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Bunuel
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Which of the following numbers is largest? 25 May 2020, 05:56
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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65% (01:24) correct 35% (01:07) wrong based on 498 sessions

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Which of the following numbers is largest?

A. \(2^{300}\)

B. \(3^{200}\)

C. \(2^{100} + 3^{100}\)

D. \(4^{100}\)

E. \(9^{60}\)


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Which of the following numbers is largest? 25 May 2020, 06:07
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The answer is B.

4^100 = 2^ 200. Thus, it is less than option A. So discarded.
Similarly, 9^60 = 3^ 120. It is less than 3^200. So discarded.
We can write option B as 3^200 = 9^100 and option A as 2^300 =8^100. On comparing we find option B to be the largest.

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Which of the following numbers is largest? 25 May 2020, 06:24
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Bunuel
Which of the following numbers is largest?


A. \(2^{300}\)

B. \(3^{200}\)

C. \(2^{100} + 3^{100}\)

D. \(4^{100}\)

E. \(9^{60}\)
Show more

Let's simplify the options to eliminate a few

A. \((2^3)^{100} = 8^{100}\)

B. \((3^2)^{100}= 9^{100}\)

C. \(2^{100} + 3^{100}≈ 3^{100} + 3^{100} ≈ 2*3^{100}\)

D. \(4^{100}\)

E. \(9^{60}\)

Now, the comparison is clear and

Option B is the winner

:inlove:

Answer: Option B
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Which of the following numbers is largest? 25 May 2020, 06:27
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Bunuel
Which of the following numbers is largest?


A. \(2^{300}\)

B. \(3^{200}\)

C. \(2^{100} + 3^{100}\)

D. \(4^{100}\)

E. \(9^{60}\)


Show more

Solution


Let’s compare answer options:
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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Which of the following numbers is largest? 25 May 2020, 20:13
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Which of the following numbers is largest? 15 Jul 2025, 06:03
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