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What is the largest prime factor of 7^a+7^b+7^c, given that a, b, c ar 16 Nov 2020, 08:31
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45% (medium)

Question Stats:

66% (01:40) correct 34% (01:34) wrong based on 249 sessions

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What is the largest prime factor of \(7^a+7^b+7^c\), given that \(a, b, c\) are consecutive positive integers?
A) 3
B) 7
C) 13
D) 19
E) 47
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D
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GMAT Focus 1: 735 Q90 V89 DI81
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What is the largest prime factor of 7^a+7^b+7^c, given that a, b, c ar 16 Nov 2020, 08:46
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TheUltimateWinner
What is the largest prime factor of \(7^a+7^b+7^c\), given that \(a, b, c\) are consecutive positive integers?
A) 3
B) 7
C) 13
D) 19
E) 47
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Since a, b and c are consecutive integers => b=a+1, and c=a+2

\(7^a+7^b+7^c=7^a+7^{a+1}+7^{a+2}=7^a+7*7^a+49*7^a=7^a(1+7+49)=7^a*57=7^a*3*19\)

Thus 19 is the largest prime factor.

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What is the largest prime factor of 7^a+7^b+7^c, given that a, b, c ar 16 Nov 2020, 08:49
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TheUltimateWinner
What is the largest prime factor of \(7^a+7^b+7^c\), given that \(a, b, c\) are consecutive positive integers?
A) 3
B) 7
C) 13
D) 19
E) 47
Show more

Plug 1, 2, and 3 for a, b, and c.

\(7^a+7^b+7^c=7^1+7^2+7^3=7(1+7+7^2)=7*57=7*3*19\).

Answer: D.
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What is the largest prime factor of 7^a+7^b+7^c, given that a, b, c ar 16 Nov 2020, 08:51
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TheUltimateWinner
What is the largest prime factor of \(7^a+7^b+7^c\), given that \(a, b, c\) are consecutive positive integers?
A) 3
B) 7
C) 13
D) 19
E) 47
Show more



Since a, b and c are consecutive integers, b = a + 1 and c = a + 2

The equation \(7^a + 7^b + 7^c\) can be written as \(7^a + 7^{a + 1} + 7^{a + 2}\)

=\(7^a + (7^{a} * 7) + (7^{a} * 7^2)\)

=\(7^a * (1 + 7 + 49)\)

= \(7^a * 57\)

= \(7^a * 3 * 19\)

Therefore the largest prime factor is 19



Option D

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What is the largest prime factor of 7^a+7^b+7^c, given that a, b, c ar 04 Dec 2020, 09:43
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What is the largest prime factor of \(7^a+7^b+7^c\), given that \(a, b, c\) are consecutive positive integers?
A) 3
B) 7
C) 13
D) 19
E) 47



Since a, b and c are consecutive integers, b = a + 1 and c = a + 2

The equation \(7^a + 7^b + 7^c\) can be written as \(7^a + 7^{a + 1} + 7^{a + 2}\)

=\(7^a + (7^{a} * 7) + (7^{a} * 7^2)\)

=\(7^a * (1 + 7 + 49)\)

= \(7^a * 57\)

= \(7^a * 3 * 19\)

Therefore the largest prime factor is 19



Option D

Arun Kumar
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CrackVerbalGMAT
Thanks for the reply. How do someone convinced that the highlighted parts are not negative?
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What is the largest prime factor of 7^a+7^b+7^c, given that a, b, c ar 04 Dec 2020, 19:09
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What is the largest prime factor of \(7^a+7^b+7^c\), given that \(a, b, c\) are consecutive positive integers?
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Hi Ultimate winner. The question states that a, b and c are consecutive positive integers. Hence they cannot be negative.

Hope this helps

Arun Kumar
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What is the largest prime factor of 7^a+7^b+7^c, given that a, b, c ar 14 Dec 2020, 08:37
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Quote:
Hi Ultimate winner. The question states that a, b and c are consecutive positive integers. Hence they cannot be negative.

Hope this helps

Arun Kumar
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thank you so much for your kind response.
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What is the largest prime factor of 7^a+7^b+7^c, given that a, b, c ar 17 Mar 2026, 01:54
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