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guddo
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If is defined for all nonnegative integers b by b = (b + 1)^b, what 27 Jan 2024, 05:40
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83% (00:55) correct 17% (00:55) wrong based on 364 sessions

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If ▲ is defined for all nonnegative integers b by \(▲b = (b + 1)^b\), what is the value of ▲(▲(▲0)) ?

A. 0
B. 2
C. 3
D. 4
E. 9

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2024-01-27_16-38-36.png
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E
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Bunuel
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If is defined for all nonnegative integers b by b = (b + 1)^b, what 27 Jan 2024, 05:42
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guddo
If ▲ is defined for all nonnegative integers b by \(▲b = (b + 1)^b\), what is the value of ▲(▲(▲0)) ?

A. 0
B. 2
C. 3
D. 4
E. 9

Show Spoiler
Attachment:
2024-01-27_16-38-36.png
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Since \(▲b = (b + 1)^b\), then:

    \(▲0 = (0 + 1)^0 = 1^0 = 1\);

    \(▲(▲0) = ▲1 = (1 + 1)^1 = 2^1 = 2\);

    \(▲(▲(▲0)) = ▲2 = (2 + 1)^2 = 3^2 = 9\).

Answer: E.
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If is defined for all nonnegative integers b by b = (b + 1)^b, what 17 Jul 2024, 21:15
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Bunuel
guddo
If ▲ is defined for all nonnegative integers b by \(▲b = (b + 1)^b\), what is the value of ▲(▲(▲0)) ?

A. 0
B. 2
C. 3
D. 4
E. 9

Show Spoiler
Attachment:
2024-01-27_16-38-36.png

Since \(▲b = (b + 1)^b\), then:

    \(▲0 = (0 + 1)^0 = 1^0 = 1\);

    \(▲(▲0) = ▲1 = (1 + 1)^1 = 2^1 = 2\);

    \(▲(▲(▲0)) = ▲2 = (2 + 1)^2 = 3^2 = 9\).

Answer: E.
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­
I am not sure I understand. What is the significance of the triangle?
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If is defined for all nonnegative integers b by b = (b + 1)^b, what 18 Jul 2024, 00:20
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Danou
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guddo
If ▲ is defined for all nonnegative integers b by \(▲b = (b + 1)^b\), what is the value of ▲(▲(▲0)) ?

A. 0
B. 2
C. 3
D. 4
E. 9

Show Spoiler
Attachment:
2024-01-27_16-38-36.png

Since \(▲b = (b + 1)^b\), then:

    \(▲0 = (0 + 1)^0 = 1^0 = 1\);

    \(▲(▲0) = ▲1 = (1 + 1)^1 = 2^1 = 2\);

    \(▲(▲(▲0)) = ▲2 = (2 + 1)^2 = 3^2 = 9\).

Answer: E.
­
I am not sure I understand. What is the significance of the triangle?
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­
▲ represents a function, which is defined for all nonnegative integers b by \(▲b = (b + 1)^b\).

For example:
If b = 0, then \(▲0 = (0 + 1)^0=1\);
If b = 1, then \(▲1 = (1 + 1)^1=2\);
If b = 2, then \(▲2 = (2 + 1)^2=9\);
If b = 3, then \(▲3 = (3 + 1)^3=64\);
...

13. Functions



For more check below:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread­

Hope it helps.­
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If is defined for all nonnegative integers b by b = (b + 1)^b, what 22 Mar 2025, 05:54
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Can someone explain how does E satisfy? I did it in a similar way but did not understand how Option E is the right answer
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If is defined for all nonnegative integers b by b = (b + 1)^b, what 22 Mar 2025, 06:31
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bdc
Can someone explain how does E satisfy? I did it in a similar way but did not understand how Option E is the right answer
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Have you checked this post? Please review that solution along with this post, and if you still have doubts, feel free to ask.
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If is defined for all nonnegative integers b by b = (b + 1)^b, what 23 Mar 2025, 00:01
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Sorry, got it.. just missed the options.
Bunuel
bdc
Can someone explain how does E satisfy? I did it in a similar way but did not understand how Option E is the right answer

Have you checked this post? Please review that solution along with this post, and if you still have doubts, feel free to ask.
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