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n is a positive integer less than 50. When n is divided by 6, the rem

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n is a positive integer less than 50. When n is divided by 6, the rem  [#permalink]

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New post 07 Aug 2018, 00:00
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[Math Revolution GMAT math practice question]

n is a positive integer less than 50. When n is divided by 6, the remainder is 2, and when n is divided by 7, the remainder is 6. What is the remainder when n is divided by 8?

A. 1
B. 2
C. 3
D. 4
E. 5

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n is a positive integer less than 50. When n is divided by 6, the rem  [#permalink]

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New post 07 Aug 2018, 00:19
when N is divided by 6, remainder is 2
when N is divided by 7, remainder is 6
\(\frac{(7x+6)}{6}\) should give remainder 2
x=2 satisfies the equation.
Hence the general equation will be 7*6x + 20 = 42x+20
Since N is less than 50. Put x=0. Then N=20.
\(\frac{20}{8}\) will leave a remainder 4.
D is the ans.
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Re: n is a positive integer less than 50. When n is divided by 6, the rem  [#permalink]

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New post 07 Aug 2018, 03:47
MathRevolution wrote:
[Math Revolution GMAT math practice question]

n is a positive integer less than 50. When n is divided by 6, the remainder is 2, and when n is divided by 7, the remainder is 6. What is the remainder when n is divided by 8?

A. 1
B. 2
C. 3
D. 4
E. 5



Note: n<50

when n is divided by 6 the reminder is 2. What could be the value of n.

n = 4 , 8 , 14, 20, 26, 32, 38, 44.

At the same when n is divided by 7 the reminder is 6.

Among the numbers listed above only 20 confirms the condition. So, n = 20.

When we divide 20 by 8 the reminder is 4.

The best answer is D.
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Re: n is a positive integer less than 50. When n is divided by 6, the rem  [#permalink]

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New post 07 Aug 2018, 06:29
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MathRevolution wrote:
[Math Revolution GMAT math practice question]

n is a positive integer less than 50. When n is divided by 6, the remainder is 2, and when n is divided by 7, the remainder is 6. What is the remainder when n is divided by 8?

A. 1
B. 2
C. 3
D. 4
E. 5

\(n_6 = { 2 , 8 , 14, 20.....................}\)
\(n_7 = { 6, 13 , 20....................}\)

So, \(n = 20\)

\(\frac{20}{8}\) = Remainder \(\ 4\), Answer must be (D)
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Re: n is a positive integer less than 50. When n is divided by 6, the rem  [#permalink]

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New post 07 Aug 2018, 06:42
MathRevolution wrote:
[Math Revolution GMAT math practice question]

n is a positive integer less than 50. When n is divided by 6, the remainder is 2, and when n is divided by 7, the remainder is 6. What is the remainder when n is divided by 8?

A. 1
B. 2
C. 3
D. 4
E. 5


n divided by 6 leaves remainder 2 means 'n' is even...
First inference:- remainder should be EVEN, as n/8 will leave even remainder
Only possibility 2 or 4

So 7*2k+6 is the number...
So the first number is k=1, so number =7*2+6=20
Now 20 divided by 8 will leave 4 as remainder..

D
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n is a positive integer less than 50. When n is divided by 6, the rem  [#permalink]

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New post 07 Aug 2018, 07:08
MathRevolution wrote:
[Math Revolution GMAT math practice question]

n is a positive integer less than 50. When n is divided by 6, the remainder is 2, and when n is divided by 7, the remainder is 6. What is the remainder when n is divided by 8?

A. 1
B. 2
C. 3
D. 4
E. 5


n/6=q+2
n/7=p+6
→6q-7p=4
plugging in increasing values,
q=3
p=2
least value of n=20
20/8 leaves remainder of 4
D
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Re: n is a positive integer less than 50. When n is divided by 6, the rem  [#permalink]

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New post 09 Aug 2018, 00:32
=>

The positive integers less than \(50\) that have a remainder of \(2\) when they are divided by \(6\) are \(n = 2, 8, 14, 20, 26, 32, 38\) and \(44\).
The positive integers less than \(50\) that have a remainder of \(6\) when they are divided by \(7\) are \(n = 6, 13, 20, 27, 34, 41\) and \(48\).
The only integer in both lists is \(n = 20\).
\(20\) has a remainder of \(4\) when it is divided by \(8\).

Therefore, the answer is D.
Answer: D
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