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

 It is currently 26 May 2019, 17:13 ### 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
Your Progress

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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. ### Request Expert Reply # The value of (10^8-10^2)/(10^7-10^3) is closest to which of

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Manager  Joined: 12 Jan 2013
Posts: 145
Re: The value of (10^8-10^2)/(10^7-10^3) is closest to which of  [#permalink]

### Show Tags

jcbruin wrote:
The value of (10^8-10^2)/(10^7-10^3) is closest to which of the following?

A. 1
B. 10
C. 10^2
D. 10^3
E. 10^4

Any thoughts on the quickest way to solve? I factored out 10^2 in the numerator and 10^3 in the denominator.

Thanks!

Factor both numerator and denominator:

10^2(10^6 - 1) / 10^3(10^4 - 1), because the subtractions in the parenthesis are extremely small, we ignore the subtraction, so we have: 10^8 / 10^7

Now, multiply the expression by 10^-7/10^-7 and thus we have 10^1/1 = 10. Answer B.
SVP  Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1812
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: The value of (10^8-10^2)/(10^7-10^3) is closest to which of  [#permalink]

### Show Tags

10^8 is way too high from 10^2, similarly 10^7 is way too high from 10^3
No need to make any further simplification calculation, just calculate 10^8 / 10^7 = 10 = Answer = B
_________________
Kindly press "+1 Kudos" to appreciate Manager  Joined: 20 Dec 2013
Posts: 226
Location: India
Re: The value of (10^8-10^2)/(10^7-10^3) is closest to which of  [#permalink]

### Show Tags

Option B.
Factor the numerator and denominator.
{[(10^4)-10] [10^4+10]}/10^3(10^4-1)
Taking 10 common from each term in numerator.
{10^2[(10^3-1)(10^3+1)]}/10^3[(10^2-1)(10^2+1)]

After further factorization and cancellation We're left with
(111*91)/10*101=9.99 or 10

Posted from my mobile device
Intern  Joined: 09 Sep 2015
Posts: 1
Re: The value of (10^8-10^2)/(10^7-10^3) is closest to which of  [#permalink]

### Show Tags

I think the easiest way to solve this is to use the quotient rule. Since all bases are the same (10), split the problem into two fractions, use the quotient rule on each, then subtract.

(10^8-10^2)/(10^7-10^3) =

(10^8/10^7) - (10^2/10^3) =

10 - (10^-1) =

10 - (1/10) =

10 - 0.1 =

9.9 =

B.
Manager  Joined: 21 Jan 2014
Posts: 96
GMAT 1: 500 Q32 V28 GPA: 4
Re: The value of (10^8-10^2)/(10^7-10^3) is closest to which of  [#permalink]

### Show Tags

Why we can't simply eliminate 10^8 with 10^7 and so on?

I did in this way and this is what I got:

1) 10^8 - 10^2 / 10^7 - 10^3;
2) I eliminate 10^8 with 10^7 and I got 10 on the up left side;
3) then I eliminate 10^2 with 10^3 and got zero on the up ritghtside and 10 on the down right side;
4) so, basically I left with 10 - 0 / - 10;
5) 10 / -10 = -1;
Because there isn't -1 on the answer choices I pick 1 that is the closest one.

What is wrong with my line of reasoning? I saw many times calculations involving exponents elimination if there is a division.

Thanks in advance for the explanation
Intern  B
Joined: 22 Jul 2016
Posts: 23
The value of (10^8-10^2)/(10^7-10^3) is closest to which of  [#permalink]

### Show Tags

As the question asks for approximation, let's tackle it in the same way :

Numerator : $$10^8-10^2$$ : $$10^2$$ is 0.00001% of $$10^8$$ ,which is negligible when compared to $$10^8$$
denominator: $$10^7-10^3$$ : $$10^3$$ is 0.0001% of $$10^7$$ ,which is negligible when compared to $$10^7$$

Hence ,($$10^8$$) - (negligible) / ($$10^7$$) - (negligible)= $$10^8$$/$$10^7$$ =10

Ans : B
Manager  B
Joined: 04 May 2014
Posts: 158
Location: India
WE: Sales (Mutual Funds and Brokerage)
Re: The value of (10^8-10^2)/(10^7-10^3) is closest to which of  [#permalink]

### Show Tags

It is not

If you multiply the denominator by 10 you get very close to the numerator. No need to do exact calculatio

999999/99990

99990X10=999900 which is only 99 less than the numerator.

gmontalvo wrote:
I've run across several variants of the following question:
$$\frac{10^8 - 10^2}{10^7 - 10^3}$$

Here is the approach I want to take:
$$\frac{10^2(10^6 - 1)}{10^3(10^4 - 1)}$$

But when I cancel the numerator/demoninator what I am left with is kind of ugly.
$$\frac{999999}{99990}$$

Is there something I am missing? Is there a better way? Or should I just suck it up and do the division?
Manager  B
Joined: 18 Jun 2017
Posts: 59
Re: The value of (10^8-10^2)/(10^7-10^3) is closest to which of  [#permalink]

### Show Tags

10^8-10^2 similar to 10^8
10^7-10^3 similar to 10^7
Now (10^8-10^2)/(10^7-10^3) will give us 10^8/10^7 i.e. 10.
Option B.
Director  V
Joined: 04 Dec 2015
Posts: 751
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)
Re: The value of (10^8-10^2)/(10^7-10^3) is closest to which of  [#permalink]

### Show Tags

jcbruin wrote:
The value of (10^8-10^2)/(10^7-10^3) is closest to which of the following?

