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If the relations shown hold for the operation ⊕ and the numbers m, n,
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gmatt1476
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If the relations shown hold for the operation ⊕ and the numbers m, n, [#permalink] New post  20 Apr 2020, 10:01
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\(m ⊕ p =n\)

\(n ⊕ r =m \)

\(n ⊕ q =q \)

\(p ⊕ q =p \)

\(q ⊕ p =r \)

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


PS45430.02
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BrentGMATPrepNow
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Re: If the relations shown hold for the operation ⊕ and the numbers m, n, [#permalink] New post  28 Apr 2020, 08:42
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gmatt1476 wrote:

I. \(m ⊕ p =n\)

II. \(n ⊕ r =m \)

III. \(n ⊕ q =q \)

IV. \(p ⊕ q =p \)

V. \(q ⊕ p =r \)

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

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

Answer: E

Cheers,
Brent
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Re: If the relations shown hold for the operation ⊕ and the numbers m, n, [#permalink] New post  20 Apr 2020, 13:55
gmatt1476 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


PS45430.02


\([(m⊕p)⊕ q]⊕ p = [n⊕q]⊕p= [q]⊕p= r\)

Answer (E).
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rahulbhusan
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Re: If the relations shown hold for the operation ⊕ and the numbers m, n, [#permalink] New post  22 Apr 2020, 06:31
gmatt1476 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


PS45430.02


Just plug in the values from the given relations above
[(m⊕p)⊕q]⊕p
=>[(n)⊕q]⊕p
=> [q]⊕p
=> r
Option E
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CrackverbalGMAT
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If the relations shown hold for the operation ⊕ and the numbers m, n, [#permalink] New post  11 Feb 2021, 03:33
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SOLUTION :

A NEW OG 2021 QUESTION

(m ⊕p)⊕q]⊕p

=(n⊕ q]⊕p (Using, m ⊕ p=n)

=q ⊕p (Using, n ⊕q=q)

=r (Given, q ⊕p=r)

(OPTION E)

Hope this helps :thumbsup:
Devmitra Sen (Math)
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Re: If the relations shown hold for the operation ⊕ and the numbers m, n, [#permalink] New post  15 May 2021, 03:15
Expert Reply
gmatt1476 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


PS45430.02


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Answer: Option E

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