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shampoo
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10^8 - 10^2)/ (10^7 - 10^3), is closest to? a. 1 b. 24 May 2006, 19:35
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67% (00:00) correct 33% (00:00) wrong based on 6 sessions

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(10^8 - 10^2)/ (10^7 - 10^3), is closest to?

a. 1
b. 10
c. 10^2
d. 10^3
e. 10^4

please explain how to tackle these type of questions I am really bad at these.



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10^8 - 10^2)/ (10^7 - 10^3), is closest to? a. 1 b. 24 May 2006, 20:07
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(10^8 - 10^2)/ (10^7 - 10^3), is closest to?

B is the answer. 10 it is.

(10^8-10^2)/(10^7-10^3) = (10*10*10^6-10^2)/10*(10^6-10^2) ≈ 10.
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Professor
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10^8 - 10^2)/ (10^7 - 10^3), is closest to? a. 1 b. 24 May 2006, 20:12
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shampoo
(10^8 - 10^2)/ (10^7 - 10^3), is closest to?
a. 1
b. 10
c. 10^2
d. 10^3
e. 10^4
please explain how to tackle these type of questions I am really bad at these.
Show more


= (10^8 - 10^2)/ (10^7 - 10^3)
= 10^2(10^6 - 1)/ [10^3(10^4 - 1)]
= (10^6 - 1)/ [10(10^4 - 1)]
= 10^6 / [10(10^4)] because (10^6 - 1) is close to 10^6 and (10^4 - 1) is close to 10^4.

= 10^6 / 10^5
= 10

so B.
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10^8 - 10^2)/ (10^7 - 10^3), is closest to? a. 1 b. 24 May 2006, 20:19
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(10^8 - 10^2) / (10^7 - 10^3)
= 10^2(10^6 - 1)/10^2(10^5-10)

10^6 - 1 --> insignificant, can be rounded off to 10^6

10^5 - 10 --> insignificant, can be rounded off to 10^5

Ans: 10
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10^8 - 10^2)/ (10^7 - 10^3), is closest to? a. 1 b. 25 May 2006, 00:37
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10 it is

(10^8 - 10^ 2)/(10^7-10^3)
=> 10^2(10^6-1)/10^3(10^4-1)
=> (10^6-1)/(10^5-10)

Can be rounded to 10^6/10^5 = 10
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10^8 - 10^2)/ (10^7 - 10^3), is closest to? a. 1 b. 25 May 2006, 07:37
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interesting approach...i didnt factor 10^2 or 10^3 out

i pretty much estimaed 10^8 is fairly large compared to 10^2 so i estimate this to 10^8

same thing with 10^7-10^3..is ~10^7

so then i get 10^8/10^7=~10
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10^8 - 10^2)/ (10^7 - 10^3), is closest to? a. 1 b. 25 May 2006, 08:17
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I am getting B

Factor out 10^2[10^6-1]/[10^3[10^4-1]

which gives

10^-1[10^2]

which is approximately 10
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10^8 - 10^2)/ (10^7 - 10^3), is closest to? a. 1 b. 25 May 2006, 09:19
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Doesnt' the rule of when bases are the same powers add applies here.

10 ^ 8 - 10 ^ 6 = 10 ^ 8-6 = 10 ^ 2

Or I got it all wrong...!!
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10^8 - 10^2)/ (10^7 - 10^3), is closest to? a. 1 b. 25 May 2006, 09:44
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thanks everyone, OA is 10.

btw, what difficulty level this question is?
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10^8 - 10^2)/ (10^7 - 10^3), is closest to? a. 1 b. 16 Mar 2009, 18:35
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What is the fastest way to solve this:
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10^8 - 10^2)/ (10^7 - 10^3), is closest to? a. 1 b. 16 Mar 2009, 19:19
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Given :

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

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

therefore 10.
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10^8 - 10^2)/ (10^7 - 10^3), is closest to? a. 1 b. 16 Mar 2009, 22:47
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The answer should be 10 only.

Lets take it this way:
(10^8-10^2)/(10^7-10^3) can be written as
10^2(10^6-1)/10^3(10^4-1) - taking 10^2 & 10^3 common from numerator and denominator respectively.
Now, 10^6>>1 so we can say that 10^6-1 is approximately equal to 10^6.
Similarly, 10^4>>1 so we can say that 10^4-1 is approximately equal to 10^4.

So, the expression now becomes : (10^2*10^6)/(10^3*10^4).

or, 10^8/10^7
or, 10.
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10^8 - 10^2)/ (10^7 - 10^3), is closest to? a. 1 b. 02 Apr 2010, 03:33
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I have a slightly different approach which is easy and takes you 30 seconds. (However I also got it wrong on my GMATprep)

You can rewrite the term: 10^8 / 10^7 - 10^2 / 10^3

Now we know that two exponents with the same base (10) and which are divided by each other can be deducted from each other.

Therefore we get: 10^1 - 10^-1
This is the same as 10 - 1/10 = This is obviously closest to 10
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10^8 - 10^2)/ (10^7 - 10^3), is closest to? a. 1 b. 02 Apr 2010, 03:36
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alimad
Doesnt' the rule of when bases are the same powers add applies here.

10 ^ 8 - 10 ^ 6 = 10 ^ 8-6 = 10 ^ 2

Or I got it all wrong...!!
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You can only apply this rule if the two numbers are divided by each other.
I used this approach in my solution:

You can rewrite the term: 10^8 / 10^7 - 10^2 / 10^3

Now we know that two exponents with the same base (10) and which are divided by each other can be deducted from each other.

Therefore we get: 10^1 - 10^-1
This is the same as 10 - 1/10 = This is obviously closest to 10



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