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When the positive integer n is divided by 7, the quotient is q and the
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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
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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.
C is the correct answer.



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Re: When the positive integer n is divided by 7, the quotient is q and the
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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
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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
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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
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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 \(n=7q+4, .....2(7q+4)=7x+1......14q+8=7x+1......7x=14q+81=14q+7.......x=2q+1\) 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
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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) Answer is kindly D Hope this helps .
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Re: When the positive integer n is divided by 7, the quotient is q and the
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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
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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. Answer: D
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Re: When the positive integer n is divided by 7, the quotient is q and the
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15 Feb 2019, 18:38






