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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
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GPA: 3.39
The value of (10^8-10^2)/(10^7-10^3) is closest to which of the follow
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14 Sep 2022, 07:07
14 Sep 2022, 07:07
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80% (01:20) correct
20% (00:51) wrong based on 5 sessions
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The value of \(\frac{10^8-10^2}{10^7-10^3}\) is closest to which of the following?
A. 1
B. 10
C. 10^2
D. 10^3
E. 10^4
A. 1
B. 10
C. 10^2
D. 10^3
E. 10^4
Re: The value of (10^8-10^2)/(10^7-10^3) is closest to which of the follow
[#permalink]
18 Sep 2022, 10:34
18 Sep 2022, 10:34
1
Expert Reply
factoring out \(10^2\) and \(10^3\) and than reducing the fraction by \(10^2\) is one way to deal with this question:
\(\frac{10^8-10^2}{10^7-10^3}=\frac{10^2(10^6-1)}{10^3(10^4-1)}=\frac{10^6-1}{10*(10^4-1)}\).
Now, \(10^6-1\) is very close to \(10^6\) and \(10^4-1\) is very close to \(10^4\), hence \(\frac{10^6-1}{10*(10^4-1)}\approx{\frac{10^6}{10*10^4}=\frac{10^6}{10^5}=10}\).
Answer: B.
Or else you can notice that we need approximate value of a fraction. Now, \(10^{8}\) is much, much, much bigger than \(10^{2}\). So subtracting \(10^{2}\) from \(10^{8}\) will be very close to \(10^{8}\), basically \(10^{2}\) is negligible in this case. The same for for \(10^{7}\) and \(10^{3}\). So \(\frac{10^8-10^2}{10^7-10^3} \approx{\frac{10^8}{10^7}}=10\).
Hope it helps.
\(\frac{10^8-10^2}{10^7-10^3}=\frac{10^2(10^6-1)}{10^3(10^4-1)}=\frac{10^6-1}{10*(10^4-1)}\).
Now, \(10^6-1\) is very close to \(10^6\) and \(10^4-1\) is very close to \(10^4\), hence \(\frac{10^6-1}{10*(10^4-1)}\approx{\frac{10^6}{10*10^4}=\frac{10^6}{10^5}=10}\).
Answer: B.
Or else you can notice that we need approximate value of a fraction. Now, \(10^{8}\) is much, much, much bigger than \(10^{2}\). So subtracting \(10^{2}\) from \(10^{8}\) will be very close to \(10^{8}\), basically \(10^{2}\) is negligible in this case. The same for for \(10^{7}\) and \(10^{3}\). So \(\frac{10^8-10^2}{10^7-10^3} \approx{\frac{10^8}{10^7}}=10\).
Hope it helps.
gmatclubot
Re: The value of (10^8-10^2)/(10^7-10^3) is closest to which of the follow [#permalink]
18 Sep 2022, 10:34
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