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Source: — Data Sufficiency |
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by sanabk » Wed Sep 15, 2010 2:57 pm
Is x > 10^10 ?

(1) x > 2^34

2^34=(2^10)(2^10)(2^10)(2^4)
=(1024)(1024)(1024)(16)
=(10^3)(10^3)(10^3)(10*1.6)
=1.6*10^10 (approximately) > 10^10

SUFFICIENT

(2) x = 2^35
3.2*10^10 (approximately) > 10^10

SUFFICIENT
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by singhsa » Thu Sep 16, 2010 2:58 am
sanabk wrote:Is x > 10^10 ?

(1) x > 2^34

2^34=(2^10)(2^10)(2^10)(2^4)
=(1024)(1024)(1024)(16)
=(10^3)(10^3)(10^3)(10*1.6)
=1.6*10^10 (approximately) > 10^10

SUFFICIENT

(2) x = 2^35
3.2*10^10 (approximately) > 10^10

SUFFICIENT
Thanks....guess i blanked out here.....2^10=10^2 (approx.)
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by GMATGuruNY » Thu Sep 16, 2010 6:48 am
singhsa wrote:Is x > 10^10 ?

(1) x > 2^34

(2) x = 2^35

Is there a quick way to solve this ?

OA - D
Since we don't need to determine the exact value of x, we can approximate. Here's a quick way:

10^10 = (2*5)^10 = (2*2*2*1.2)^10 = (2^3)^10 * (1.2)^10 = (2^30)*6 = approximately.

So the question becomes: Is x > (2^30)*6?

1. 2^34 = (2*30)*(2^4) = (2^30)*16. (2^30)*16 > (2^30)*6. Sufficient.
2. Since we saw in statement 1 that 2^34 > (2^30)*6, we know that 2^35 > (2^30)*6. Sufficient.

The correct answer is D.
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