This problem is a mess😒
• The given information is so poorly written that it's difficult to comprehend in general.
Some of it, I genuinely have no clue how to interpret. The meaning of "both pumps need to be full of water to exclude trapped air", for instance, is a complete mystery to me; I'm not immediately able to understand that statement in any way that doesn't seem to contradict the fact that "Pump B ... has to be placed outside the water source". So I just ignored that part... la la la ̄\_(ツ)_/ ̄
• To take things from bad to worse, the wording isn't even consistent from one sentence to another—e.g., "at least 13 feet
above the bottom of the source" and "at least 18 feet
above the source" are meant to be two instances of the same kind of measurement (...or at least I
think they are... hahah), a realization it's hard to make with confidence given the differing phrasings.
• To take the next step from worse to downright infuriating, the given information explicitly contradicts itself! We're told that Pump B is "the lower-cost pump", even though "the costs ... do not significantly differ" between the two pumps. Huh? ( •᷄ࡇ•᷅ )
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With so many problems baked into the problem statement itself, you'd do well to just skip this one entirely. Buuuuutttt... here's my best attempt to read the problem in a way that actually makes enough sense to be solvable, and then to solve it.
Here's how I decided to interpret the givens. (These interpretations are NOT authoritative! If you read the given statements quite differently, there's a very good chance that your interpretation is justified too.)
Pump A had to be continuously immersed in the water source—at least 13 feet above the bottom of the source.—> I took this to mean that Pump A has to be anchored to the bottom of the lake, and that its total height has to be less than the depth of the lake at all times (so that the entire apparatus is completely underwater at all times). Under that interpretation, it follows that
we can only use Pump A if the depth of the lake NEVER goes below 13 feet at any time ever.
Pump B, had to be placed outside the water source——> Yeaaaahhhh... okay.
First of all, it's not clear whether this means "above the surface of the lake (but installed into the lake bottom)" or "actually OUTSIDE the lake" (the latter of which seems pretty weird to my intuition, but statement 2—which talks about the lake overflowing its banks—encourages that line of thought). I also can't say with any certainty how either of these possibilities would interact with the requirement that the pump be "full of water" in perpetuity (a statement I frankly had no idea how to use).
at a height not exceeding 18 feet above the source.—> I'll assume that this is a height above the BOTTOM of the source, like the 13 feet above.
Unfortunately, this condition COULD be consistent with either of the two interpretations above. (We can clearly read it together with the idea that Pump B is installed into the bottom of the lake but sits above the surface. It may seem at first glance to contradict the "outside the lake itself" interpretation—since the banks of the lake are 19 feet above the bottom—but we don't know whether the land slopes back downward on Andy's side after cresting the 19-foot bank. If it does so, then the sometimes-flooded land described in statement 2 COULD lie at an elevation that's less than 18 feet above that of the lake bottom.)
Buuuutttt... the second interpretation can't be used in any way that's definite (since we know nothing about the topography of Andy's land near the lakefront). So,
I guess I'll go with the first interpretation—which means that, if the lake is 18 FEET DEEP OR DEEPER, then we CAN'T use pump B as it would then be submerged.
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Mmmmmkay. With
that set of interpretations (which, once again, is far from the only way you could've read the given information....):
Quote:
(1) The lake has water at least 18 feet deep throughout the year.
—> If the givens mean what I wrote above, then this statement tells us both that we can ALWAYS use Pump A, AND that we can NEVER use Pump B. This is nice, since it's "sufficient" regardless of whether the question is asking which pump we COULD use or which pump we MUST use (another ambiguity!). Yay! Whoo hoo! Sufficient.
Quote:
(2) The lake sometimes floods Andy's end of the bank during a certain time of the year
—> So we know that the lake is 19 feet deep at certain times of year. "Sometimes", however, is not good enough to determine sufficiency, since literally anything could happen during the rest of the year (the lake might even dry up completely in the summer, for all we know). And, on top of that, we still don't know anything about the topography of the flooded land—although the specs of the flooded land are only relevant if my SECOND interpretation of the rules for Pump B (the one I didn't use here... lol) is actually what was meant here.
No matter what, though, we're not getting sufficiency out of this one.
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So, overall, A... if you make all 99,999 of the assumptions I did in interpreting the paragraph. >____<