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

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Founder
Joined: 18 Apr 2015
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Kudos [?]: 1710 [0], given: 7485

If integer x were divided by 7, the quotient would be 12 [#permalink]  03 Sep 2019, 09:56
Expert's post
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Question Stats:

100% (00:23) correct 0% (00:00) wrong based on 6 sessions
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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GRE Instructor
Joined: 10 Apr 2015
Posts: 2387
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Kudos [?]: 2358 [1] , given: 33

Re: If integer x were divided by 7, the quotient would be 12 [#permalink]  04 Sep 2019, 09:15
1
KUDOS
Expert's post
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

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Intern
Joined: 09 Aug 2019
Posts: 10
Followers: 0

Kudos [?]: 7 [1] , given: 0

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

Therefore, the number = 1 + (12*7) = 1+84 = 85
Intern
Joined: 28 Aug 2019
Posts: 36
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Kudos [?]: 7 [0], given: 6

Re: If integer x were divided by 7, the quotient would be 12 [#permalink]  06 Sep 2019, 01:55
Ans D
Manager
Joined: 19 Nov 2018
Posts: 83
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Kudos [?]: 64 [1] , given: 45

Re: If integer x were divided by 7, the quotient would be 12 [#permalink]  14 Sep 2019, 10:11
1
KUDOS
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.
Manager
Joined: 19 Nov 2018
Posts: 83
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Kudos [?]: 64 [1] , given: 45

Re: If integer x were divided by 7, the quotient would be 12 [#permalink]  14 Sep 2019, 17:45
1
KUDOS
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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