Problem Solving

Which of the following best approximates the value of q if 528+311=5q ?

39
30
28
27
17


qa is 28

There is something wrong with this problem. Either the problem in its original form is wrong, or you did not copy it correctly. 28 multiplied by 5 is 140, and 140 does not equal nor is an approximation of 839. If you use long division, for 839 = 5q you will end up with 167.8. Please double check this problem. Otherwise, provide the explanation from the text where this problem appeared.

Also, given that you wrote it is an exponent problem, you should include the exponent shorthand ^ in order to indicate where the power is to be placed.

Which of the following best approximates the value of q if 5^28+3^11=5q ?

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28
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qa is 28


something must have went wrong with my pc. thanks
p.s. I got the spoiler part down as you can see.

d

Sorry: Don't pay attention to this.

I don't know the concept behind this one, but I'll write my approach for it.

Basically, 5^28 is huge. You really have only 3 choices for your answer; A, B, or C.

You can easily calculate that 3^11 is about 170k. You can do this by doing (3^4)(3^4)(3^3) on paper. The calculation doesn't take a long time and doesn't need to be precise.

Now, you've got to decide with the answers. You can have 5^28, 5^30, or 5^39. So basically, you've got to kind of use intuition to see whether (5^28)(5)(5) - (5^28) is close to 170k or not. Well, you're multiplying a really large number (5^28) by 25, so your intuition could say that no, the result would be way over 170k that 3^11 produced, and therefore, the answer is just simply 5^28.

I'm sure there must be a simpler, algorithmic way to solve this, though.

resilient wrote:Which of the following best approximates the value of q if 5^28+3^11=5q ?

39
30
28
27
17


qa is 28


something must have went wrong with my pc. thanks
p.s. I got the spoiler part down as you can see.

Are you still sure of the question? In my opinion the question should be
5^28+3^11=5^q

In this scenario, its pretty simple, 5^28 is much greater than 3^11 and thus we can just ignore the addition and say
5^q ~ 5^28
or q ~ 28

simplyjat wrote:Are you still sure of the question? In my opinion the question should be
5^28+3^11=5^q

In this scenario, its pretty simple, 5^28 is much greater than 3^11 and thus we can just ignore the addition and say
5^q ~ 5^28
or q ~ 28

That is what I solved it based on.

Can somebody please explain why 3^11 has been ignored in the calculation??

Since 5 to the power of 28 is such an enormous number, 3 to the power of 11 is pretty much negligible compared to it. Therefore, it can be ignored, especially since you are being asked to approximate. This question does not test your ability to sit and figure out exactly what each number is. Instead, it tests your intuition with how large or small the numbers are. If you even interview for McKinsey or any other consulting firm, they will ask you to work with numbers large and small and require estimations, which is a lot like the work they initially do when they try to "rough-number" the estimates during engagements, before moving on to more rigorous analysis of the numbers.

Anyway, there you have it.

To emphasize the point being made here, 3^11 = 177,147

However, Excel and Matlab, two computer programs that use double-point precision, cannot accurately calculate 5^28 because it calculates to 20 digits. If you're DYING to evaluate it to exactness then you can go from here:

5^28 = 5^21 * 5^7 = 476,837,158,203,125 * 78,125

That product is SO much larger than 3^11 that you can forget about it, as has been mentioned.

moneyman wrote:Can somebody please explain why 3^11 has been ignored in the calculation??

If you want the mathematical reason:

5^28 = 37252902984619140625
3^11 = 177147

5^28 + 3^11 = 37252902984619317772

Look how little effect the 3^11 had on the 5^28. It's basically still 5^28.