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# Q6: For all integers x and y, the operation ? is defined by

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Director
Joined: 27 Jun 2008
Posts: 505
WE 1: Investment Banking - 6yrs
Q6: For all integers x and y, the operation ? is defined by  [#permalink]

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Updated on: 17 Oct 2008, 09:21
Q6:
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

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

EDIT : its (x+2)^2 + (y+3)^2

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Originally posted by pm4553 on 17 Oct 2008, 06:08.
Last edited by pm4553 on 17 Oct 2008, 09:21, edited 1 time in total.
Manager
Joined: 15 Apr 2008
Posts: 159
Re: GMAT Set - Q6  [#permalink]

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17 Oct 2008, 06:29
pawan203 wrote:
Q6:
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

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

statement 1: t ? 2=(t+2)2+(2+3)2=74
statement 2: same way to solve as for statement 1

what is the OA
Director
Joined: 27 Jun 2008
Posts: 505
WE 1: Investment Banking - 6yrs
Re: GMAT Set - Q6  [#permalink]

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17 Oct 2008, 08:57
VP
Joined: 30 Jun 2008
Posts: 1004
Re: GMAT Set - Q6  [#permalink]

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17 Oct 2008, 09:07
pawan203 wrote:
Q6:
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

is the question (x+2)^2 + (y+3)^2
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Director
Joined: 27 Jun 2008
Posts: 505
WE 1: Investment Banking - 6yrs
Re: GMAT Set - Q6  [#permalink]

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17 Oct 2008, 09:22
Thanks Amit - have edited the question.
Retired Moderator
Joined: 05 Jul 2006
Posts: 1733
Re: GMAT Set - Q6  [#permalink]

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Updated on: 19 Oct 2008, 08:20
[quote="pawan203"]Q6:
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

t?2 = (t+2)^2 + (2+3)^2 = 74

t+2 = 7 or -t-2 = 7 t = 5 or -9.....insuff

from 2

4^2 + (t+3)^2 = 80

(t+3)^2 = 64 = 8^2
t+3 = 8.....or -t-3 = 8, t = -512 .......insuff

both.......T = 5

c

Originally posted by yezz on 19 Oct 2008, 06:24.
Last edited by yezz on 19 Oct 2008, 08:20, edited 2 times in total.
Intern
Joined: 19 Oct 2008
Posts: 1
Re: GMAT Set - Q6  [#permalink]

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19 Oct 2008, 06:55
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

Statement I:

(t+2)^2 = 49
t^2+4t-49 = 0
(t+9)(t-5) = 0
t => -9, 5 => Not sufficient

Statement II:
(t+3)^2=64
(t+11)(t-5)=0
t=> -11,5 => Not sufficient

Both statements taken together => t = 5

Senior Manager
Joined: 21 Apr 2008
Posts: 456
Schools: Kellogg, MIT, Michigan, Berkeley, Marshall, Mellon
Re: GMAT Set - Q6  [#permalink]

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19 Oct 2008, 11:30
Hi guys,

IMO: C

1 (t+2)^2+25=74. We have here a second degree eq. therefore, two possible solutions. Not suff.

2 16+(t+3)^2=80 We have here a second degree eq. therefore, two possible solutions. Not suff.

1+2 we have two different eqs. and therefore, just one solution will comply with both

C

OA?

Cheers
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VP
Joined: 17 Jun 2008
Posts: 1474
Re: GMAT Set - Q6  [#permalink]

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19 Oct 2008, 23:44
Agree C.

It does not say that t is positive. Hence, two possible values from both the statements and only common value that satisfies both statements is 5.
Senior Manager
Joined: 21 Apr 2008
Posts: 265
Location: Motortown
Re: GMAT Set - Q6  [#permalink]

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20 Oct 2008, 16:25
Agree with C

1. t = 5, -9
2. t = -11, 5

Together : t =5
Manager
Joined: 15 Oct 2008
Posts: 102
Re: GMAT Set - Q6  [#permalink]

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20 Oct 2008, 17:00
pawan203 wrote:
Q6:
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

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

EDIT : its (x+2)^2 + (y+3)^2

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Re: GMAT Set - Q6 &nbs [#permalink] 20 Oct 2008, 17:00
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# Q6: For all integers x and y, the operation ? is defined by

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