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
