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26 Oct 2021, 07:30
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
31% (02:20) correct
69%
(02:22)
wrong
based on 270
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A renowned medical store must purchase a set of n metal weights, each weighing an integer number of grams, such that all integer weights from 1 to 300 grams (inclusive) can be made with a combination of one or more of the weights. What is the minimum number of metal weights that the medical store must purchase?
(A) 6
(B) 8
(C) 9
(D) 10
(E) 12
(A) 6
(B) 8
(C) 9
(D) 10
(E) 12
11 Mar 2023, 01:26
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Bunuel
We can begin the process by starting with the smallest weight, 1 gram. Using this weight alone, we can only weigh 1 gram, but not 2 grams. However, by adding the weight of 2 grams, we can weigh 1 gram, 2 grams, and 3 grams, but not 4 grams. Again, adding the weight of 4 grams, we can weigh 1 gram, 2 grams, 3 grams, 4 grams, 5 grams, 6 grams, and 7 grams, but not 8 grams.
To weigh the weight of the next power of 2, we always need to include the weight of that power of 2. For example, to weigh 8 grams, we need a weight of 8 grams. Continuing this process, we can observe that we can never weigh the weight of the next power of 2 without the weight of that power of 2.
For example:
1 gram, 2 grams, 4 grams, and 8 grams will allow us to weigh all weights up to 15 grams.
1 gram, 2 grams, 4 grams, 8 grams, and 16 grams will allow us to weigh all weights up to 31 grams.
...
1 gram, 2 grams, 4 grams, 8 grams, 16 grams, 32 grams, 64 grams, and 128 grams (8 weights), will allow us to weigh any weight up to 255 grams.
1 gram, 2 grams, 4 grams, 8 grams, 16 grams, 32 grams, 64 grams, 128 grams, and 256 grams (9 weights) will allow us to weigh any weight up to 511 grams.
Therefore, the minimum number of weights the store needs to purchase is 9.
Answer: C.
Also, consider this similar challenging question: https://gmatclub.com/forum/a-scientist- ... 02036.html
General Discussion
26 Oct 2021, 07:42
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The minimum number would be 8 since 300 is between 256 and 512.
Option B
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Option B
Posted from my mobile device
and will such questions come as official questions? 
