Is x> 10^10?
1) x> 2^34
2) x= 2^35
Quick solution to verify A?
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Tricky option A.
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Mike@Magoosh
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Hi, there. I'll give my 2 cents on this. 
Is x> 10^10?
1) x> 2^34
2) x= 2^35
The first thing I'll say is --- this seem to me well beyond what the real GMAT expects of students. This kind of exponential estimation is not something I have seen asked on the real GMAT.
So, without a calculator, what can we do?
We know 2^10 = 1024 ~ 1000 = 10^3, so
2^20 ~ 10^6
2^30 ~ 10^9
(BTW, the "kilo-" and "Mega-" they use in computer science, as in kb or Mb, are actually 2^10 and 2^20, not 1000 and 100000.)
Technically, the powers of two are slightly larger than the powers of 10, so 2^30 > 10^9.
Well, 2^4 = 16 > 10, so 2^34 = (2^30)*(2^4) > (10^9)*(10) = 10^10
So, this implies that if x is 2^34 or anything greater than that, then it's greater than 10^10. The calculator verifies that 17,179,869,184, which is slightly larger than 10^10.
Both statements are sufficient. Answer = D
Again, this kind of estimation is beyond what I have seen the GMAT asking of students.
Here's an example of an estimation question the GMAT is much more likely to ask.
https://gmat.magoosh.com/questions/50
When you submit your answer to that, the next page will have the video explanation of the problem.
Does all this make sense? Please let me know if you have any questions.
Mike
Is x> 10^10?
1) x> 2^34
2) x= 2^35
The first thing I'll say is --- this seem to me well beyond what the real GMAT expects of students. This kind of exponential estimation is not something I have seen asked on the real GMAT.
So, without a calculator, what can we do?
We know 2^10 = 1024 ~ 1000 = 10^3, so
2^20 ~ 10^6
2^30 ~ 10^9
(BTW, the "kilo-" and "Mega-" they use in computer science, as in kb or Mb, are actually 2^10 and 2^20, not 1000 and 100000.)
Technically, the powers of two are slightly larger than the powers of 10, so 2^30 > 10^9.
Well, 2^4 = 16 > 10, so 2^34 = (2^30)*(2^4) > (10^9)*(10) = 10^10
So, this implies that if x is 2^34 or anything greater than that, then it's greater than 10^10. The calculator verifies that 17,179,869,184, which is slightly larger than 10^10.
Both statements are sufficient. Answer = D
Again, this kind of estimation is beyond what I have seen the GMAT asking of students.
Here's an example of an estimation question the GMAT is much more likely to ask.
https://gmat.magoosh.com/questions/50
When you submit your answer to that, the next page will have the video explanation of the problem.
Does all this make sense? Please let me know if you have any questions.
Mike
Magoosh GMAT Instructor
https://gmat.magoosh.com/
https://gmat.magoosh.com/
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GMATGuruNY
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To compare exponents, try to get SIMILAR BASES.bryan88 wrote:Is x> 10^10?
1) x> 2^34
2) x= 2^35
Quick solution to verify A?
It is helpful to have memorized the powers of 2 up to 2¹�.
2¹� = 1024 ≈ 10³.
Statement 1: x > 2³�
2³� > 10¹�
2¹� * 2¹� * 2¹� * 2� > 10¹�
10³ * 10³ * 10³ * 16 > 10¹�
10� * 16 > 10� * 10
The lefthand side is greater than the righthand side.
Thus, x > 10¹�.
SUFFICIENT.
Statement 2: x = 2³�
Since the value of x is known, we can determine whether x > 10¹�.
SUFFICIENT.
The correct answer is D.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
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10^10 = (2*5)^10 = (2^10)*(5^10)bryan88 wrote:Is x> 10^10?
1) x> 2^34
2) x= 2^35
Quick solution to verify A?
I use the following approximation:
5^3 = 125 ≈ 128 = 2^7 and 5 ≈ 2^2
Thus,
10^10 = 2^10 * (5^3)^3 * 5 ≈ 2^10 * 2^21 * 2^2 ≈ 2^33
Hence, both statements are sufficient
