  x + x = 2x 
 
So Van Cedar will not have more parcels than Van Maple. Thus, the answer to the question is NO. Sufficient.
 
Answer: C

parthk24 · Answer

I don't understand how the answer to this question is C, while solving I got E. Here's how I solved it:

Let's assume the number of parcels originally with Van Cedar is  c  and with Van Maple is  m .

Statement 1: After the transfer, Van Cedar will have  33 1/3  % fewer parcels than it had before the transfer.
Hence now parcels with Van Cedar will be  2c/3  and those with Van Maple would be  m+c/3 . The question stem asks us if Van Cedar will have more parcels than Van Maple.
Or, if  2c/3  >   m + c/3 
Otherwise, if  c > 3m ?
We don't know the original values of  c  &   m , hence the answer is Insufficient.

Statement 2: After the transfer, Van Maple will have 100% more parcels than it had before the transfer.
Similar to above, now parcels with Van Cedar will be  c-m  and parcels with Van Maple is  2m .
Comparing these as per the question stem, is  c-m  >  2m ?
Or, is  c  >  3m ?
This statement is the same as what we have in Statement 1, and no new information is provided hence this is Insufficient.

Putting (1) & (2) together, we still cannot determine whether  c  >  m , hence I selected E.

Bunuel , can you please let me know where I'm going wrong with this reasoning?

Bunuel · Answer

This is a tricky question.

The missing point is that the  same number of parcels is transferred  in both statements.

From (1), the number transferred is c/3.
From (2), the number transferred is m.

Therefore, when combined:

c/3 = m, so c = 3m.

Thus, after the transfer both vans have the  same  number of parcels. The answer to the stem is definitely  No , so the statements together are sufficient.

M47-137

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