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If integer x were divided by 7, the quotient would be 12

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If integer x were divided by 7, the quotient would be 12 [#permalink] New post 03 Sep 2019, 09:56
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If integer x were divided by 7, the quotient would be 12 with a remainder of 1. Therefore, x equals

(A) 91

(B) 90

(C) 88

(D) 85

(E) 83
[Reveal] Spoiler: OA

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Re: If integer x were divided by 7, the quotient would be 12 [#permalink] New post 04 Sep 2019, 09:15
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Carcass wrote:
If integer x were divided by 7, the quotient would be 12 with a remainder of 1. Therefore, x equals

(A) 91

(B) 90

(C) 88

(D) 85

(E) 83


----ASIDE--------------
There's a nice rule that says, If N divided by D equals Q with remainder R, then N = DQ + R
For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2
Likewise, since 53 divided by 10 equals 5 with remainder 3, then we can write 53 = (10)(5) + 3
-----------------------

GIVEN: If integer x were divided by 7, the quotient would be 12 with a remainder of 1
Apply above RULE to write: x = (7)(12) + 1 = 84 + 1 = 85

Answer: D

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Re: If integer x were divided by 7, the quotient would be 12 [#permalink] New post 04 Sep 2019, 22:26
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The approach: (a number) minus 12*7 = 1

Therefore, the number = 1 + (12*7) = 1+84 = 85
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Re: If integer x were divided by 7, the quotient would be 12 [#permalink] New post 06 Sep 2019, 01:55
Ans D
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Re: If integer x were divided by 7, the quotient would be 12 [#permalink] New post 14 Sep 2019, 10:11
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Given how mixed fractions are set up, you could set this up as a mixed fraction and solve (although this might not be applicable to a wide variety of division and remainder GRE problems).


Mixed fraction form:

Quotient\(\frac{Remainder}{Divisor}\)

. then plug in what we are given for quotient, remainder and divisor ("divided by 7, the quotient would be 12 with a remainder of 1"

12\(\frac{1}{7}\)

. convert mixed fraction to standard fraction form (multiply 7 by 12 and add 1)

\(\frac{85}{7}\)

. we were told to find the numerator (essentially), and we did. It's 85.
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Re: If integer x were divided by 7, the quotient would be 12 [#permalink] New post 14 Sep 2019, 17:45
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Here is another way of looking at it. If I forget, N = DQ + R, I found I could remember it by picking it out of a typical division problem.
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Re: If integer x were divided by 7, the quotient would be 12   [#permalink] 14 Sep 2019, 17:45
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If integer x were divided by 7, the quotient would be 12

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