Jamal wants to save 30 files onto disks, each with 1.44 MB space. 3 of

Question

Jamal wants to save 30 files onto disks, each with 1.44 MB space. 3 of the files take up 0.8 MB, 12 of the files take up 0.7 MB, and the rest take up 0.4 MB. It is not possible to split a file onto 2 different disks. What is the smallest number of disks needed to store all 30 files?

(A) 12
(B) 13
(C) 14
(D) 15
(E) 16

Are You Up For the Challenge: 700 Level Questions

Show Answer

Official Answer

B

(A) 12
(B) 13
(C) 14
(D) 15
(E) 16

Are You Up For the Challenge: 700 Level Questions

GMATWhizTeam · Answer

Each disk has a capacity of 1.44 MB. Jamal has 30 files to be saved.

Of these, 3 files take up 0.8 MB each; that makes up a total of 2.4 MB (3 * 0.8). A minimum of 2 disks are needed to save these 3 files.

12 other files take up 0.7 MB each; that accounts for 8.4 MB (12 * 0.7). A minimum of 6 disks are needed to save these files.
 
The rest of the 15 files take 0.4 MB each; this amounts to 6 MB (15 * 0.4).

A minimum of 4 disks are needed to save these 15 files. Note that one of these files can be saved on one of the disks storing the 0.8 MB files (the first category), since there is enough space left over.
Therefore, we do not need a minimum of 5 disks for 6 MB, we need only 4 of them.

The smallest number of disks needed to store all 30 files = (2 + 6 + 4) = 12.

The correct answer option is A.

Bunuel , when the question says, “3 of the files take up 0.8 MB”, it probably means “3 of the files take up 0.8 MB each” and so on for the other two categories also. Otherwise, none of the answer options would make sense. Could you please clarify if this is so?

IanStewart · Answer

You need three disks to store the three 0.8 Mb files, because a file cannot be split between disks.

Since we can't put two 0.8 Mb files on a single disk, they'll need to go on three separate disks. We have space left over on those disks, so we might as well put one 0.4 Mb file on each. Then we have used 3 disks, and only have the twelve 0.7 Mb files and twelve of the 0.4 Mb files left. We can put two 0.7 Mb files on a single disk, so using 6 disks we can store all of them. That uses almost all of the space on a disk, so it's almost certainly going to be the most efficient approach (the alternative, putting one 0.7 Mb and one 0.4 Mb file on a disk, leaves the most unused space on a disk, so it's less efficient and we'll need more disks if we do that). We can then fit 3 of the 0.4 Mb files on one disk, so we can store all of them on 4 disks. So we need 3 + 6 + 4 = 13 disks in total, at minimum.

WizakoBaskar · Answer

From the question,
1. 3 of the files take up 0.8 MB each.
2. 12 of the files take up 0.7 MB each.
3. 15 of the files take up 0.4 MB each.
4. The capacity of each disc is 1.44 MB.
5. A file cannot be split and stored in more than one disc.

To find:  Minimum number of discs to store all 30 files.
Those discs that store a 0.8 MB file cannot accommodate another 0.8 MB or 0.7 MB file.

Two important inferences
a. Any disc can store a maximum of one 0.8 MB file or two 0.7 MB files or three 0.4 MB files. 
b. Only a 0.4 MB file can be added to any disc that stores a 0.8 MB file.

We need 3 discs to store the three 0.8 MB files. In addition, we can add one 0.4 MB file in each of the 3 discs. We have stored all 0.8 MB files and three of the fifteen 0.4 MB files.

Files left : 
12 files of 0.7 MB each.
12 files of 0.4 MB each.

Those discs that store 0.7 MB can accommodate either another 0.7 MB file or a 0.4 MB file.

If we store two 0.7 MB files in a disc, empty space after storing the two files would be 0.04 (i.e., 1.44 - 2 * 0.7 = 0.04).
If we store a 0.4 MB file and a 0.7 MB file in a disc, empty space after storing the two files would be 0.34 (i.e., 1.44 - 0.7 - 0.4 = 0.34).
Our objective is to minimize the number of discs. So, we need to minimize empty space in the discs. We should fill the disc that contains 0.7 MB with another 0.7 MB file.
6 such discs will be created.

Files left : 
12 files of 0.4 MB each.

Each disc can accommodate 3 such files. (i.e., 3 * 0.4 = 1.2 < 1.44)
4 such discs will be created.

Total number of discs required is 3 + 6 + 4 = 13.

This is the minimum number of discs required to store 30 files. This is the combination that minimizes empty space across the discs and stores all the files without splitting a file.

Thus the answer is  Choice-B 13

bumpbot · Answer

Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

Jamal wants to save 30 files onto disks, each with 1.44 MB space. 3 of

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Jamal wants to save 30 files onto disks, each with 1.44 MB space. 3 of

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards