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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42 GPA: 3.82
n is a positive integer less than 50. When n is divided by 6, the rem  [#permalink]

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Question Stats: 90% (01:47) correct 10% (02:13) wrong based on 57 sessions

### HideShow timer Statistics [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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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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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.

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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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1
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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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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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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Joined: 16 Aug 2015
Posts: 7609
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: n is a positive integer less than 50. When n is divided by 6, the rem  [#permalink]

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=>

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 $$8$$.

_________________ Re: n is a positive integer less than 50. When n is divided by 6, the rem   [#permalink] 09 Aug 2018, 01:32
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