Question

Given that P is a natural number. Is $P>{10}^{10}$?

1) $P>2^{34}$
2) $P=2^{35}$

• A. IF statement (1) alone is sufficient, but statement (2) is not
• B. If Statement (2) alone is sufficient but statement (1) is not
• C. If Both statements TOGETHER are sufficient, but neither statement ALONE is sufficient
• D. If Each statement ALONE is sufficient
• E. Statements (1) and (2) TOGETHER are not sufficient

Answer 1

The correct option is D If Each statement ALONE is sufficient

From statement $1-P>2^{34}$

$2^{34}=(2^{10}{)}^3\times 24=16\times (2^{10}{)}^3$

Now $2^{10}=1024$, and 1024 is greater than ${10}^3.$

Therefore
$2^{34}>16\times ({10}^3{)}^3=1.6({10}^{10})$

Since $2^{34}>1.6\left({10}^{10}\right)>{10}^{10}$, from statement 1 alone; the answer can be determined

From statement $2-P=2^{35}$