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

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

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

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New post 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




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

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New post 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
1+2---> t=5 sufficient Answer C

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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]

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New post 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.

Answer: C.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

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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