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Which of the following options is closest to (3^10)(33^10)?
[#permalink]
03 Nov 2022, 01:30
03 Nov 2022, 01:30
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A
B
C
D
E
Difficulty:
25%
(medium)
Question Stats:
69% (01:19) correct
31%
(01:22)
wrong
based on 126
sessions
Which of the following options is closest to \((3^{10})(33^{10})\)?
A. \(10^{10}\)
B. \(10^{14}\)
C. \(10^{18}\)
D. \(10^{20}\)
E. \(10^{22}\)
A. \(10^{10}\)
B. \(10^{14}\)
C. \(10^{18}\)
D. \(10^{20}\)
E. \(10^{22}\)
Re: Which of the following options is closest to (3^10)(33^10)?
[#permalink]
03 Nov 2022, 12:16
03 Nov 2022, 12:16
1
Kudos
given
3^10 * 33^10
we can rewrite eq as follows
now (3^2)^5 * (3^2)^5*11*10
9^5 *9^5*11^10
9^10*11^10
(10-1)^10 * (10+1)^10
10^20 -1^20
option D is correct
3^10 * 33^10
we can rewrite eq as follows
now (3^2)^5 * (3^2)^5*11*10
9^5 *9^5*11^10
9^10*11^10
(10-1)^10 * (10+1)^10
10^20 -1^20
option D is correct
Quant Chat Moderator
Joined: 22 Dec 2016
Posts: 3129
Given Kudos: 1860
Location: India
Concentration: Strategy, Leadership
Re: Which of the following options is closest to (3^10)(33^10)?
[#permalink]
04 Nov 2022, 01:13
04 Nov 2022, 01:13
\(3^{10} * 33^{10}\)
= \(3^{10}*3^{10}*11^{10}\)
= \(3^{20} * 11^{10}\)
=\(9^{10} * 11^{10}\)
So we can see that the value is close enough to \(10^{10} * 10^{10}\) = \(10^{20}\)
IMO D
= \(3^{10}*3^{10}*11^{10}\)
= \(3^{20} * 11^{10}\)
=\(9^{10} * 11^{10}\)
So we can see that the value is close enough to \(10^{10} * 10^{10}\) = \(10^{20}\)
IMO D
