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# If the relations shown hold for the operation ⊕ and the numb

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Founder
Joined: 18 Apr 2015
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Kudos [?]: 3178 [0], given: 11677

If the relations shown hold for the operation ⊕ and the numb [#permalink]  27 Jul 2020, 09:02
Expert's post
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Question Stats:

91% (00:25) correct 8% (00:36) wrong based on 12 sessions
$$m ⊕ p =n$$

$$n ⊕ r =m$$

$$n ⊕ q =q$$

$$p ⊕ q =p$$

$$q ⊕ p =r$$

If the relations shown hold for the operation ⊕ and the numbers m, n, p, q, and r, then $$[(m⊕p)⊕ q]⊕ p =$$

(A) m
(B) n
(C) p
(D) q
(E) r
[Reveal] Spoiler: OA

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Founder
Joined: 18 Apr 2015
Posts: 12642
Followers: 269

Kudos [?]: 3178 [0], given: 11677

Re: If the relations shown hold for the operation ⊕ and the numb [#permalink]  27 Jul 2020, 09:02
Expert's post
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
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Intern
Joined: 10 Aug 2019
Posts: 19
Followers: 0

Kudos [?]: 7 [1] , given: 2

Re: If the relations shown hold for the operation ⊕ and the numb [#permalink]  27 Jul 2020, 09:56
1
KUDOS
[(m⊕p)⊕q]⊕p

m⊕p = n
n⊕q = q
q⊕p = r

Ans E) r
GRE Instructor
Joined: 10 Apr 2015
Posts: 3677
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Kudos [?]: 4249 [1] , given: 67

Re: If the relations shown hold for the operation ⊕ and the numb [#permalink]  27 Jul 2020, 12:28
1
KUDOS
Expert's post
Carcass wrote:
$$m ⊕ p =n$$

$$n ⊕ r =m$$

$$n ⊕ q =q$$

$$p ⊕ q =p$$

$$q ⊕ p =r$$

If the relations shown hold for the operation ⊕ and the numbers m, n, p, q, and r, then $$[(m⊕p)⊕ q]⊕ p =$$

(A) m
(B) n
(C) p
(D) q
(E) r

[/quote]
We want to find the value of [(m ⊕ p) ⊕ q] ⊕ p

From statement I, we can write: [(m ⊕ p) ⊕ q] ⊕ p = [(n) ⊕ q] ⊕ p = [n ⊕ q] ⊕ p
From statement III, we can write: [n ⊕ q] ⊕ p = [q] ⊕ p = q ⊕ p
From statement V, we can write: q ⊕ p = r

Cheers,
Brent
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Re: If the relations shown hold for the operation ⊕ and the numb   [#permalink] 27 Jul 2020, 12:28
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