Given that P is a natural number. Is P>1010? 1) P>234 2) P=235

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Given that P is a natural number. Is $P > 10^{10}$ ?
1) $P > 2^{34}$
2) $P = 2^{35}$

Options:

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: Option D
:
D
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 (10^{10}) > 10^{10}

, from statement 1 alone; the answer can be determined
From statement

2 - P = 2^{35}

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