How many rectangular boxes with the dimensions 1 foot by 3 f

VERITAS PREP OFFICIAL SOLUTION

Correct Answer: C

Explanation: (1) Without any dimensions for the cube, we cannot determine how many boxes it can contain. Thus, the statement is insufficient.

(2) This statement is also insufficient, because we don't know the shape of the carton. For example, if the carton was 600 x 1 x .5, no boxes would fit into it.

Together, we know that the carton is a cube with volume 300, and can use that information to determine the dimensions of the cube. Once we know the length of each side of the cube, we can determine how many boxes will fit inside of it. The beauty of Data Sufficiency questions is that we do not have to actually do that work! Since both statements together are sufficient to answer the question, the correct choice is C.

hi Bunuel, thank you for your response, but I still don't understand, I picked A) because since we are told that the volume of the carton is "v" (I assumed that since v is given to us in the question, it's factual information) and with (1) we now know that the form of the carton is a cube, we could compute

v^(1/3)= x, where x is any side of the cube, and with that we could know how many boxes would fit in the carton (the answer may be yes or no, but still it gets answered)

Could you please clarify me? thank you very much for this spectacular community!

When a DS question asks about the value of some variable, then the statement(s) is sufficient ONLY if you can get the single numerical value of this variable.

In a Yes/No Data Sufficiency questions, statement(s) is sufficient if the answer is “always yes” or “always no” while a statement(s) is insufficient if the answer is "sometimes yes" and "sometimes no".


Hope it helps.

I got the ans B here coz when the way i interpreted the scenerio was when n number of boxes has to be placed with dimensions of 1by 3 by 10 then that volume has to be equal to the volume of the rectangular box as given in the question. so what i did was N(1*3*10)= 300( as per second statement) so i got the N value 10. So, there are 10 boxes to be placed. I just find statement 1 is insufficient coz it talks about the cube and in this question it states all about rectangular boxes. Please correct me if i am wrong! Cheers!

That's not correct. If the dimensions of the carton are 0.5 by 1 by 600, then 0 boxes can be placed. Please re-read the solution and follow the links provided.

Hope it helps.

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

How many rectangular boxes with the dimensions 1 foot by 3 feet by 10 feet can be placed into a rectangular carton that has a volume of v cubic feet?

(1) The carton is a cube.
(2) v = 300

There are 3 variables (length, width, height) and 2 equations are given from the 2 conditions, so there is high chance (E) will be our answer.
Looking at the conditions together ,
if we let the length of one side of the carton be x, x^3=300, x=6.7. We cannot put in even one box, so the conditions are sufficient and the answer becomes (C).

For cases where we need 3 more equation, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.

Hi Bunuel

Considering both the statements together we know cartoon is of approx dimension 6.7*6.7*6.7 as its a cube.
The box is of size 1*3*10, so my understanding is as one side of the box (i.e side of 10) is bigger than all the 3 sides of the cube . So, still 0 boxes can be fit into the cartoon
Plz correct if my understanding is wrong

Yes, when we combine the statements we get that 0 boxes can fit into the carton.

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