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# Which of the following numbers is largest?

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Re: Which of the following numbers is largest? [#permalink]
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Bunuel wrote:
Which of the following numbers is largest?

A. $$2^{300}$$

B. $$3^{200}$$

C. $$2^{100} + 3^{100}$$

D. $$4^{100}$$

E. $$9^{60}$$

Solution

Option A
• $$2^{300} = 4^{150} = 8^{100} ……………Eq.(i)$$
o We can eliminate Option D since $$4^{150} > 4^{100}$$
• For now, let’s keep answer option A.
Option B
• $$3^{200} = 9^{100} …………….Eq.(ii)$$
o Now, $$9^{100} > 9^{60}$$, so we can eliminate answer option E.
• Also, comparing eq.(i) and (ii), $$9^{100} > 8^{100}$$
o So, we can eliminate answer option A too.
• Also, $$3^{200} =3^{100}*3^{100} > 3^{100} + 3^{100} > 3^{100} + 2^{100}$$
o So, we can also eliminate option C.

Thus, the correct answer is Option B.
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Re: Which of the following numbers is largest? [#permalink]
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Re: Which of the following numbers is largest? [#permalink]
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Re: Which of the following numbers is largest? [#permalink]
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