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championspunch
- Newbie | Next Rank: 10 Posts
- Posts: 7
- Joined: Mon Apr 08, 2013 3:51 pm
Target question: Is x > 10^10?championspunch wrote:Is x > 10^10 ?
(1) x > 2^34
(2) x = 2^35
Statement 2: x = 2^35
Notice that I'm looking at statement 2 first. Why?
Well, this statement tells me the exact value of x.
So, if I wanted to, I could evaluate 2^35, and then determine whether or not x is greater 10^10
So, since I could use statement 2 to answer the target question with certainty, statement 2 is SUFFICIENT
Important: Now that I know statement 2 is sufficient, the correct answer must be either B or D. Great! After 5 seconds work, I have a 50% chance of guessing correctly.
Statement 1: x > 2^34
We basically need to compare 2^34 with 10^10.
Now notice that 2^34 = (2^10)(2^24)
Also notice that 10^10 = (2^10)(5^10)
So, if we divide both quantities by 2^10, we can see that we need to compare 2^24 with 5^10
Now notice that:
2^24 = (2^12)^2
and 5^10 = (5^5)^2
So, if we find the square root of both quantities , we can see that we need to compare 2^12 with 5^5
This is pretty manageable.
2^12 = (2^6)(2^6)
= (64)(64)
= 3600+
5^5 = (5^4)(5)
= (625)(5)
= 3100 (approx)
So, since 2^12 > 5^5, we can be certain that 2^24 > 5^10, which means 2^34 > 10^10, which means x must be greater than 10^10
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Answer = D
Cheers,
Brent
