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The length, breadth, and height of a rectangular box are in the ratio [#permalink]
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27 Apr 2017, 22:48
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The length, breadth, and height of a rectangular box are in the ratio of 6: 5: 4. If the length is halved, the breadth is doubled and the height is decreased by 50%, what would be percentage change in the volume of the box? A. 25% increase B. 25% decrease C. 50% increase D. 50% decrease E. No change in volume. Thanks, Saquib Quant Expert eGMATRegister for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the realtime guidance of our Experts
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The length, breadth, and height of a rectangular box are in the ratio [#permalink]
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27 Apr 2017, 22:49
The official solution has been posted. Looking forward to a healthy discussion..
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Re: The length, breadth, and height of a rectangular box are in the ratio [#permalink]
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28 Apr 2017, 12:41
EgmatQuantExpert wrote: The length, breadth, and height of a rectangular box are in the ratio of 6: 5: 4. If the length is halved, the breadth is doubled and the height is decreased by 100%, what would be percentage change in the volume of the box? A. 25% increase B. 25% decrease C. 50% increase D. 50% decrease E. No change in volume. Thanks, Saquib Quant Expert eGMAT"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 88=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 654, got 50% decrease. Tried it with 12108, 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 http://wakullasprings.org/wpcontent/uploads/2014/10/WildlifeSurveyAnalysis20131003.docYou'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 =\(\frac{12060}{120}\) = \(\frac{60}{120}\) = 50%, which is option D. Why does THIS one work? Sub600 question?
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Last edited by generis on 29 Apr 2017, 08:28, edited 1 time in total.



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Re: The length, breadth, and height of a rectangular box are in the ratio [#permalink]
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29 Apr 2017, 08:11
EgmatQuantExpert wrote: The length, breadth, and height of a rectangular box are in the ratio of 6: 5: 4. If the length is halved, the breadth is doubled and the height is decreased by 100%, what would be percentage change in the volume of the box? A. 25% increase B. 25% decrease C. 50% increase D. 50% decrease E. No change in volume. Thanks, Saquib Quant Expert eGMATRegister for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the realtime guidance of our Experts 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 = 1200/120 *100 = 100% Where am i going wrong? Thank you Sent from my SMN9200 using GMAT Club Forum mobile app



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Re: The length, breadth, and height of a rectangular box are in the ratio [#permalink]
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29 Apr 2017, 09:45
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.
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Re: The length, breadth, and height of a rectangular box are in the ratio [#permalink]
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29 Apr 2017, 10:22
EgmatQuantExpert wrote: The length, breadth, and height of a rectangular box are in the ratio of 6: 5: 4. If the length is halved, the breadth is doubled and the height is decreased by 100%, what would be percentage change in the volume of the box?
A. 25% increase B. 25% decrease C. 50% increase D. 50% decrease E. No change in volume 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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Re: The length, breadth, and height of a rectangular box are in the ratio [#permalink]
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29 Apr 2017, 21:22
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EgmatQuantExpert wrote: The length, breadth, and height of a rectangular box are in the ratio of 6: 5: 4. If the length is halved, the breadth is doubled and the height is decreased by 100%, what would be percentage change in the volume of the box? A. 25% increase B. 25% decrease C. 50% increase D. 50% decrease E. No change in volume. Thanks, Saquib Quant Expert eGMAT 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
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Re: The length, breadth, and height of a rectangular box are in the ratio [#permalink]
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30 Apr 2017, 01:58
stonecold wrote: EgmatQuantExpert wrote: The length, breadth, and height of a rectangular box are in the ratio of 6: 5: 4. If the length is halved, the breadth is doubled and the height is decreased by 100%, what would be percentage change in the volume of the box? A. 25% increase B. 25% decrease C. 50% increase D. 50% decrease E. No change in volume. Thanks, Saquib Quant Expert eGMAT 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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Re: The length, breadth, and height of a rectangular box are in the ratio [#permalink]
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30 Apr 2017, 02:10
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 eGMATRegister for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the realtime guidance of our Experts
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Re: The length, breadth, and height of a rectangular box are in the ratio [#permalink]
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30 Apr 2017, 18:52
Even with incorrect value initially, many got the correct answer




Re: The length, breadth, and height of a rectangular box are in the ratio
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30 Apr 2017, 18:52






