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

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

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New post 17 Oct 2008, 06:08
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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

Last edited by pm4553 on 17 Oct 2008, 09:21, edited 1 time in total.

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Re: GMAT Set - Q6 [#permalink]

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New post 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.


answer is D
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

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Re: GMAT Set - Q6 [#permalink]

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New post 17 Oct 2008, 08:57
Can you explain please?

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Re: GMAT Set - Q6 [#permalink]

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New post 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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Re: GMAT Set - Q6 [#permalink]

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New post 17 Oct 2008, 09:22
Thanks Amit - have edited the question.

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Re: GMAT Set - Q6 [#permalink]

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New post 19 Oct 2008, 06:24
[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

Last edited by yezz on 19 Oct 2008, 08:20, edited 2 times in total.

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Re: GMAT Set - Q6 [#permalink]

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New post 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

Answer: C

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Re: GMAT Set - Q6 [#permalink]

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New post 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?

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Re: GMAT Set - Q6 [#permalink]

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New post 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.

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Re: GMAT Set - Q6 [#permalink]

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New post 20 Oct 2008, 16:25
Agree with C

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

Together : t =5

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Re: GMAT Set - Q6 [#permalink]

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New post 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


C is the correct answer.

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Re: GMAT Set - Q6   [#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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