Q.) Is x > 10^10 ?
(1) x > 2^34
(2) x = 2^35
Someone explain.
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Exponent Problem
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akshatgupta87
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GMATGuruNY
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akshatgupta87 wrote:Q.) Is x > 10^10 ?
(1) x > 2^34
(2) x = 2^35
Someone explain.
Statement 1: x > 2^34.
We need to compare 2^34 to 10^10.
To make the comparison easier, take the square root of each value.
√(2^34) = 2^17.
√(10^10) = 10^5.
Now compare:
2^17 > 10^5
2^17 > (2^5)*(5^5)
2^12 > 5^5
4^6 > 5^5.
4^6 = (4^3)*(4^3) = 64*64 ≈ 4000.
5^5 = 5*(5^4) = 5*625 ≈ 3000.
Thus, 4^6 > 5^5.
Sufficient.
Statement 2: x = 2^35.
Gives us the exact value of x.
Thus, we can determine whether x > 10^10.
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.
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jaymw
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On the GMAT, it is occasionally very helpful to know the values of 2 raised to common powers. 2^10=1024 and is thus a little more than 10³akshatgupta87 wrote:
Q.) Is x > 10^10 ?
(1) x > 2^34
(2) x = 2^35
Someone explain.
Statement 1:
x > 2^34
x > 2^10*2^10*2^10*2^4
x > 1000*1000*1000*16 = 10^9*16 > 10^10
Sufficient.
Statement 2:
GMATGuruNY has already explained this in the most concise way possible. Whenever some variable is EQUAL to a certain value, it can ALWAYS be determined whether it is bigger or smaller than another value.
Sufficient.
Hence, D.
