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The remainder when 4(10^n)+1
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05 Sep 2026, 05:19
05 Sep 2026, 05:19
Expert Reply
00:00
Question Stats:
50% (02:09) correct
50% (01:08) wrong based on 6 sessions
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n is a positive integer.
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
The remainder when \(4(10^n)+1\) is divided by 7 |
The remainder when \(4(10^{n+2})+1\) is divided by 7 |
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
- Part of the project: GRE Daily Quant Challenge ALL 4 CORE QUANT AREAS
- Also replying to the unanswered questions
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The remainder when 4(10^n)+1
[#permalink]
08 Sep 2026, 11:09
08 Sep 2026, 11:09
1
Expert Reply
Solution
We have:
\(A=4(10^n)+1,\)
\(B=4(10^{n+2})+1\)
Quick trick: pick \(n=1\)
\(A:\)
\(4(10)+1=41\)
\(41\div7 \text{ leaves } {6}\)
\(B:\)
\(4(10^3)+1\)
Since \((10^3=1000),\) and \((1000\div7)\) leaves (6):
\(4(6)+1=25\)
Remainder \((=4).\)
So for \((n=1): A>B\)
But we need to see whether another positive integer gives the opposite.
Try \((n=2)\)
A:
\(4(100)+1=401\)
Remainder when divided by 7:
\({2}\)
For B, \((n+2=4):\)
\(4(10^4)+1\)
Since \((10^4)\) leaves (4) when divided by 7:
\(4(4)+1=17\)
Remainder =3
Thus: \(A<B\)
We have found both possibilities:
\(n=1\Rightarrow A>B\)
\(n=2\Rightarrow A<B\)
Therefore:
Answer: D
We have:
\(A=4(10^n)+1,\)
\(B=4(10^{n+2})+1\)
Quick trick: pick \(n=1\)
\(A:\)
\(4(10)+1=41\)
\(41\div7 \text{ leaves } {6}\)
\(B:\)
\(4(10^3)+1\)
Since \((10^3=1000),\) and \((1000\div7)\) leaves (6):
\(4(6)+1=25\)
Remainder \((=4).\)
So for \((n=1): A>B\)
But we need to see whether another positive integer gives the opposite.
Try \((n=2)\)
A:
\(4(100)+1=401\)
Remainder when divided by 7:
\({2}\)
For B, \((n+2=4):\)
\(4(10^4)+1\)
Since \((10^4)\) leaves (4) when divided by 7:
\(4(4)+1=17\)
Remainder =3
Thus: \(A<B\)
We have found both possibilities:
\(n=1\Rightarrow A>B\)
\(n=2\Rightarrow A<B\)
Therefore:
Answer: D
gmatclubot
The remainder when 4(10^n)+1 [#permalink]
08 Sep 2026, 11:09
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