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What is (100,016)(99,984)?

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What is (100,016)(99,984)?  [#permalink]

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New post 06 Feb 2016, 18:17
1
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A
B
C
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E

Difficulty:

  15% (low)

Question Stats:

78% (01:20) correct 22% (01:29) wrong based on 122 sessions

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What is (100,016)(99,984)?


A) \(10^{10}\) – \(2^6\)

B) \(10^{10} – 2^7\)

C) \(10^{10} – 2^8\)

D) \(10^{10} – 2^9\)

E) \((10)^{10} (2)^8\)
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Re: What is (100,016)(99,984)?  [#permalink]

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New post 06 Feb 2016, 22:11
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zxcvbnmas wrote:
What is (100,016)(99,984)?


A) \(10^{10}\) – \(2^6\)

B) \(10^{10} – 2^7\)

C) \(10^{10} – 2^8\)

D) \(10^{10} – 2^9\)

E) \((10)^{10} (2)^8\)


(100,016)(99,984) can be written as (100,000 + 16)*(100,000 - 16)
= (10^5 +5 2^4)*(10^ - 2^4)

We know that a^2 - b^2 = (a+b)*(a-b)

Therefore (100,000 + 2^4)*(100,000 - 2^4) = 10^10 - 2^8
Option C
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Re: What is (100,016)(99,984)?  [#permalink]

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New post 21 Mar 2018, 02:50
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zxcvbnmas wrote:
What is (100,016)(99,984)?


A) \(10^{10}\) – \(2^6\)

B) \(10^{10} – 2^7\)

C) \(10^{10} – 2^8\)

D) \(10^{10} – 2^9\)

E) \((10)^{10} (2)^8\)


\((100,016)(99,984)\)

Or \((100,000 + 16) (100,000 - 16)\)

Or \((100,000)^2 - (16)^2\)

\(10^{10} - (2^4)^2\)

\(10^{10} - 2^8\)

(C)
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What is (100,016)(99,984)?  [#permalink]

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New post 21 Mar 2018, 03:14
zxcvbnmas wrote:
What is (100,016)(99,984)?


A) \(10^{10}\) – \(2^6\)

B) \(10^{10} – 2^7\)

C) \(10^{10} – 2^8\)

D) \(10^{10} – 2^9\)

E) \((10)^{10} (2)^8\)


\((100,016)(99,984) = (100,000 + 16)(100,000 - 16) = 10^{10} - 4^2 = 10^{10} - 2^8\) => Answer (C)
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Re: What is (100,016)(99,984)?  [#permalink]

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New post 22 Mar 2018, 15:46
zxcvbnmas wrote:
What is (100,016)(99,984)?


A) \(10^{10}\) – \(2^6\)

B) \(10^{10} – 2^7\)

C) \(10^{10} – 2^8\)

D) \(10^{10} – 2^9\)

E) \((10)^{10} (2)^8\)


Solution:

We see that 100,016 x 99,984 will have a units digit of 4.

Since 10^10 has a units digit of 0, we see that answer choice E ends in a zero, so we do not have to test that answer.

We also see that answers A - D, have some power of 10, which ends in zero, minus an integer.

The way for a number ending in zero to subtract to get a units digit of 4 is to subtract another number ending in a 6.

Since 2^8 = 256, we see that 10^10 - 2^8 will end in a 4.

Alternate solution:

(100,016)(99,984)

(100,000 + 16)(100,000 - 16)

(10^5 + 2^4)(10^5 - 2^4)

10^10 - 2^8

Answer: C
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Re: What is (100,016)(99,984)? &nbs [#permalink] 22 Mar 2018, 15:46
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