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
e-GMAT"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
http://wakullasprings.org/wp-content/uploads/2014/10/Wildlife-Survey-Analysis-2013-10-03.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 =\(\frac{120-60}{120}\) = \(\frac{60}{120}\) = 50%, which is option D. Why does THIS one work?
Sub-600 question?
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