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

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10^180-10^30. Which of the following best approximates [#permalink] New post 24 Sep 2009, 09:08
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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
[Reveal] Spoiler: OA

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Re: GMAT, Number Properties, Exponents [#permalink] New post 24 Sep 2009, 10:03
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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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Re: GMAT, Number Properties, Exponents [#permalink] New post 17 Jan 2012, 09:18
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?
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Re: GMAT, Number Properties, Exponents [#permalink] New post 17 Jan 2012, 14:27
Expert's post
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.
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Re: 10^180-10^30. Which of the following best approximates [#permalink] New post 17 Jan 2012, 19:17
+1 for B

Is this an actual question for somewhere? It feels ridiculously easy
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Re: GMAT, Number Properties, Exponents [#permalink] New post 08 Jul 2013, 17:25
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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Re: GMAT, Number Properties, Exponents [#permalink] New post 08 Jul 2013, 22:09
Expert's post
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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Hope it helps.
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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

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Re: GMAT, Number Properties, Exponents [#permalink] New post 08 Jul 2013, 23:27
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, 22:01
10^180 is way too higher than 10^30,
10^180 is the Answer = A
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Re: 10^180-10^30. Which of the following best approximates   [#permalink] 26 Feb 2014, 22:01
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