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# For all integers x and y, the operation  is defined by xy = (x+2)^2

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Math Expert
Joined: 02 Sep 2009
Posts: 41873

Kudos [?]: 128579 [0], given: 12180

For all integers x and y, the operation  is defined by xy = (x+2)^2 [#permalink]

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18 Aug 2016, 07:38
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65% (hard)

Question Stats:

59% (01:26) correct 41% (01:15) wrong based on 108 sessions

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For all integers x and y, the operation  is defined by xy = (x+2)^2 + (y+3)^2. What is the value of integer t?

(1) t  2 = 74
(2) 2  t = 80
[Reveal] Spoiler: OA

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Kudos [?]: 128579 [0], given: 12180

Senior Manager
Joined: 23 Apr 2015
Posts: 332

Kudos [?]: 112 [2], given: 36

Location: United States
WE: Engineering (Consulting)
For all integers x and y, the operation  is defined by xy = (x+2)^2 [#permalink]

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18 Aug 2016, 08:48
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Bunuel wrote:
For all integers x and y, the operation  is defined by xy = (x+2)^2 + (y+3)^2. What is the value of integer t?

(1) t  2 = 74
(2) 2  t = 80

Answer is (C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

With 1) t  2 = 74 , gives, $$(t+2)^2 + (2+3)^2 = 74 => (t+2)^2= 49$$ and t can be -7-2=-9 or 7-2 =5. Hence insufficient , Eliminate A and D
With 2) 2  t = 80 , gives, $$(2+2)^2 + (t+3)^2 = 80 => (t+3)^2 = 64$$ and t can be -8-3 = -11 or 8-3=5. Hence insufficient, Eliminate B.

With 1) and 2) together, t = 5 . Hence sufficient and answer is C

+1 for kudos

Kudos [?]: 112 [2], given: 36

Intern
Joined: 26 Jul 2016
Posts: 30

Kudos [?]: 1 [0], given: 16

Re: For all integers x and y, the operation  is defined by xy = (x+2)^2 [#permalink]

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15 Jun 2017, 22:44
St. 1--> t  2 = 74--> (t+2)^2+(2+3)^2=74
(t+2)^2= 74-25---> t+2=+/-7
t=5 or t=-9 Not sufficient
St. 2--> 2  t = 80--> (2+2)^2+(t+3)^2=80
t+3= +/-8--> t=5 ot t=-11 Not sufficient

Kudos [?]: 1 [0], given: 16

Math Expert
Joined: 02 Sep 2009
Posts: 41873

Kudos [?]: 128579 [0], given: 12180

Re: For all integers x and y, the operation  is defined by xy = (x+2)^2 [#permalink]

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05 Oct 2017, 05:49
For all integers x and y, the operation  is defined by xy = (x+2)^2 + (y+3)^2. What is the value of integer t?

(1) t  2 = 74 --> $$(t + 2)^2 + (2 + 3)^2 = 74$$ --> $$t^2 + 4t - 45 = 0$$ --> $$t = 5$$ OR $$t = -9$$. Two values for t. Not sufficient.

(2) 2  t = 80 --> $$(2 + 2)^2 + (t + 3)^2 = 80$$ --> $$t^2 +6t - 55 = 0$$ --> $$t = 5$$ OR $$t = -11$$. Two values for t. Not sufficient.

(1)+(2) t=5. Sufficient.

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Kudos [?]: 128579 [0], given: 12180

Re: For all integers x and y, the operation  is defined by xy = (x+2)^2   [#permalink] 05 Oct 2017, 05:49
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