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505-555 (Easy)|   Exponents|      
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gmatjon
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10^180-10^30. Which of the following best approximates 24 Sep 2009, 10:08
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A
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15% (low)

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73% (00:45) correct 27% (01:12) wrong based on 439 sessions

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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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10^180-10^30. Which of the following best approximates 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 17 Jan 2012, 15:27
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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

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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10^180-10^30. Which of the following best approximates 08 Jul 2013, 18:25
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Bunuel
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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.
Show more

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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Bunuel
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10^180-10^30. Which of the following best approximates 08 Jul 2013, 23:09
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cumulonimbus
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Baten80
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.
Show more

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 \(10^{30}(10^{150}-1)\approx{10^{30}10^{150}=10^{180}}\).

Similar questions to practice:
the-value-of-10-8-10-2-10-7-10-3-is-closest-to-which-of-95082.html
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
if-x-10-10-x-2-2x-7-3x-2-10x-2-is-closest-to-143897.html
1-0-0001-0-04-10-the-value-of-the-expression-above-is-59398.html
m24-q-7-explanation-76513.html

Hope it helps.
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10^180-10^30. Which of the following best approximates 09 Jul 2013, 00:27
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cumulonimbus
Bunuel
Baten80
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.
Show more

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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10^180-10^30. Which of the following best approximates 26 Feb 2014, 23:01
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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 29 Nov 2016, 14:13
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gmatjon
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
Show more

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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10^180-10^30. Which of the following best approximates 20 Jun 2024, 22:20
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