GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 23 Jul 2018, 08:52

# Happening SOON:

How to craft the best MBA Application Resume - 9 AM PST

### 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

# 999,999^2-1 equals:

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 47221

### Show Tags

14 Sep 2015, 05:03
5
20
00:00

Difficulty:

35% (medium)

Question Stats:

69% (01:05) correct 31% (01:16) wrong based on 455 sessions

### HideShow timer Statistics

$$999,999^2-1$$ equals:

(A) $$(9^6)(11^6)$$

(B) $$(10^6)(10^5 -2)$$

(C) $$(10^6)(10^6 -2)$$

(D) $$(10^5)^2$$

(E) $$(10^6)^2$$

Kudos for a correct solution.

_________________
SVP
Joined: 08 Jul 2010
Posts: 2120
Location: India
GMAT: INSIGHT
WE: Education (Education)

### Show Tags

Updated on: 14 Sep 2015, 07:15
4
1
Bunuel wrote:
999,999^2-1 equals:

(A) (9^6)(11^6)

(B) (10^6)(10^5 -2)

(C) (10^6)(10^6 -2)

(D) (10^5)^2

(E) (10^6)^2

Kudos for a correct solution.

Just trying to find a different method (Not a better method essentially)

$$999,999^2-1 = (1000000-1)^2 - 1 = (10^6-1)^2 - 1 = (10^{12} +1 - 2*1*10^6) - 1 = (10^{12} - 2*10^6) = 10^6*(10^6-2)$$

_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Originally posted by GMATinsight on 14 Sep 2015, 06:52.
Last edited by GMATinsight on 14 Sep 2015, 07:15, edited 1 time in total.
Intern
Joined: 30 Aug 2015
Posts: 31
Concentration: Marketing, Finance
WE: Brand Management (Manufacturing)

### Show Tags

14 Sep 2015, 11:15
7
shailendra79s wrote:
999,999² - 1 = 999,999² - 1² = (999,999-1) (999,999+1) = 10^6 (999,998) = 10^6(10^6 - 2)

999,9992−1=(1000000−1)2−1=(106−1)2−1=(1012+1−2∗1∗106)−1=(1012−2∗106)=106∗(106−2)

_________________

Please award kudos if you like my explanation.
Thanks

##### General Discussion
Intern
Joined: 02 Sep 2015
Posts: 1

### Show Tags

14 Sep 2015, 05:14
4
2
$$(999,999)^2-1 = (999,999-1)(999,999+1) = 999,998 \times 1,000,000 = (10^6 - 2) \times 10^6$$
Current Student
Joined: 20 Mar 2014
Posts: 2641
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)

### Show Tags

14 Sep 2015, 07:10
5
2
GMATinsight wrote:
Bunuel wrote:
999,999^2-1 equals:

(A) (9^6)(11^6)

(B) (10^6)(10^5 -2)

(C) (10^6)(10^6 -2)

(D) (10^5)^2

(E) (10^6)^2

Kudos for a correct solution.

Just trying to find a different method (Not a better method essentially)

$$999,999^2-1 = (1000000-1)^2 - 1 = (10^6-1)^2 - 1 = (10^{12} +1 - 2*1*10^6) - 1 = (10^{12} - 2*10^6) = 10^6*(10^6-2)$$

GMATinsight, your answer is correct but the option is NOT E. It should be C.

Alternate method:

$$999999^2-1$$ will have a unit's digit of 0 . Eliminate option A.

For, options B,C,D, look at it like this: using $$a^2-b^2=(a+b)(a-b)$$

$$999999^2-1 = (999999+1)(999999-1) = 10^6*(10^6-2)$$, C is the correct answer. NOte here that maximum power of 10 in $$10^6*(10^6-2)$$ is 11. Thus the answer is in order of 11.

Alternately, to eliminate options B,D,E look below:

Option B is in the order of $$10^6*(10^4)=10^{10}$$. We need $$10^{11}$$. Eliminate.

Option D is in the order of $$10^{10}$$. We need $$10^{11}$$. Eliminate.

Option E is in the order of $$10^{12}$$. We need $$10^{11}$$. Eliminate.
SVP
Joined: 08 Jul 2010
Posts: 2120
Location: India
GMAT: INSIGHT
WE: Education (Education)

### Show Tags

14 Sep 2015, 07:17
2
Engr2012 wrote:

GMATinsight, your answer is correct but the option is NOT E. It should be C.

