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23 Oct 2021, 11:38
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Boxes in a factory were stamped ABCDEF, such that the first box received A, second box B, third box C, etc. What letters were stamped on the 713, 714, and 715th boxes?
A) ABC
B) BCD
C) CDE
D) DEF
E) EFA
A) ABC
B) BCD
C) CDE
D) DEF
E) EFA
23 Oct 2021, 12:13
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Stackitup
Good question. The way I solved this one was to focus on where the 714th box would land in the sequence, since it is the only even-numbered box of the three in question, and we have 6 letters altogether. That is, using 714 as a benchmark, we can quickly deduce what the 713th and 715th boxes would look like, in terms of letters. To get things started, consider that the 6th box and each 6th box thereafter would be an "F":
ABCDEFABCDEF ("F" appears in the 6th and 12th slots)
Regardless of what we calculate from 714 divided by 6, we will be able to tell which box is labeled what. First, we should run the calculation to figure out the number of cycles of six that we would run through:
\(\frac{714}{6}=119\)
Since there will be exactly 119 cycles of the six boxes to get to the 714th box, we know that that box will be labeled with the last letter of the sequence, "F." We can then figure out the 713th and 715th boxes quickly.
__ F __
E F A
The answer must be (E).
------------
Alternative Approach: Note that we could just as easily have worked with a number such as 700 to figure out where we would be in the cycle.
\(\frac{700}{6}=116.6666666666\)
This means that 116 cycles would have passed plus another two-thirds of a cycle, so if the last box of the 116th cycle was an "F," two-thirds of the way through would be four places into the 117th cycle:
ABCDEF
We could further deduce that if the 700th box was a "D," then so, too, would be the 706th and 712th boxes. The 713th box would have to be labeled "E," and the rest is academic.
Good luck with your studies, everyone.
- Andrew
23 Oct 2021, 12:27
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Given: Boxes in a factory were stamped ABCDEF, such that the first box received A, second box B, third box C, etc.
Asked: What letters were stamped on the 713, 714, and 715th boxes?
Letters are stamped ABCDEF and the same letters are repeated after every six boxes.
714/6 = 119; 714th box will be stamped F
713th box will be stamped E and 715th box will be stamped A.
EFA is the answer
IMO E
Asked: What letters were stamped on the 713, 714, and 715th boxes?
Letters are stamped ABCDEF and the same letters are repeated after every six boxes.
714/6 = 119; 714th box will be stamped F
713th box will be stamped E and 715th box will be stamped A.
EFA is the answer
IMO E
