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M09-32

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Math Expert
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M09-32  [#permalink]

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New post 15 Sep 2014, 23:40
2
2
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

49% (00:22) correct 51% (00:23) wrong based on 130 sessions

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Re M09-32  [#permalink]

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New post 15 Sep 2014, 23:40
1
1
Official Solution:

What is the last digit of \(3^{3^3}\)?

A. 1
B. 3
C. 6
D. 7
E. 9


THEORY

If exponentiation is indicated by stacked symbols, the rule is to work from the top down, thus:

\(a^{m^n}=a^{(m^n)}\) and not \((a^m)^n\), which on the other hand equals to \(a^{mn}\).

So:

\((a^m)^n=a^{mn}\);

\(a^{m^n}=a^{(m^n)}\) and not \((a^m)^n\).

BACK TO THE QUESTION

According to the above: \(3^{3^3}=3^{(3^3)}=3^{27}\)

Next, the units digit of 3 in positive integer power repeats in pattern of 4: {3, 9, 7, 1}. So, the units digit of \(3^{27}\) (27=4*6+3) is the same as the units digit of \(3^3\), which is 7.


Answer: D
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Re: M09-32  [#permalink]

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New post 09 Apr 2016, 23:17
(27=4*6+3) so you add 4 + 3 = 7 (Please more details)
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Re: M09-32  [#permalink]

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New post 10 Apr 2016, 03:26
MohammadManda7awi wrote:
(27=4*6+3) so you add 4 + 3 = 7 (Please more details)


Here are the details:
Cyclicity on the GMAT
Divisibility Tips

Divisibility and Remainders on the GMAT

Theory on remainders problems
Tips on remainders

Units digits, exponents, remainders problems

DS remainders problems
PS remainders problems

DS divisibility problems
PS divisibility problems
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re M09-32  [#permalink]

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New post 06 Sep 2018, 00:16
I think this is a high-quality question and I agree with explanation. You have it as a Fractions/Ratios/Decimals question when it should be Exponents and Roots?
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Re M09-32  [#permalink]

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New post 17 Nov 2018, 07:03
I think this is a high-quality question and I agree with explanation.
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Re: M09-32  [#permalink]

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New post 13 Jan 2019, 00:40
I am not clear with the explanation as I know
3^3 * 3^3 * 3^3 = (3^3)^3 = 3^9

The question has (3^3)^3 what is equal to 3^9 and the unit digit of 3^9 is 3

Please give a details explanation with example. Thanks
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Re: M09-32  [#permalink]

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New post 13 Jan 2019, 02:17
smoni wrote:
I am not clear with the explanation as I know
3^3 * 3^3 * 3^3 = (3^3)^3 = 3^9

The question has (3^3)^3 what is equal to 3^9 and the unit digit of 3^9 is 3

Please give a details explanation with example. Thanks


I think you did not read the discussion above carefully enough.

The question does not ask about the units digit of \((3^3)^3\), it asks about the units digit of \(3^{3^3}\). The solution clearly explains the difference between these two expression. Please re-read.
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Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: M09-32 &nbs [#permalink] 13 Jan 2019, 02:17
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