Thank you for bringing in notice.
_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Intern
Joined: 03 Feb 2014
Posts: 38
Location: United States
Concentration: Entrepreneurship, General Management
WE: General Management (Other)

### Show Tags

14 Sep 2015, 10:58
3
999,999² - 1 = 999,999² - 1² = (999,999-1) (999,999+1) = 10^6 (999,998) = 10^6(10^6 - 2)
_________________

--Shailendra

Manager
Joined: 21 Jun 2014
Posts: 138
Location: United States
Concentration: General Management, Strategy
GMAT 1: 630 Q45 V31
GPA: 3.4
WE: Engineering (Computer Software)

### Show Tags

15 Sep 2015, 18:59
4
Consider this an algebraic expression of x2-1 .Break it down to (x-1)(x+1) .so it becomes (999,999+1)(999,999-1)
Reducing it further leads to (1000,000)(999,998) .This expression can be simplified further to be written as: 10^6(10^6 -2) .
Option C is the correct choice.
_________________

Regards,
Manish Khare
"Every thing is fine at the end. If it is not fine ,then it is not the end "

Manager
Joined: 29 Jul 2015
Posts: 159

### Show Tags

17 Sep 2015, 13:33
3
Bunuel wrote:
999,999^2-1 equals:

(A) (9^6)(11^6)

(B) (10^6)(10^5 -2)

(C) (10^6)(10^6 -2)

(D) (10^5)^2

(E) (10^6)^2

Kudos for a correct solution.

$$999,999^2-1$$

= $$(10^6-1)^2 - 1$$

= $$((10^6)^2) + 1 - 2(10^6) -1$$

=$$((10^6)^2) - 2(10^6)$$

= $$(10^6)(10^6 -2)$$

Math Expert
Joined: 02 Sep 2009
Posts: 47221

### Show Tags

20 Sep 2015, 09:10
4
Bunuel wrote:
999,999^2-1 equals:

(A) (9^6)(11^6)

(B) (10^6)(10^5 -2)

(C) (10^6)(10^6 -2)

(D) (10^5)^2

(E) (10^6)^2

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

Here, the given information is in a quite-unusable form. You have no interest in squaring 999999. It’s a ridiculously large number, it will require an insanely long calculation, and most importantly it won’t look at all like the answer choices. The work would all be for naught, as ultimately you’d have to repackage the number to look like one of the expressions in A-E. Your mission here is not to calculate this number; as on many algebra-based problems, your mission is to repackage the given information as something much more useful. Two things should lead you to this decision:

1. The number itself is incalculable by hand, so it’s not a calculation-based problem
2. The answer choices are in algebraic form, so you’re looking for an expression and not a number

Seeing this, you should recognize that your job is to take the statement given and re-frame it as a restatement of the same fact…just a more useful form. Restatements can come in several ways:

* Factor common terms to turn addition/subtraction into multiplication
* Multiply a fraction by the same numerator and denominator (so it equals 1) to give it a new expression
* Take an equation and do the same thing to both sides to change the look of the expression

Here, we can use arguably the most powerful repackaging tool in all of algebra; the Difference of Squares rule. This rule states that $$x^2 -y^2 =(x -y)(x +y)$$. And since we already have $$999999^2-1^2$$ (remember: 1 is the same as 1^2), we can change it to $$(999999 + 1)(999999-1)$$. Why? because now we have 1000000 on the left, and that can be repackaged in exponent form as 10^6, which matches the notation in the answer choices. We needed something with an exponent, and transforming this expression as we did allowed us to do that. So we have:

$$(10^6)(999998)$$

And it’s our job now to repackage the term on the right to match an answer choice. This can be done by stating 999998 as (10^6-2), giving us:

$$(10^6)(10^6 -2)$$ which is answer choice C.

What’s important to recognize here is that many algebra-based problems will hinge on your ability to take what you’re given and repackage it as something more useful. In this situation, know your assets. Tools like Difference of Squares can make repackaging algebra quite transformative. Seeing the answer choices as a guide is also instrumental to many of these problems as the choices give you a blueprint of what the algebra ultimately needs to look like. Repackaging is a huge component of the business world, as you can see with products like the Nike Free running shoes (want to run barefoot? We can make that happen – just buy these barefoot-running shoes!) and nearly every movie nowadays (remakes having replaced sequels as the easy-to-greenlight film category). Keep this principle in mind on the GMAT and you, too, can turn nothing into something, repackaging your 570 as a 750 in no time!
_________________
Manager
Joined: 21 Jun 2017
Posts: 78

### Show Tags

15 Oct 2017, 06:48
Bunuel wrote:
$$999,999^2-1$$ equals:

(A) $$(9^6)(11^6)$$

(B) $$(10^6)(10^5 -2)$$

(C) $$(10^6)(10^6 -2)$$

(D) $$(10^5)^2$$

(E) $$(10^6)^2$$

Kudos for a correct solution.

(999,9999 -1)(999,999 + 1) = 999,998 x 1,000,000 = (10^6 - 2) (10^6)
Re: 999,999^2-1 equals: &nbs [#permalink] 15 Oct 2017, 06:48
Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.