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Which of the following is closest to 11^5*9^5–7*10^7?

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Math Revolution GMAT Instructor
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Which of the following is closest to 11^5*9^5–7*10^7?  [#permalink]

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New post 21 Feb 2018, 01:07
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

56% (01:31) correct 44% (02:07) wrong based on 56 sessions

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[GMAT math practice question]

Which of the following is closest to \(11^5*9^5–7*10^7?\)

\(A. 10^2\)
\(B. 10^7\)
\(C. 10^8\)
\(D. 10^9\)
\(E. 10^{10}\)

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Re: Which of the following is closest to 11^5*9^5–7*10^7?  [#permalink]

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New post 21 Feb 2018, 03:31
MathRevolution wrote:
[GMAT math practice question]

Which of the following is closest to \(11^5*9^5–7*10^7?\)

\(A. 10^2\)
\(B. 10^7\)
\(C. 10^8\)
\(D. 10^9\)
\(E. 10^{10}\)



11^5*9^5–7*10^7 = (10+1)^5(10-1)^5 - 7*10^7 = (10^10 -1) - 7*10^7 (a+b)(a-b0 = a^2-b^2

10^10-10^7 = 10^7(10^3 -1 ) = 10^10

(E)
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Re: Which of the following is closest to 11^5*9^5–7*10^7?  [#permalink]

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New post 21 Feb 2018, 03:42
APPROXIMATION TECHNIQUE :-

Here is what I did on this one ->

\(11^{5} * 9^{5}– 7*10^{7} = 99^{5} -7*10^{7}\)

Now, lets approximate. Lets say time is running out and we have 30 seconds to get to the correct answer.

\(99^{5} - 7*10^{7} = 100^{5} - 7*10^{7} = 10^{10} - 7*10^{7}\)

Notice that \(10^{10}\) is extremely large as compared to \(7*10^{7}\)

Hence the value would be close to \(10^{10}\)

Smash that E.

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Re: Which of the following is closest to 11^5*9^5–7*10^7?  [#permalink]

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New post 25 Feb 2018, 18:40
=>

Since \(11\) is close to \(10\) and \(9\) is close to \(10, 11^5*9^5\) is close to \(10^5*10^5 = 10^{10}.\)
Since \(7*10^7\) is a relatively small number compared with \(10^{10}, 11^5*9^5 – 7*10^7\) is approximately equal to \(10^{10}\).

Therefore, the answer is E.

Answer: E
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Re: Which of the following is closest to 11^5*9^5–7*10^7?  [#permalink]

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New post 25 Feb 2018, 20:22
\(11^5×9^5 = (11×9)^5 ≈ 100^5 = 10^{10}\)

Now, \(10^{10}-7×10^7 = 10^7(10^3-7)\)

Since 7 is very tiny and hence can be ignored as we only need approx value.

\(10^7×10^3 = 10^{10}\)
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Re: Which of the following is closest to 11^5*9^5–7*10^7?   [#permalink] 25 Feb 2018, 20:22
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