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# A computer has three hard-drives; the smallest and largest hard-drives

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Math Expert
Joined: 02 Sep 2009
Posts: 60778
A computer has three hard-drives; the smallest and largest hard-drives  [#permalink]

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13 Dec 2019, 00:06
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Difficulty:

45% (medium)

Question Stats:

69% (02:03) correct 31% (02:07) wrong based on 52 sessions

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Competition Mode Question

A computer has three hard-drives; the smallest and largest hard-drives account for 25 and 45 percent of the total storage space on the computer, respectively; due to a catastrophic error, the largest hard-drive lost approximately 22% of its storage space; after this error, the hard drive that was originally the second largest accounts for approximately what percent of the total hard-drive space on the reduced computer?

A) 22%
B) 33%
C) 20%
D) 39%
E) 45%

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Re: A computer has three hard-drives; the smallest and largest hard-drives  [#permalink]

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13 Dec 2019, 00:18
1
Approach:
- Assume Total Space = 100
- Space occupied by three hard drives be 25, 45, and 30

- largest hard-drive lost approximately 22% of its storage space -> .78 of 45 = 35.1
- Now total space becomes : 25 + 35.1 + 30 = 90.1

To Find: the hard drive that was originally the second largest(30) accounts for approximately what percent of the total hard-drive space on the reduced computer?

We get: 30 is approx 33% of 90.1

IMO Option B
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Re: A computer has three hard-drives; the smallest and largest hard-drives  [#permalink]

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13 Dec 2019, 02:03
1
Lets assume:
Before reduction, three hard drives had storage capacity of 25,30,45, respectively. Total was 100.

After reduction, three hard drives have storage capacity of 25,30,~35, respectively. Total is ~90.

Thus, the second largest hard drive now accounts for 30/90=~33%.

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Re: A computer has three hard-drives; the smallest and largest hard-drives  [#permalink]

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13 Dec 2019, 02:33
1
Answer seems to be B) 33%.

Adopting a combination of smart values and approximation techniques this can be solved and this seems a good problem to practice that.

Given,
We can assume the total to be 100GB.

so =>
Largest drive (A): 45GB
Smallest drive (B): 25 GB
and
The third drive (C): 100-70=30GB

To find Percentage of B in new total storage.

Solution

Total=100 GB

So New_A = A - 22/100 * A = 35GB Approx

Total_New = 90GB

Percentage of B = 30/90 = 1/3 = 33% Approx.

So, Choice B.
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Re: A computer has three hard-drives; the smallest and largest hard-drives  [#permalink]

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13 Dec 2019, 02:48
1
A computer has three hard-drives; the smallest and largest hard-drives account for 25 and 45 percent of the total storage space on the computer, respectively; due to a catastrophic error, the largest hard-drive lost approximately 22% of its storage space; after this error, the hard drive that was originally the second largest accounts for approximately what percent of the total hard-drive space on the reduced computer?

A) 22%
B) 33%
C) 20%
D) 39%
E) 45%

Let total storage space be = 100GB
HD1 = 25GB (smallest)
HD2 = 30GB (middle)
HD3 = 45GB (largest)

After crash HD3 has space = (1-0.22)45 = 35.1
New Total space = 25 + 30 + 35.1 = 90.1

Now, A and C are straight out, 45 looks too high. B and D are left.
HD2 = $$\frac{30}{90.1} * 100 ~ 33%$$

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A computer has three hard-drives; the smallest and largest hard-drives  [#permalink]

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Updated on: 16 Dec 2019, 04:56
Quote:
A computer has three hard-drives; the smallest and largest hard-drives account for 25 and 45 percent of the total storage space on the computer, respectively; due to a catastrophic error, the largest hard-drive lost approximately 22% of its storage space; after this error, the hard drive that was originally the second largest accounts for approximately what percent of the total hard-drive space on the reduced computer?

