Is x > 10^10?

1) x > 2^34
2) x = 2^35

Target question: Is x > 10^10?

Statement 1: x > 2^34
NOTE: if 2^34 > 10^10, then x will be greater than 10^10, in which case the statement is sufficient.
If 2^34 < 10^10, then x may or may not be greater than 10^10, in which case the statement is not sufficient

Since the statement is sufficient only if 2^34 > 10^10, we can reword the target question as Is 2^34 > 10^10?
- Apply exponent laws to rewrite both sides: Is (2^10)(2^24) > (2^10)(5^10)?
- Divide both sides by 2^10 to get: Is 2^24 > 5^10?
- Apply exponent laws to rewrite both sides: Is (2^12)² > (5^5)²?
- Take the square root of both quantities to get: Is 2^12 > 5^5?

This is pretty manageable.
- Rewrite both sides to get: Is (2^6)(2^6) > (5^4)(5)?
- Evaluate to get: Is (64)(64) > (625)(5)?
- Estimate to get: Is 3600+ > ≈3000?
The answer is a definite YES
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x = 2^35
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

Answer = D

Cheers,
Brent

Hi nandinitaneja,

Brent has shown one of the ways to re-organize the given values for comparison purposes. Here's another way to re-organize the numbers:

Once we get down to 2^12 vs. 5^5, to figure out which is bigger, we need to find a point at which the values are "pretty close"

2^7 = 128
3^5 = 125

With a little "playing around", it's not tough to get these values. So now we have....

2^12 = (2^7)(2^5) = (128)(32)
5^5 = (5^3)(5^2) = (125)(25)

Notice how each "piece" of 2^12 is bigger than the corresponding "piece" in 5^5. Those numbers prove that 2^12 is greater than 5^5.

GMAT assassins aren't born, they're made,
Rich