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Anindya Madhudor
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Anindya Madhudor wrote:Is x > 10^10?
i. x> 2^34
ii. x=2^35
Target question: Is x > 10^10?
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
This one is much trickier. Here's how I'd approach the question.
Edit: This is a lengthy solution. I realized a faster approach, which can be found in the post after this one.
I basically need to compare 2^34 with 10^10.
If 2^34 is less than 10^10, then x could be greater than or less than 10^10
If 2^34 is greater than 10^10, then x must be greater than 10^10
Important: Notice that 2^34 = (2^3.4)^10
So rather than compare (2^3.4)^10 with 10^10, we can compare 2^3.4 with 10
Which is greater?
A calculator would be nice, but no such luck.
Now I do happen to know that sqrt(2) = 1.4 (approximately), and this will help us get a feel for the value of 2^3.4
Aside: I recommend that students memorize the following roots:
sqrt(2) = 1.4 (approximately)
sqrt(3) = 1.7 (approximately)
sqrt(5) = 2.2 (approximately)
These can come in handy at times . . . like now!
So, let's examine 2^3.5 (which is kind of close to 2^3.4)
2^3.5 = (2^3)(2^0.5)
= (8)(sqrt2) [since k^0.5 = sqrtk]
= (8)(1.4) ...approximately
= 11.2 approximately
So, I know that 2^3.5 = 11.2 (approx)
From this, what can we conclude about 2^3.4?
Well, we might use a bit of number sense to conclude (correctly) that 2^3.4 is greater than 10.
So, if 2^3.4 > 10, we can be certain that (2^3.4)^10 > 10^10, 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