A) 22%
B) 33%
C) 20%
D) 39%
E) 45%

total=100
large=45
small=25
middle=100-45-25=30

large*(1-0.22)=45*78/100=35.1

30/(25+30+35.1)=30/90.1~30/90=1/3=33%

Ans (B)

Originally posted by exc4libur on 13 Dec 2019, 04:39.
Last edited by exc4libur on 16 Dec 2019, 04:56, edited 1 time in total.
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Re: A computer has three hard-drives; the smallest and largest hard-drives  [#permalink]

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13 Dec 2019, 08:00
1
original total space = 100
low; 25
middle ; 20
high ; 45
after error
total ; .78*45 ; 35
loss of 10 ;
new total 90
so ; low ; 25
middle ; 30
high ; 35
30/90 ; ~33.33%
IMO B

A computer has three hard-drives; the smallest and largest hard-drives account for 25 and 45 percent of the total storage space on the computer, respectively; due to a catastrophic error, the largest hard-drive lost approximately 22% of its storage space; after this error, the hard drive that was originally the second largest accounts for approximately what percent of the total hard-drive space on the reduced computer?

A) 22%
B) 33%
C) 20%
D) 39%
E) 45%
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Re: A computer has three hard-drives; the smallest and largest hard-drives  [#permalink]

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13 Dec 2019, 10:21
Three hard drives, x=25%, y=30% and z=45%.
z has reduced to 23% after losing 22%.

Revised % of y= 30*100/(30+25+23) = 3000/78= 500/13 and Revised percentage should be less than 520/13=40%. From the answer choices the nearest value less than 40% is 39%.

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Re: A computer has three hard-drives; the smallest and largest hard-drives  [#permalink]

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13 Dec 2019, 15:25
1
Let Total hard drive space be 100 points
—> 3 hard drives:
Smallest —25 points
Largest —45 points
Second largest — 30

—> if Largest lose 22 % of storage space — 45*(22/100)= 99/10= 9.9 points
45 —9.9= 35.1 points ( largest)
—> Total hard drive space in the reduced computer —25+ 30 + 35.1= 90.1 points
—> rate of the second largest= (30*100)/90.1 = 33.(3)

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Re: A computer has three hard-drives; the smallest and largest hard-drives  [#permalink]

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14 Dec 2019, 03:30
1
THE RATIO'S ARE 25,30,45
the largest one lost 22%.....which results in 45-45(0.22)=35.1
so resulted in 25,30,35.1
ans: 30/90.1= 33%

OA:B
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Posts: 60778
Re: A computer has three hard-drives; the smallest and largest hard-drives  [#permalink]

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15 Dec 2019, 23:07
Bunuel wrote:

Competition Mode Question

A computer has three hard-drives; the smallest and largest hard-drives account for 25 and 45 percent of the total storage space on the computer, respectively; due to a catastrophic error, the largest hard-drive lost approximately 22% of its storage space; after this error, the hard drive that was originally the second largest accounts for approximately what percent of the total hard-drive space on the reduced computer?

A) 22%
B) 33%
C) 20%
D) 39%
E) 45%

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OFFICIAL EXPLANATION

1. Since there are only three hard drives and these account for 100% of the space on the computer, you can write the following equation:
(Smallest Hard Drive) + (Medium Hard Drive) + (Large Hard Drive) = 100%
25% + (Medium Hard Drive) + 45% = 100%

2. You now know the size of the medium hard drive:
(Medium Hard Drive) = 30%

3. If the largest hard-drive lost approximately 22% of its storage space, it now accounts for (1-.22)(.45) = .351 or 35.1% of the old total space.

4. You can now find what percent of the total hard-drive space the second largest hard drive accounts for:
= (Drive Originally 2nd Largest) / (New Total Drive Space)
= 30%/(35.1%+25% + 30%) = 30%/90% = ~ 33%

5. If the concept of manipulating and dividing percents throws you off, this is an excellent problem to pick numbers on. Simply let the percents be actual hard-drive space. In other words, set the total hard drive space to be 100GB. Then, the smallest hard-drive is 25GB, the medium hard-drive is 30GB, and the largest is 45GB.
After the largest shrinks by 22%, it is now 45*(1-.22) = 35GB. So, the reduced hard drive is 25+30+35 = 90GB and the second largest hard drive is 30GB/90GB = 33%.
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Re: A computer has three hard-drives; the smallest and largest hard-drives   [#permalink] 15 Dec 2019, 23:07
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