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Sub 505 (Easy)|   Exponents|      
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guddo
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3^41 + 3^42 + 3^43 = 30 Jan 2024, 08:53
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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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5% (low)

Question Stats:

92% (00:38) correct 8% (01:12) wrong based on 388 sessions

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\(3^{41} + 3^{42} + 3^{43} =\)

A. \(7(3^{41})\)

B. \(13(3^{41})\)

C. \(3(3^{42})\)

D. \(5(3^{42})\)

E. \(7(3^{42})\)

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2024-01-30_19-51-49.png
2024-01-30_19-51-49.png [ 11.31 KiB | Viewed 5249 times ]
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3^41 + 3^42 + 3^43 = 30 Jan 2024, 08:54
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guddo
\(3^{41} + 3^{42} + 3^{43} =\)

A. \(7(3^{41})\)

B. \(13(3^{41})\)

C. \(3(3^{42})\)

D. \(5(3^{42})\)

E. \(7(3^{42})\)

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2024-01-30_19-51-49.png
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    \(3^{41} + 3^{42} + 3^{43} =\)

    \(=3^{41}(1 + 3 + 3^{2}) =\)

    \(=3^{41}(13)\)

Answer: B.
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3^41 + 3^42 + 3^43 = 09 Dec 2024, 10:36
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All you can do is factor out 3^41 and then do the remaining math in parentheses:
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3^41 + 3^42 + 3^43 = 12 Dec 2024, 22:08
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guddo
\(3^{41} + 3^{42} + 3^{43} =\)

A. \(7(3^{41})\)

B. \(13(3^{41})\)

C. \(3(3^{42})\)

D. \(5(3^{42})\)

E. \(7(3^{42})\)

Show Spoiler
Attachment:
2024-01-30_19-51-49.png
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Since, the best explanation is already present here for this question so let me share a different perspective to find correct option ...

Trust me this perspective is very helpful! :)

Look at the unit digits

Unit digit of \(3^{41} + 3^{42} + 3^{43} =3+9+7 = 9\)

Cyclicity of unit digit repetition for exponents of 3 is 4

So the correct option shoul dgive unit digit 9

A. \(7(3^{41})\) = 7*3 = 1 (Unit digit)

B. \(13(3^{41})\) = 3*3 = 9 (Potential Answer)

C. \(3(3^{42})\) = 7 at Unit place (naah)

D. \(5(3^{42})\) = 5 at unit place (naah)

E. \(7(3^{42})\) = 7*9 = 3 at Unit place (naah)

so Our correct option is B

I hope you find it useful! :)

For cyclicity, check the playlist of number properties on my Youtube channel www.Youtube.com/GMATinsight
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3^41 + 3^42 + 3^43 = 13 Dec 2024, 08:04
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Very good idea to use the units digits. I love it
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guddo
\(3^{41} + 3^{42} + 3^{43} =\)

A. \(7(3^{41})\)

B. \(13(3^{41})\)

C. \(3(3^{42})\)

D. \(5(3^{42})\)

E. \(7(3^{42})\)

Show Spoiler
Attachment:
2024-01-30_19-51-49.png
Since, the best explanation is already present here for this question so let me share a different perspective to find correct option ...

Trust me this perspective is very helpful! :)

Look at the unit digits

Unit digit of \(3^{41} + 3^{42} + 3^{43} =3+9+7 = 9\)

Cyclicity of unit digit repetition for exponents of 3 is 4

So the correct option shoul dgive unit digit 9

A. \(7(3^{41})\) = 7*3 = 1 (Unit digit)

B. \(13(3^{41})\) = 3*3 = 9 (Potential Answer)

C. \(3(3^{42})\) = 7 at Unit place (naah)

D. \(5(3^{42})\) = 5 at unit place (naah)

E. \(7(3^{42})\) = 7*9 = 3 at Unit place (naah)

so Our correct option is B

I hope you find it useful! :)

For cyclicity, check the playlist of number properties on my Youtube channel http://www.Youtube.com/GMATinsight
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3^41 + 3^42 + 3^43 = 12 Sep 2025, 07:39
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This is a classic factoring question that trips up many students who try to calculate \(3^{41}\) directly. Let me show you the elegant approach.

Strategic Approach: Factor Out the Common Power
The key insight here is recognizing that all three terms share a common factor - they're all powers of 3. Instead of calculating massive numbers, we can factor strategically.

Step 1: Identify the Common Factor
Looking at \(3^{41} + 3^{42} + 3^{43}\), the smallest power is \(3^{41}\). This will be our common factor.

Step 2: Rewrite Each Term
Using exponent rules:

\(3^{41} = 3^{41} \times 1\)
\(3^{42} = 3^{41} \times 3^1 = 3^{41} \times 3\)
\(3^{43} = 3^{41} \times 3^2 = 3^{41} \times 9\)

Step 3: Factor Out \(3^{41}\)
\(3^{41} + 3^{42} + 3^{43} = 3^{41}(1) + 3^{41}(3) + 3^{41}(9)\)
\(= 3^{41}(1 + 3 + 9)\)
\(= 3^{41}(13)\)

Step 4: Match to Answer Choices
Our result \(13(3^{41})\) matches choice B.
The beauty of this approach is that you never need to calculate actual values - just apply the factoring principle and basic arithmetic.

Want to master the systematic framework for all exponential sum problems and discover alternative solving methods? Check out the complete solution on Neuron by e-GMAT, which includes time-saving techniques and pattern recognition strategies that work across similar GMAT questions. Access detailed explanations for official questions with practice quizzes here on Neuron.
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