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10^180-10^30. Which of the following best approximates

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gmatjon
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10^180-10^30. Which of the following best approximates [#permalink] New post   24 Sep 2009, 10:08
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10^180 - 10^30 =
Which of the following best approximates the value of the expression above?

(A) 10^180
(B) 10^179
(C) 10^170
(D) 10^160
(E) 10^150
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A
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AKProdigy87
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Re: GMAT, Number Properties, Exponents [#permalink] New post   24 Sep 2009, 11:03
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The answer is A: 10^180.

10^180 - 10^30
= 10^30 (10^150 - 1)
~ 10 ^30 (10^150)
~ 10^180

This is more about the relative scale of the quantities than anything. It's easier to think about it with numbers you can picture, so assume you have an equation like 1 000 000 000 (10^7) - 100 (10^2). This equation can still be approximated as 10^7, since the latter term is so insignificantly small compared to the former term.
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10^180-10^30. Which of the following best approximates [#permalink] New post   17 Jan 2012, 15:27
Expert Reply
10^180 - 10^30 =
Which of the following best approximates the value of the expression above?

(A) 10^180
(B) 10^179
(C) 10^170
(D) 10^160
(E) 10^150

10^180 - 10^30 =
Which of the following best approximates the value of the expression above?

Yes, answer 10^180 is correct. Note that we need approximate value of the given expression and as 10^(180) is much larger number than 10^(30) then 10^(30) is pretty much negligible in this case: 10^(180)-10^(30)=~10^(180).

Check similar question for practice: https://gmatclub.com/forum/tough-and-tri ... l#p1029229

Hope it helps.
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Re: GMAT, Number Properties, Exponents [#permalink] New post   08 Jul 2013, 18:25
Bunuel wrote:
Baten80 wrote:
I found the answer options are:
a. 10^210
b. 10^180
c. 10^150
d. 10^90
e. 10^6

I answered B.
What is correct?


10^180 - 10^30 =
Which of the following best approximates the value of the expression above?

Yes, answer 10^180 is correct. Note that we need approximate value of the given expression and as 10^(180) is much larger number than 10^(30) then 10^(30) is pretty much negligible in this case: 10^(180)-10^(30)=~10^(180).

Check similar question for practice: tough-and-tricky-exponents-and-roots-questions-125956-40.html#p1029229

Hope it helps.


Hi Bunnel,
Their are two sets of options on this page.
How to decide b/w 10^180 and 10^179.
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10^180-10^30. Which of the following best approximates [#permalink] New post   08 Jul 2013, 23:09
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cumulonimbus wrote:
Bunuel wrote:
Baten80 wrote:
I found the answer options are:
a. 10^210
b. 10^180
c. 10^150
d. 10^90
e. 10^6

I answered B.
What is correct?


10^180 - 10^30 =
Which of the following best approximates the value of the expression above?

Yes, answer 10^180 is correct. Note that we need approximate value of the given expression and as 10^(180) is much larger number than 10^(30) then 10^(30) is pretty much negligible in this case: 10^(180)-10^(30)=~10^(180).

Check similar question for practice: tough-and-tricky-exponents-and-roots-questions-125956-40.html#p1029229

Hope it helps.


Hi Bunnel,
Their are two sets of options on this page.
How to decide b/w 10^180 and 10^179.


Still 10^180 would be correct.

To illustrate: \(10^{180}-10^{30}=10^{30}(10^{150}-1)\).

Now, \(10^{150}-1\) is VERY close to \(10^{150}\), thus \(10^{30}(10^{150}-1)\approx{10^{30}10^{150}=10^{180}}\).

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which-of-the-following-is-closest-to-10180-1030-a-110224.html
which-of-the-following-best-approximates-the-value-of-q-if-99674.html
new-tough-and-tricky-exponents-and-roots-questions-125956-40.html
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Hope it helps.
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Re: GMAT, Number Properties, Exponents [#permalink] New post   09 Jul 2013, 00:27
cumulonimbus wrote:
Bunuel wrote:
Baten80 wrote:
I found the answer options are:
a. 10^210
b. 10^180
c. 10^150
d. 10^90
e. 10^6

I answered B.
What is correct?


10^180 - 10^30 =
Which of the following best approximates the value of the expression above?

Yes, answer 10^180 is correct. Note that we need approximate value of the given expression and as 10^(180) is much larger number than 10^(30) then 10^(30) is pretty much negligible in this case: 10^(180)-10^(30)=~10^(180).

Check similar question for practice: tough-and-tricky-exponents-and-roots-questions-125956-40.html#p1029229

Hope it helps.


Hi Bunnel,
Their are two sets of options on this page.
How to decide b/w 10^180 and 10^179.


Hi cumulonimbus

I think 10^180 is closer. Because 1 is very small, 10^x - 1 is closer to 10^x than 10^(x-1).

Let try few examples, you can see the pattern.
10^2 - 1= 99 ==> closer to 10^2 = 100 than 10^1 = 10
10^3 - 1 = 999 ==> closer to 10^3 = 1000 than 10^2 = 100
10^4 - 1 = 9999 ===> closer to 10^4 = 10000 than 10^3 = 1000
.....
10^180 - 1 ==> closer to 10^180 than 10^179

Hope it helps.
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Re: 10^180-10^30. Which of the following best approximates [#permalink] New post   26 Feb 2014, 23:01
10^180 is way too higher than 10^30,
10^180 is the Answer = A
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10^180-10^30. Which of the following best approximates [#permalink] New post   29 Nov 2016, 14:13
gmatjon wrote:
10^180 - 10^30 =
Which of the following best approximates the value of the expression above?

(A) 10^180
(B) 10^179
(C) 10^170
(D) 10^160
(E) 10^150


Nice Question this one.
This is how i solved this one up
I didn't realise that 10^30 was negligible straight away

10^30 can be factored out here.
10^30(10^150 - 1)
Now 1 is definitely negligible w.r.t 10^150
Hence expression reduced to 10^30*10^150 => 10^180

Hence A
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Re: 10^180-10^30. Which of the following best approximates [#permalink] New post   30 Oct 2021, 05:29
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Re: 10^180-10^30. Which of the following best approximates [#permalink]
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