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Exponent Problem

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Source: — Data Sufficiency |
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by GMATGuruNY » Sun Apr 24, 2011 2:01 pm
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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by jaymw » Mon Apr 25, 2011 1:43 am
akshatgupta87 wrote:
Q.) Is x > 10^10 ?

(1) x > 2^34

(2) x = 2^35

Someone explain.
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 10³

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.
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