A. 1
B. 10
C. 10^2
D. 10^3
E. 10^4

Any thoughts on the quickest way to solve? I factored out 10^2 in the numerator and 10^3 in the denominator.

Thanks!

$$\frac{(10^8-10^2)}{(10^7-10^3)}$$

$$\frac{10^2(10^6-1)}{10^3(10^4-1)}$$

'$$1$$' is very small value compared to $$10^6$$ and $$10^4$$, hence we can approximate value to $$10^6$$ and $$10^4$$. Therefore;

$$\frac{10^2*10^6}{10^3*10^4}$$

$$\frac{10^8}{10^7} = 10^{(8-7)} = 10^1 = 10$$

Answer (B)...
Senior Manager  V
Joined: 22 Feb 2018
Posts: 428
Re: The value of (10^8-10^2)/(10^7-10^3) is closest to which of  [#permalink]

### Show Tags

jcbruin wrote:
The value of (10^8-10^2)/(10^7-10^3) is closest to which of the following?

A. 1
B. 10
C. 10^2
D. 10^3
E. 10^4

Any thoughts on the quickest way to solve? I factored out 10^2 in the numerator and 10^3 in the denominator.

Thanks!

OA:B
$$\frac{(10^8-10^2)}{(10^7-10^3)}=\frac{10^2(10^6-1)}{10^3(10^4-1)}=\frac{10^2(10^3-1)(10^3+1)}{10^3(10^2-1)(10^2+1)}=\frac{10^2(10-1)(10^2+10*1+1)(10^3+1)}{10^3(10-1)(10+1)(10^2+1)}$$
$$\frac{10^2(10-1)(10^2+10*1+1)(10^3+1)}{10^3(10-1)(10+1)(10^2+1)}=\frac{10^2(9)(111)(1001)}{10^3(9)(11)(101)}=\frac{(111)(1001)}{10(11)(101)}≈10$$
_________________
Good, good Let the kudos flow through you
Target Test Prep Representative D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6241
Location: United States (CA)
Re: The value of (10^8-10^2)/(10^7-10^3) is closest to which of  [#permalink]

### Show Tags

jcbruin wrote:
The value of (10^8-10^2)/(10^7-10^3) is closest to which of the following?

A. 1
B. 10
C. 10^2
D. 10^3
E. 10^4

We see that since 10^2 is MUCH SMALLER than 10^8 and 10^3 is MUCH smaller than 10^7, subtracting 10^2 from 10^8 does not appreciably change the value, and subtracting 10^3 from 10^7 does not appreciably change the value. Thus, the approximate value of (10^8-10^2)/(10^7-10^3) is:

(10^8)/(10^7) = 10

Answer: B
_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

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

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 14209
Location: United States (CA)
GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: The value of (10^8-10^2)/(10^7-10^3) is closest to which of  [#permalink]

### Show Tags

Hi All,

We're asked to choose the answer that is CLOSEST in value to (10^8-10^2)/(10^7-10^3). While you might be tempted to try lots of 'math steps', if you consider how the answer choices are written, you can use a bit of estimation and logic to get to the correct answer without doing too much math.

To start, when the answer choices are based around increased exponents, it's worth noting that those answers are NOT "close" to one another. Each of the answers here is a 'power of 10', and each answer is 10 TIMES greater than the one immediately above it.

With the numerator of the given fraction, instead of factoring, consider how 10^8 compares to (10^8 - 10^2)....

10^8 = 100,000,000
10^2 = 100

Difference = 99,999,900

100,000,000 is essentially the same as 99,999,900. Next, we can think about the denominator in the same terms...

10^7 = 10,000,000
10^3 = 1,000

Difference = 9,999,000

This means that 10,000,000 is essentially the same as 9,999,999...

Thus, we're essentially just asked to divide 10 million by 1 million... and that equals 10.

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

# Rich Cohen

Co-Founder & GMAT Assassin Follow
Special Offer: Save \$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/
Senior Manager  G
Status: Gathering chakra
Joined: 05 Feb 2018
Posts: 263
The value of (10^8-10^2)/(10^7-10^3) is closest to which of  [#permalink]

### Show Tags

1) Factor powers of 10 and reduce. 10^2*(10^6-1) / 10^2*(10^5-1)

2) Thinking about it logically, 10^6 has 7 place values from 1, so when we subtract 1 it loses a 0 place value. Same for 10^5 - 1.
Therefore, we have 6 place values / 4 place values. But we also have an additional 10 in the denominator, so it's actually 6 place values / 5 place values = 1 place value more in numerator so it should be B. The value of (10^8-10^2)/(10^7-10^3) is closest to which of   [#permalink] 10 Mar 2019, 07:48

Go to page   Previous    1   2   [ 33 posts ]

Display posts from previous: Sort by

# The value of (10^8-10^2)/(10^7-10^3) is closest to which of

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics 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®.

#### MBA Resources  