Respuesta :
Answer:
None of the above
Step-by-step explanation:
Oooh, this is a fun question. Now, you could of course brute force the problem and just try each of the four alternatives by adding each alternative to 27202 and then divide by 75 to see if you get an integer result but that would take a bit of time even with a calculator.
So instead we will use our brains and see what we know about multiples of 75. Let's multiply 75 by a few integers to see if we can find a pattern.
75*1 = 75; 75*2 = 150; 75*3 = 225; 75*4 = 300; 75*5 = 375; 75*6 = 450;
What we notice is that the end digit in the six examples always toggle between 5 or 0. It can be proved that this happens for all multiples of 75.
This means that whatever number we add to 27202 must have the last digit 3 or 8 for its sum to be divisible by 75. You can easily spot that there's only one alternative that matches that requirement, namely alternative D.
Note that this is not a proof that the sum of 27202 + 48 is exactly divisible by 75 but it does rule out the 3 other options. To make sure, you should calculate [tex]\frac{27250}{75} = 363\frac{1}{3}[/tex]. Oh what.. this is not a valid answer either.. I guess all the alternatives are wrong.
