The edge of a cube is measured as 100 centimeters. This Measurement

Question

The edge of a cube is measured as 100 centimeters. This Measurement has some error, but the error is no more than 1 centimeter. Which of the following is closet to the maximum possible difference, in cubic centimeters, between the actual volume of the cube and the volume computed using this measurement?

A. 10,000
B. 30,000
C. 50,000
D. 70,000
E. 90,000

A. 10,000
B. 30,000
C. 50,000
D. 70,000
E. 90,000

Bunuel · Accepted Answer

The options are well spread so we can approximate . Changing the length by 1 cm results in a change of the volume by 1 * 100 * 100 = 10,000 cubic centimeters; Changing the width by 1 cm results in a change of the volume by 100 * 1 * 100 = 10,000 cubic centimeters; Changing the height by 1 cm results in a change of the volume by 100 * 100 * 1 = 10,000 cubic centimeters. So, the approximate maximum possible difference is 10,000 + 10,000 + 10,000 = 30,000 cubic centimeters. Answer: B. P.S. I believe GMAC does not consider knowing the formula for the volume of a cube as geometry knowledge but rather as general knowledge. Furthermore, this question primarily assesses one's ability to approximate. P.P.S. Similar questions to practice: https://gmatclub.com/forum/the-measurem ... 60295.html https://gmatclub.com/forum/a-rectangula ... 53393.html https://gmatclub.com/forum/a-closed-alu ... 41049.html https://gmatclub.com/forum/a-cylindrica ... 22366.html https://gmatclub.com/forum/in-measuring ... 47595.html Hope it helps.

MartyMurray · Answer

I personally would do 101*101*101.

Then, 101 is 1 percent greater than 100.

101*101 is going to be about 2 percent greater than 100*100 because we can ignore the increase resulting from multiplying the units digits.

So, we see that each time we use 101 instead of 100, we end up with a about 1 percent increase. Thus, 101*101*101 will be about 3 percent greater than 100*100*100.

3% of 1,000,000 is 30,000.

So, the correct answer is (B).

AnkurGMAT20 · Answer

bb   chetan2u   Bunuel  does this qualify to be a geometry question? Because I believe one needs to remember the formula for volume of cube in order to do the calculation. Your thoughts?

AnkurGMAT20 · Answer

I solved this by the following way:

If edge of cube is 100, then it's  volume = a^3 >> 100^3.......................(1)

We are told that error is no more than 1 centimeter and need to find the maximum possible difference, hence, take error as 1 cm and then edge would be 99 cm.

Volume in this case would be = a^3 >> 99^3, which can be written as (100-1)^3

Now here we can use the formula of (a-b)^3 = a^3 -b^3 -3a^2b + 3ab^2
 
100^3 - 1^3 -3(100)^2 (1) + 3(100)(1)^2......................2

Next step is to find the max possible difference, it would be:

Eq 1-Eq2

100^3 - (100^3 -1 -30000 + 300)

we are left with: 1+30000-300 =~ 30000

Answer is B.

lessgoogmat · Answer

Hi  Bunuel ,

The question stem says "the error is no more than 1 centimeter". Should we interpret this to mean that the minimum and maximum limits of the actual value are 99 and 101 respectively, or one of those cases where the actual value is 99.5\leq{x}m < 100.5, where x is the actual value.

I feel like I am mixing two different concepts here but I am not able to figure out the difference. Can you please address my confusion and explain the differences between the two? Also, can you please suggest some problems based on the latter as well?

Thanks in advance!

Bunuel · Answer

I think studying similar questions should help: https://gmatclub.com/forum/the-measurem ... 60295.html https://gmatclub.com/forum/a-rectangula ... 53393.html https://gmatclub.com/forum/a-closed-alu ... 41049.html https://gmatclub.com/forum/a-cylindrica ... 22366.html https://gmatclub.com/forum/in-measuring ... 47595.html

sayan640 · Answer

KarishmaB  Can you please help on this question ? 
SHould it not be 99*99*99 or 101*101*101 ? Not able to interpret it properly.  gmatophobia   MartyMurray

sayan640 · Answer

Bunuel  s method is also nice , though  MartyMurray  you relied on approximation. 
There are three edges in the cube i.e length , breadth and width.
The approximate change can happen either for length or for breadth or for width.
After change in length , the volume = 101*100*100
Volume before change = 100*100*100
Change in volume = 100*100*(101 -100) =10,000
Similar way , the same change can happen for breadth and width and hence total change = 10000 + 10000+ 10000 = 30000

Posted from my mobile device

KarishmaB · Answer

Since you need maximum difference 101^3 is more appropriate but since you need an approximate, either will work just fine.

Estimated Volume  = 100^3

Max Actual Volume  = 101^3 = (100 + 1)^3 = 100^3 +1 + 3*100 (100 + 1)  (Use (a+b)^3 formula)

We need to find the extra (what is more than 100^3) so ignore the first term. Since we are approximating, ignore 1's. 30,000 is extra.

Answer (B)

Dream009 · Answer

Go by the idea of successive % change - 1% + 1% + 1*1% = 2.01%
Again
2.01% + 1% + some points ~ 3%
On (10)^6 this will be an error of 3*(10)^4

Legallyblond · Answer

this is not coordinate geometry right? then why is it in focus?

Bunuel · Answer

Please read the thread: https://gmatclub.com/forum/the-edge-of- ... l#p3333955

The edge of a cube is measured as 100 centimeters. This Measurement

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The edge of a cube is measured as 100 centimeters. This Measurement

Prep Toolkit

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