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If operation p # q is defined for all integers p and q, such that

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Joined: 07 Jun 2017
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If operation p # q is defined for all integers p and q, such that [#permalink]

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New post 19 Oct 2017, 04:45
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A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

50% (01:18) correct 50% (01:32) wrong based on 28 sessions

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If operation p # q is defined for all integers p and q, such that t p # q = p+q+pq, which of the following must be true?

I. p # q = q # p
II. p # 1 = 2p + 1
III. p # (q # r) = (p # q) # r


A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III
[Reveal] Spoiler: OA

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email: nkmungila@gmail.com
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Kudos [?]: 138 [0], given: 379

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Re: If operation p # q is defined for all integers p and q, such that [#permalink]

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New post 19 Oct 2017, 07:24
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nkmungila wrote:
If operation p # q is defined for all integers p and q, such that t p # q = p+q+pq, which of the following must be true?

I. p # q = q # p
II. p # 1 = 2p + 1
III. p # (q # r) = (p # q) # r


A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III


I - p # q = p+q+pq
q # p = q+p+qp
which is the same.

II - p # 1 = p+1+p*1=2p+1 which is true

III - p # (q # r) = p#(q+r+qr)=p+q+r+qr+p*(q+r+qr) = p+q+r+qr+pq+pr+pqr
(p # q) # r = (p+q+pq)#r = p+q+pq+r+(p+q+pq)*r=p+q+pq+r+pr+qr+pqr
comparing both the terms it is the same.

Hence all three are true.

Answer E.

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Re: If operation p # q is defined for all integers p and q, such that   [#permalink] 19 Oct 2017, 07:24
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