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A natural number N is a multiple of 5. If N is divided by 6, the quoti
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11 Jul 2023, 00:16
11 Jul 2023, 00:16
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Question Stats:
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56% (01:51) wrong based on 30 sessions
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A natural number N is a multiple of 5. If N is divided by 6, the quotient comes same as the remainder, how many values can N are possible if N is less than 100?
A. 1
B. 2
C. 3
D. 4
E. 5
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\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
\(\Longrightarrow\) GRE NUMBER PROPERTIES
A. 1
B. 2
C. 3
D. 4
E. 5
Post A Detailed Correct Solution For The Above Questions And Get Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
\(\Longrightarrow\) GRE NUMBER PROPERTIES
Re: A natural number N is a multiple of 5. If N is divided by 6, the quoti
[#permalink]
07 Aug 2023, 22:31
07 Aug 2023, 22:31
1
Expert Reply
OE
Given that the natural number ๐ is a multiple of 5, thus ๐ = 5๐ผ1
Also, when ๐ is divided by 6, the quotient is same as the remainder,
Thus ๐ = 6๐ผ2 + ๐ผ2 = 7๐ผ2
Since, ๐ is divisible 5 and 7, thus it must be divisible by ๐ฟ๐ถ๐ ๐๐ (5,7) = 35
Thus, ๐ is a multiple of 35
As ๐ is a natural number less than 100, therefore the possible values ๐ will have will
be 35 and 70
But 70 will not be the value of ๐ as when we divide 70 by 6 we get quotient as 11
and remainder as 4
As, 70 = 6 ร 11 + 4
Thus for 70, we do not get the remainder same as the quotient when divided by 6.
Ans. (A)
Given that the natural number ๐ is a multiple of 5, thus ๐ = 5๐ผ1
Also, when ๐ is divided by 6, the quotient is same as the remainder,
Thus ๐ = 6๐ผ2 + ๐ผ2 = 7๐ผ2
Since, ๐ is divisible 5 and 7, thus it must be divisible by ๐ฟ๐ถ๐ ๐๐ (5,7) = 35
Thus, ๐ is a multiple of 35
As ๐ is a natural number less than 100, therefore the possible values ๐ will have will
be 35 and 70
But 70 will not be the value of ๐ as when we divide 70 by 6 we get quotient as 11
and remainder as 4
As, 70 = 6 ร 11 + 4
Thus for 70, we do not get the remainder same as the quotient when divided by 6.
Ans. (A)
Re: A natural number N is a multiple of 5. If N is divided by 6, the quoti
[#permalink]
08 Sep 2023, 08:01
08 Sep 2023, 08:01
1
Not sure if this is the right logic, but I completed the problem a similar way:
You know N is a multiple of 5, but when divided by 6 it has the same remainder as the quotient.
N/6 = x * x/6 --> meaning N/6 = (6x + x)/6
N = 7x
From here, you know that N needs to be divisible by 7 and 5, the first number is 35. 35/6 = 5 R 5, which works. The next is 70. 70/6 = 11 R 4, which doesn't work.
There's only one correct number, meaning the answer is choice A.
You know N is a multiple of 5, but when divided by 6 it has the same remainder as the quotient.
N/6 = x * x/6 --> meaning N/6 = (6x + x)/6
N = 7x
From here, you know that N needs to be divisible by 7 and 5, the first number is 35. 35/6 = 5 R 5, which works. The next is 70. 70/6 = 11 R 4, which doesn't work.
There's only one correct number, meaning the answer is choice A.
