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

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Manager
Joined: 06 Jun 2014
Posts: 89
Location: United States
Concentration: Finance, General Management
GMAT 1: 450 Q27 V21
GPA: 3.47

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06 Feb 2016, 17:17
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3
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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) $$(10)^{10} (2)^8$$
SVP
Joined: 06 Nov 2014
Posts: 1877

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06 Feb 2016, 21:11
2
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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GMAT 1: 480 Q38 V22
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21 Mar 2018, 01:50
1
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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Joined: 28 Jan 2018
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Location: Netherlands
Concentration: Finance
GMAT 1: 710 Q50 V36
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21 Mar 2018, 02:14
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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22 Mar 2018, 14:46
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

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Re: What is (100,016)(99,984)? &nbs [#permalink] 22 Mar 2018, 14:46
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