The length, breadth, and height of a rectangular box are in the ratio

The official solution has been posted. Looking forward to a healthy discussion..
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"Fools rush in where even angels fear to tread." Even after searching fora to no avail, I have a feeling I'm going to regret this post, but I want to understand what I am missing, not including my reasoning ability at this point.

The question seems to imply some difference between "decreased by" 100% and "decreased 100%." Maybe there exists some diabolical rule that makes no damn sense in plain English. I am entirely confused at this point. Can't wait to see OA.

Running the numbers, and using the formula for percent decrease, I ended up with new H=0, and new volume = 0.

I still can't see the difference between "decreased BY" 100% and "decreased 100%." No matter what height is, let's say 8, to decrease 8 by 100% of 8 means 8-8=0. If height is 8 and decreases 100%, it goes from 8 (minus 100% of itself = 8) = 0

Worse, even when I decided to tangle with phrasing and postulated that if "increased by 100%" meant "double the number," then perhaps "decreased by 100%" meant "halve the number," I got different values for percent decrease with values that, because proportional, should have returned the same percentage decrease.
(Tried it with 6-5-4, got 50% decrease. Tried it with 12-10-8, got 67% decrease.)

100% of any number is itself. To decrease a number BY 100% of that number is to subtract a number by that number. Alternatively, a number that "decreased 100%" similarly started at its full value and "shrunk" by its full value.

Scientists seem to agree with me. For example, see "A STRONG DECREASING TREND IN THE NUMBER OF AMERICAN WIDGEONS WAS IDENTIFIED - The mean number of widgeons decreased by 153 birds from 153 to 0 birds (a decrease by 100 percent) over 20 years, from 1993 to 2012," at https://wakullasprings.org/wp-content/uploads/2014/10/Wildlife-Survey-Analysis-2013-10-03.doc

You'll get answer D if you use numbers 6*5*4 (and use hypo that decreased by 100 = halve the #).

Original volume = 120.
New volume = 3*10*2 = 60
Percent decrease =\(\frac{120-60}{120}\) = \(\frac{60}{120}\) = 50%, which is option D. Why does THIS one work?

Sub-600 question?
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Using same ratio l:b:h::6:5:4

Original volume = 120

New ratio l:b:h::3:10:0

New volume = 0

Hence,
Change in volume = 120-0/120 *100 = 100%

Where am i going wrong?

Thank you

Sent from my SM-N9200 using GMAT Club Forum mobile app

IMO D
Even i failed to understand what does 100% decrease in value mean but i then took a different way to solve the problem.
We are given that the length of a box becomes half that means it is now 50% of its previous value , its breadth is doubled that means 100% increase , then we are given that its height is decreased by 100 %.
So we have volume as a product of length , height and breadth.
Any change in the value of these quantities will reflect in the volume .So we have 50% decrease*100% increase*100% decrease which means that we need 50% more of length to get to our original value.
Hence D is answer.
Please correct me if i am wrong.

Original Volume is 6*5*4 = 120

Increased Volume is 3*10*2 = 60

Thus, decrease in volume is 60

Percentage change in the volume of the box = 60/120*100 => 50%

Hence, answer must be (D) 50% decrease in volume...
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Hi Saquib

Can you please elaborate this statement => "100 percent decrease in height"

How is that ever possible?

If you reduce the height by 100% then the Rectangular Box would cease to Exist.
If that is true.
New volume => Zero

And we none of the options would suffice.
If something gets reduced by 100 percent =>its new value would be Zero.


I hope i am not missing anything.

Regards
Stone Cold

Hey Stone Cold,



Apologies for the inconvenience, I somehow missed the updates for this post. The decrease would be 50% and not 100%. I have updated the question.


Regards,
Saquib
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Hey Everyone,

Sorry for the mistake. I somehow confused everyone with the "100% decrease" information.

Otherwise the question is very straightforward.

• Let the length, breadth and height be 6a, 5a and 4a.

• Therefore, the initial volume of the box \(= 6a * 5a * 4a = 120a^3\).
• New length \(= 6a * \frac{1}{2} = 3a\)
• New breadth \(= 5a* 2 = 10a\)
• New height \(= 4a * \frac{1}{2} = 2a\)

o Therefore, the New Volume \(= 3a * 10a * 2a = 60a^3\).

• Thus, Percentage change in volume \(= \frac{(120 – 60)*100}{120} = \frac{1}{2}*100 = 50\)% decrease.

Thus, the correct answer is Option D.


Thanks,
Saquib
Quant Expert
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