I12-23

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 · 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"

Bunuel · Answer

I have revised the question, solution, and formatting by adding more details to enhance clarity.

Feb2024 · Answer

Hello  Bunuel

In your solution above, once you calculated the upper and lower limits for  x , how did you select the final values of  x . I understand the least possible value shall be 948 liters and not 949 liters.

Thanks in Advance!

Bunuel · Answer

We are given that 948.7 < x < 1264.9, and since x is an integer greater than 948.7, the least possible value is 949, and since x is an integer less than 1264.9, the greatest possible value is 1264.

Nipunh · Answer

I like the solution - it’s helpful.

GMAT1034 · Answer

If this que is solved like: 
301=k20
399=k20
x=301/20.20root10
x=399/20.root10
and taking root10 as 3.16, I am not able to land at the correct ans, could someone explain whats wrong with this approach?  Bunuel

Bunuel · Answer

Your approach has two problems.

Using 301 and 399 as if they were the endpoints tightens the true bounds. From 300 < 20k < 400 the extreme k are just-above 15 and just-below 20, not 301/20 and 399/20. Your choice shrinks the interval and can exclude valid integers.
 
 You used  \sqrt{10} \approx 3.3 , which is too large.  \sqrt{10} \approx 3.16 .

Hope it helps.

GMAT1034 · Answer

But shouldnt K be an integer value? 301/20=15.05, 399/20=19.95. Here k will be from 16 to 19 anything, inclusive, just exactly what the official says? What values are missing ? Yep even if root 10 is taken as 3.16, then also 2nd part is coming as 1260.84

Bunuel · Answer

No, k doesn’t have to be an integer. The question only says the water requirement is proportional to √(weight), so k can be any real number. That’s why the valid range is just above 15 and just below 20, giving x between 949 and 1264. Please check the OE.

Hope it helps.

yashpandey7144 · Answer

I like the solution - it’s helpful.

niteshmotwani · Answer

Very near answer choice it should have 2 or 3 count difference in Actual GMAT very less chance will get this kind of close answer choice. Another ask is why max is not 1265 (option radio e) as you calculate answer 1264.9 ?

Bunuel · Answer

The maximum is not 1265 because we have a strict inequality:

x < 1264.9

Since x must be an integer, the greatest possible integer less than 1264.9 is 1264, not 1265. This is not a rounding question.

sequiipsum · Answer

I like the solution - it’s helpful.

SKP220292 · Answer

if we take just one decimal place (because we may be running short on time lol as was the case with me), then upper limit comes to 1264 - making it less than 1264 which made me mark 1263. So here basically are we just supposed to do a sqrt of 4000 and use that direct value to multiply with the upper and lower limits and not bother with n number of decimals? because taking fewer decimals can definitely lead to a wrong choice here.

Bunuel · Answer

Since  x  is an integer,  you need enough decimal places in the bounds  to see which integers satisfy the strict inequality.

Here,  20\sqrt{4000} \approx 1264.91 , so  1264 is allowed . Rounding this bound to 1264 would incorrectly exclude it.

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