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

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(10^8 - 10^2) / (10^7 - 10^3)  [#permalink]

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New post 07 Sep 2016, 17:30
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Difficulty:

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Question Stats:

69% (01:56) correct 31% (02:13) wrong based on 282 sessions

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I struggled with this seemingly simple problem and would like some help.

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


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

PROPER VERSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/the-value-of ... 95082.html
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Re: (10^8 - 10^2) / (10^7 - 10^3)  [#permalink]

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New post 07 Sep 2016, 17:46
1
3
Let's look at numerator:

10^8 - 10^2 -> we can factor out 10^2.

10^8 - 10^2
= 10^2 * (10^6 - 1)
Now, 10^6 is way more than 1 so (10^6 - 1) can be reduced to 10^6.
Numerator = 10^2 * (10^6) = 10^8


Let's look at denominator:

10^7 - 10^3 -> we can factor out 10^3.

10^7 - 10^3
= 10^3 * (10^4 - 1)
Now, 10^4 is way more than 1 so (10^4 - 1) can be reduced to 10^4.
Denominator = 10^3 * (10^4) = 10^7

So, the original expression is reduced to 10^8 / 10^7 and this is equal to 10.

Answer (B).
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Re: (10^8 - 10^2) / (10^7 - 10^3)  [#permalink]

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New post 07 Sep 2016, 17:55
Donnie84 wrote:
Let's look at numerator:

10^8 - 10^2 -> we can factor out 10^2.

10^8 - 10^2
= 10^2 * (10^6 - 1)
Now, 10^6 is way more than 1 so (10^6 - 1) can be reduced to 10^6.
Numerator = 10^2 * (10^6) = 10^8


Let's look at denominator:

10^7 - 10^3 -> we can factor out 10^3.

10^7 - 10^3
= 10^3 * (10^4 - 1)
Now, 10^4 is way more than 1 so (10^4 - 1) can be reduced to 10^4.
Denominator = 10^3 * (10^4) = 10^7

So, the original expression is reduced to 10^8 / 10^7 and this is equal to 10.

Answer (B).


Thanks for the response, I appreciate it. I was not aware that I could simply eliminate the -1 :!: This is where I was getting stuck because I could not get the top & bottom to match up so that I could simplify.
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Re: (10^8 - 10^2) / (10^7 - 10^3)  [#permalink]

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New post 07 Sep 2016, 18:05
1
Gonaives wrote:
Donnie84 wrote:
Let's look at numerator:

10^8 - 10^2 -> we can factor out 10^2.

10^8 - 10^2
= 10^2 * (10^6 - 1)
Now, 10^6 is way more than 1 so (10^6 - 1) can be reduced to 10^6.
Numerator = 10^2 * (10^6) = 10^8


Let's look at denominator:

10^7 - 10^3 -> we can factor out 10^3.

10^7 - 10^3
= 10^3 * (10^4 - 1)
Now, 10^4 is way more than 1 so (10^4 - 1) can be reduced to 10^4.
Denominator = 10^3 * (10^4) = 10^7

So, the original expression is reduced to 10^8 / 10^7 and this is equal to 10.

Answer (B).


Thanks for the response, I appreciate it. I was not aware that I could simply eliminate the -1 :!: This is where I was getting stuck because I could not get the top & bottom to match up so that I could simplify.


Yes, in such problems, try to factor out as much as possible. You will be left with one very large term and either a very small term added or subtracted. The very small term can be safely ignored. There are several problems on this forum that test this concept. Please search the tag and try them out. You will definitely get the hang of it.
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Re: (10^8 - 10^2) / (10^7 - 10^3)  [#permalink]

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New post 07 Sep 2016, 19:16
1
Hi Gonaives,

While this prompt might appear 'scary', It might help to think about this question conceptually:

10^2 = 100
10^3 = 1,000

10^7 = 10,000,000
10^8 = 100,000,000

Notice how much BIGGER 10^8 and 10^7 are, relative to 10^3 and 10^2? That's the 'key' to this question. In the numerator, subtracting 100 from 100,000,000 would have almost no mathematical 'impact' on the calculation (and the same can be said about the subtraction in the denominator). As such, the question is ultimately asking...

10^8/10^7 = ?

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Re: (10^8 - 10^2) / (10^7 - 10^3)  [#permalink]

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New post 09 Jan 2017, 03:30
Gonaives wrote:
I struggled with this seemingly simple problem and would like some help.

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


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

It is a really easy problem... According to division rule of powers with same base. we need to subtract the powers. so the question goes like

10^8-10^2 / 10^7-10^3
subtract power 8 from power 7 We get 10^1
then, subtract power 2 with power 3 we get 10^-1
in the end we are left with 10^1-10^-1 and the answer is 10
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Re: (10^8 - 10^2) / (10^7 - 10^3)  [#permalink]

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New post 09 Jan 2017, 03:39
Tanyanagra wrote:
Gonaives wrote:
I struggled with this seemingly simple problem and would like some help.

