If n is greater than 20, what is the number closest to n^100 - n^90?

Question

A) n^90
B) n^100
C) n^99
D) n^190
E) n^10

Bunuel · Accepted Answer

BeingHan · Answer

It can be deduced to 
n^90(n^10-1)
Since n is greater than 20 so n^10-1~ n^10.
So it will be closest to n^100.
B

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haardiksharma · Answer

Bunuel 
Thank you so much

harikrish · Answer

Solution:

n>20.
n^100-n^90 .Take n to be 100 for example. 100^100-100^90.
Simplifying, 100^90{(10^10) -1}
Comparing to the value of 10^10, 1 is negligible.

Therefore, the answer is Option B.

elegantm · Answer

n^100 - n^90
n^90 (n^10 - 1)
Since n is greater than 20, n^20 would be a very large number. Thus we may we write
n^90 (n^10 - 1) = n^90 (n^10) = n^100

Answer B

PKN · Answer

n^{100}-n^{90}  can be written as  n^{90}(n^{10}-1) 
 (n^{10}-1)  can be approximated to  n^{10}  since 1 is negligible in comparison to  n^{10}  when n>20.
So our expression becomes  n^{90}*n^{10}=n^{100} .
Ans. (B)

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pushpitkc · Answer

Since n is a number greater than 20, for simplicity sake, let's assume this number to be  25  or  5^2

(5^2)^{100} - (5^2)^{90} = 5^{200} - 5^{180} = 5^{180}(5^{20} - 1) = 5^{180}(5^{20}) = 5^{180+20} = 5^{200} = (5^2)^{100}

This is because  3125*3125*3125*3125 - 1  is almost the same as  3125*3125*3125*3125 .

So, we can extrapolate this result for n = 25 to show that  n^{100} - n^{90} = n^{100}  (Option B)

lfc · Answer

n^{90} (n^{10}-1) 
 n^{90+10}  (1 can be neglected)
 B

CAMANISHPARMAR · Answer

n^{90}  *  (n^{10}-1)  is as good as  n^{90}*n^{10} = n^{100}

Hence option B is the correct answer.

ScottTargetTestPrep · Answer

Factoring n^90 from both terms, we have:

n^90(n^10 - 1). Now, since n is relatively large, we see that (n^10 - 1) is essentially equal to n^10. We can thus simplify the expression n^90(n^10 - 1) to n^90(n^10) = n^100.

Answer: B

dave13 · Answer

pushpitkc what is formula of exponents when i need to perform subtraction Y^x-z^q

for example 6^{18}-5^8 how should I solve this

pushpitkc · Answer

Hey  dave13

Unfortunately, there is no formula to solve  6^{18} - 5^8  as the bases have no common factor

However, if the expression we were asked to find the value for was  6^{18} - 3^8 ,
we could simplify it as follows -  3*2^{18} - 3^8  =  3^8(3^{10}*2^{18} - 1)

P.S there must be a common factor in Y and z(which I have highlighted in your post) for us to make this
simplification. Hope this clears your confusion!

Bunuel · Answer

You can factor  6^{18} - 5^8  by applying a^2 - b^2 = (a - b)(a + b):

6^{18} - 5^8=(6^{9})^2 - (5^4)^2=(6^9 - 5^4)(6^9 + 5^4) .

But the easiest approach to solve this problem is given  HERE  or in any of the links given in  this post .

bumpbot · Answer

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If n is greater than 20, what is the number closest to n^100 - n^90?

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If n is greater than 20, what is the number closest to n^100 - n^90?

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