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# When the positive integer n is divided by 7, the quotient is q and the

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Joined: 02 Sep 2009
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When the positive integer n is divided by 7, the quotient is q and the  [#permalink]

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06 Feb 2019, 02:49
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When the positive integer n is divided by 7, the quotient is q and the remainder is 4. When 2n is divided by 7, the remainder is 1 and the quotient, in terms of q, is

A. q/2

B. q/2 + 1

C. 2q

D. 2q+1

E. 2q+2

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Re: When the positive integer n is divided by 7, the quotient is q and the  [#permalink]

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06 Feb 2019, 02:54
Bunuel wrote:
When the positive integer n is divided by 7, the quotient is q and the remainder is 4. When 2n is divided by 7, the remainder is 1 and the quotient, in terms of q, is

A. q/2

B. q/2 + 1

C. 2q

D. 2q+1

E. 2q+2

$$\frac{n}{7}$$= q + 4

n = 7q + 4

2n = 14q + 8

$$\frac{2n}{7}$$ =$$\frac{(14q + 8 )}{7}$$

we have remainder 1 but quotient 2q.

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Re: When the positive integer n is divided by 7, the quotient is q and the  [#permalink]

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06 Feb 2019, 06:46
Bunuel wrote:
When the positive integer n is divided by 7, the quotient is q and the remainder is 4. When 2n is divided by 7, the remainder is 1 and the quotient, in terms of q, is

A. q/2

B. q/2 + 1

C. 2q

D. 2q+1

E. 2q+2

lets use some no to solve
When the positive integer n is divided by 7, the quotient is q and the remainder is 4.
n=7q+4
n=11
q=1

now
when When 2n is divided by 7, the remainder is 1 and the quotient, in terms of q, is

22=7*3+1
q=3
out of given options
D sufficies relation
IMO D
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Re: When the positive integer n is divided by 7, the quotient is q and the  [#permalink]

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06 Feb 2019, 08:00
Bunuel wrote:
When the positive integer n is divided by 7, the quotient is q and the remainder is 4. When 2n is divided by 7, the remainder is 1 andthe quotient, in terms of q, is

A. q/2

B. q/2 + 1

C. 2q

D. 2q+1

E. 2q+2

Let $$n = 11$$, So $$q = 1$$ and $$r = 4$$

When $$2n$$ is divided by $$7$$ then we have $$\frac{22}{7} = 7*3(q) + 1(r)$$

Thus, the value of quotient in terms of $$q(3)$$ = $$2*1(q) + 1$$, Answer must be (D)
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Re: When the positive integer n is divided by 7, the quotient is q and the  [#permalink]

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06 Feb 2019, 08:13
Bunuel wrote:
When the positive integer n is divided by 7, the quotient is q and the remainder is 4. When 2n is divided by 7, the remainder is 1 and the quotient, in terms of q, is

A. q/2

B. q/2 + 1

C. 2q

D. 2q+1

E. 2q+2

IMO D

Plug in some values n = 11, q = 1, remainder = 4

Now n becomes 2n = 22 here q = 3, remainder = 1

So only D satisfies the above relation

2*1 + 1 = 3
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Re: When the positive integer n is divided by 7, the quotient is q and the  [#permalink]

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06 Feb 2019, 08:35
Bunuel wrote:
When the positive integer n is divided by 7, the quotient is q and the remainder is 4. When 2n is divided by 7, the remainder is 1 and the quotient, in terms of q, is

A. q/2

B. q/2 + 1

C. 2q

D. 2q+1

E. 2q+2

Two ways..

(I) Algebraic
the positive integer n is divided by 7, the quotient is q and the remainder is 4 MEANS n=7q+4.
2n is divided by 7, the remainder is 1 and the quotient, in terms of q..2n=7x+1.
substitute $$n=7q+4, .....2(7q+4)=7x+1......14q+8=7x+1......7x=14q+8-1=14q+7.......x=2q+1$$
D

(II) Substitute n as some value..
take q as 2, so n=7*2+4=18..
so 2n = 2*18=36
36=7x+1.......7x=35..x=5

Substitute q as 2 and see which choice gives you 5 ..
2q+1=2*2+1=5

so D
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Re: When the positive integer n is divided by 7, the quotient is q and the  [#permalink]

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06 Feb 2019, 12:35
Let quotient interms of q =?
Now since dividend is n ,divisor is 7 ,quotient is q and remainder being 4 can be in this form ,n=7q+4.......(1)
Now second statement says ,
2n=?+1.....(2)
Multiply eqn.....(1) by 2
2n=14q+8
2n=?+1 —> 14q+8=?+1 —> 14q+7=? —> 7(2q+1)=?
Haha so there we have it divisor*quotient ,so quotient interms of q is (2q+1)
Hope this helps .

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Re: When the positive integer n is divided by 7, the quotient is q and the  [#permalink]

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13 Feb 2019, 17:18
Hello everyone!

Could someone please tell me if my logic is good or it was just a coincidence?

"the remainder is 1.."

So in my head, I just canceled out A, C and E because they do not hold a remainder of 1.
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Re: When the positive integer n is divided by 7, the quotient is q and the  [#permalink]

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15 Feb 2019, 18:38
Bunuel wrote:
When the positive integer n is divided by 7, the quotient is q and the remainder is 4. When 2n is divided by 7, the remainder is 1 and the quotient, in terms of q, is

A. q/2

B. q/2 + 1

C. 2q

D. 2q+1

E. 2q+2

We can create the equations:

n/7 = q + 4/7

n = 7q + 4

and

2n/7 = z + 1/7

2n = 7z + 1

Multiplying the first equation by 2, we have:

2n = 14q + 8

Setting the two equations equal to each other, we have:

14q + 8 = 7z + 1

14q + 7= 7z

2q + 1 = z

Alternate Solution:

Since the remainder is 4 when n is divided by 7, we see that n could be 11, 18, 25, 32, …

For simplicity’s sake, let’s let n = 11. When 11 is divided by 7, the quotient q is 1, with a remainder of 4.

Now, we see that 2n = 22. When 22 is divided by 7, the quotient is 3, with a remainder of 1.

The original quotient q is 1, and the new quotient is 3. Of the answer choices, only D. 2q + 1 gives us an answer of 3 when q = 1.

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Re: When the positive integer n is divided by 7, the quotient is q and the   [#permalink] 15 Feb 2019, 18:38
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