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


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

It is a really easy problem... According to division rule of powers with same base. we need to subtract the powers. so the question goes like

10^8-10^2 / 10^7-10^3
subtract power 8 from power 7 We get 10^1
then, subtract power 2 with power 3 we get 10^-1
in the end we are left with 10^1-10^-1 and the answer is 10


Unfortunately this is not correct approach.

1. \(\frac{(10^{8} - 10^{2})}{(10^{7} - 10^{3})}\) does not equal to \(\frac{10^{8}}{10^{7}}-\frac{10^2}{10^3}\). For example, (6-2)/(2-1)=4 does not equal to 6/2 - 2/1 = 1. You cannot break a fraction this way.

2. 10^1 - 10^(-1) = 99/10 not 10.

Theory on Exponents: math-number-theory-88376.html
Tips on Exponents: exponents-and-roots-on-the-gmat-tips-and-hints-174993.html

All DS Exponents questions to practice: search.php?search_id=tag&tag_id=39
All PS Exponents questions to practice: search.php?search_id=tag&tag_id=60

Tough and tricky DS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125967.html
Tough and tricky PS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125956.html

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Re: (10^8 - 10^2) / (10^7 - 10^3)  [#permalink]

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New post 11 Jan 2017, 06:59
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Gonaives wrote:
I struggled with this seemingly simple problem and would like some help.

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


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


This problems is testing us on our knowledge of the relationship between bases raised to exponents as well as estimation of exponents.

Starting with the numerator, we see that 10^8 = 100,000,000 is much larger than 10^2 = 100; therefore 10^8 - 10^2 is still approximately 10^8.

In the denominator, 10^7 = 10,000,000 is much larger than 10^3 = 1,000; therefore 10^7 - 10^3 is still approximately 10^7.

Thus, (10^8 - 10^2)/(10^7 - 10^3) is approximately 10^8/10^7 = 10.

Answer: B

(Note: this problem should have asked for the approximate value of (10^8 - 10^2)/(10^7 - 10^3)).
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Re: (10^8 - 10^2) / (10^7 - 10^3)  [#permalink]

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New post 11 Jan 2017, 18:14
Didn't really know that we could just ignore the 1.

I was stuck at (10^6 - 1) / 10(10^4 - 1) ..

Thanks for the explanation.
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Re: (10^8 - 10^2) / (10^7 - 10^3)  [#permalink]

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New post 28 Jan 2017, 05:03
So the question is wrong? I mean if they told they want the APPROXIMATE value, I would have done it in a completely different way and not waste time trying to cancel out the fraction to get a round number.

Is it "mandatory" that the official question specifies that they want the approximate value in such cases? Because this realy induces the test taker in error!..

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Re: (10^8 - 10^2) / (10^7 - 10^3)  [#permalink]

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New post 30 Jan 2017, 16:37
2
iliavko wrote:
So the question is wrong? I mean if they told they want the APPROXIMATE value, I would have done it in a completely different way and not waste time trying to cancel out the fraction to get a round number.

Is it "mandatory" that the official question specifies that they want the approximate value in such cases? Because this realy induces the test taker in error!..

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what do you think? Thank you!


Yes, on the GMAT such a question would ask something like, “What is the approximate value of (10^8 - 10^2)/(10^7 - 10^3)?” or “(10^8 - 10^2)/(10^7 - 10^3) is closest to which of the following?”

In fact, I think the original poster meant to post this exact question: https://gmatclub.com/forum/the-value-of ... 95082.html

Notice the words “closest to” in the question stem.
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Re: (10^8 - 10^2) / (10^7 - 10^3)  [#permalink]

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New post 04 Sep 2018, 12:20
ScottTargetTestPrep wrote:
iliavko wrote:
So the question is wrong? I mean if they told they want the APPROXIMATE value, I would have done it in a completely different way and not waste time trying to cancel out the fraction to get a round number.

Is it "mandatory" that the official question specifies that they want the approximate value in such cases? Because this realy induces the test taker in error!..

ScottTargetTestPrep
what do you think? Thank you!


Yes, on the GMAT such a question would ask something like, “What is the approximate value of (10^8 - 10^2)/(10^7 - 10^3)?” or “(10^8 - 10^2)/(10^7 - 10^3) is closest to which of the following?”

In fact, I think the original poster meant to post this exact question: https://gmatclub.com/forum/the-value-of ... 95082.html

Notice the words “closest to” in the question stem.



HiBunuel,

Since the question is not correctly presented as it is in the Official Gmat Prep, could you merge the questions and correct the Question Stem.

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Re: (10^8 - 10^2) / (10^7 - 10^3)  [#permalink]

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New post 04 Sep 2018, 20:05
Gonaives wrote:
I struggled with this seemingly simple problem and would like some help.

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


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


PROPER VERSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/the-value-of ... 95082.html
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: (10^8 - 10^2) / (10^7 - 10^3) &nbs [#permalink] 04 Sep 2018, 20:05
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