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27 Apr 2020, 03:22
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A
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Difficulty:
55%
(hard)
Question Stats:
56% (01:41) correct
44%
(01:49)
wrong
based on 152
sessions
History
Date
Time
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What is the remainder when positive integer n is divided by 3?
(1) when n+6 is divided by 3, the remainder is 1.
(2) when n^2 is divided by 3, the remainder is 1.
Are You Up For the Challenge: 700 Level Questions
(1) when n+6 is divided by 3, the remainder is 1.
(2) when n^2 is divided by 3, the remainder is 1.
Are You Up For the Challenge: 700 Level Questions
27 Apr 2020, 03:58
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Bunuel
(Statement1): when \(n+6\) is divided by \(3\), the remainder is \(1\).
\(n+6 = 3*k +1 \)
\(n+ 3*2 = 3*k +1\)
--> \(n = 3(k-2) +1\)
The remainder will be \(1\).
Sufficient
(Statement2): when \(n^2\) is divided by \(3\), the remainder is \(1\).
if \(n^{2} = 4^{2}\), then \(16= 3*5 +1\)
--> \(4= 3*1+1\) (remainder is \(1\))
if \(n^{2} = 5^{2}\), then \(25= 5*5 +1\)
--> \(5= 3*1+2\) (remainder is \(2\))
Insufficient
Answer (A).
27 Apr 2020, 05:01
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Bunuel
Solution
Step 1: Analyse Question Stem
- • n is a positive integer.
Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE
Statement 1: When n+6 is divided by 3, the remainder is 1.
- • n + 6 = 3Q + 1
• n = 3Q +1-6
• n = 3(Q-2)+1
- o When n is divided by 3, the remainder is 1
Statement 2: When \(n^2\) is divided by 3, then the remainder is 1.
- • Whenever the square of a positive integer is divided by 3, then the remainder is either 0 or 1.
- o n is either be of the form 3q + 1 or 3q + 2, where p is a positive integer.
- If n = 3q+1, then remainder is 1
If n =3q+2, then the remainder is 2.
