Raphael works as a caretaker at a zoo, where his responsibilities

Question

Raphael works as a caretaker at a zoo, where his responsibilities include bathing and feeding the animals. According to the guidelines, an animal’s daily water requirement is directly proportional to the square root of its weight.

Based on this, a tiger weighing 400 kg requires more than 300 liters but less than 400 liters of water. Similarly, an elephant weighing 4000 kg requires  x  liters of water, where  x  is an integer.

Select for  Minimum  the least possible value of  x , and for  Maximum  the greatest possible value of  x . Make only two selections, one in each column.

Bunuel · Accepted Answer

Official Solution: An animal’s daily water requirement being directly proportional to the square root of its weight implies that the water requirement equals \sqrt{weight} * k for some constant k . Given that a tiger weighing 400 kg requires more than 300 liters but less than 400 liters of water, we have: 300 < \sqrt{400} * k < 400 300 < 20k < 400 15 < k < 20 An elephant weighing 4000 kg would require x = \sqrt{4000} * k liters. Multiplying the above inequality by \sqrt{4000} gives: 15\sqrt{4000} < \sqrt{4000} * k < 20\sqrt{4000} 15\sqrt{4000} < x < 20\sqrt{4000} Evaluating 15\sqrt{4000} using a calculator, we get approximately 948.7. Evaluating 20\sqrt{4000} using a calculator, we get approximately 1264.9. Thus: 948.7 < x < 1264.9 Since x is an integer, the least possible value of x is 949, and the greatest possible value of x is 1264. Correct answer: Minimum "949" Maximum "1264" GMAT-Club-Forum-4lcc78kd.png

coolsies · Answer

I think the main point here is to remember that we have calculator for the data insights section. Reaching 300*sqrt(10)<water<400*sqrt(10) is a small job. But if we start solving this thing to see which option fits in terms of ratio or anything for options. That is going to ruin the whole question. Instead we need to remind ourself that this is the moment they have given that amazing toolbox for!

Bismuth83 · Answer

1. The question asks us to  find the maximum and minimum integer values for the amount of water an elephant needs .

2. It is known that "an animal’s daily water requirement is directly proportional to the square root of its weight." This can be written as  k\sqrt{w} , where w is the weight of the animal and k is a constant.

3. "A tiger weighing 400 kg requires more than 300 liters but less than 400 liters of water." In other words,  300 < k\sqrt{400} < 400 \rightarrow \frac{300}{20} < k < \frac{400}{20} \rightarrow 15 < k < 20 .

4. For an elephant, who weighs 4000 kg, the amount of water it needs is x, or  k\sqrt{4000} . We can put it in the following inequality:  15 * \sqrt{4000} < k\sqrt{4000} = x < 20 * \sqrt{4000} \rightarrow \sim948.68 < x < \sim1264.91 . Since x is an integer it's lowest and highest bounds are 949 and 1264.

5. Our answer will be:   Minimum - 949 and Maximum - 1264  .

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Raphael works as a caretaker at a zoo, where his responsibilities

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Minimum	Maximum
		947
		948
		949
		1263
		1264
		1265

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