GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 05 Jul 2020, 19:25

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 06 Jun 2014
Posts: 84
Location: United States
Concentration: Finance, General Management
GMAT 1: 450 Q27 V21
GPA: 3.47

### Show Tags

06 Feb 2016, 17:17
1
7
00:00

Difficulty:

25% (medium)

Question Stats:

74% (01:23) correct 26% (01:36) wrong based on 108 sessions

### HideShow timer Statistics

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: 1856

### Show Tags

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
SVP
Status: It's near - I can see.
Joined: 13 Apr 2013
Posts: 1676
Location: India
GPA: 3.01
WE: Engineering (Real Estate)

### Show Tags

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)
_________________
"Do not watch clock; Do what it does. KEEP GOING."
Manager
Joined: 28 Jan 2018
Posts: 50
Location: Netherlands
Concentration: Finance
GMAT 1: 710 Q50 V36
GPA: 3

### Show Tags

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)
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2799

### Show Tags

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

_________________

# Jeffrey Miller

Jeff@TargetTestPrep.com
225 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

Non-Human User
Joined: 09 Sep 2013
Posts: 15377

### Show Tags

19 Aug 2019, 18:00
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: What is (100,016)(99,984)?   [#permalink] 19 Aug 2019, 18:00