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# if X^2=y+5 , y=z-2 , z=2x Is x^3 + y^2 +z divisible by 7 a)

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Senior Manager
Joined: 19 Sep 2004
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if X^2=y+5 , y=z-2 , z=2x Is x^3 + y^2 +z divisible by 7 a) [#permalink]

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02 May 2007, 17:37
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

if X^2=y+5 , y=z-2 , z=2x
Is x^3 + y^2 +z divisible by 7

a) x>0
b) y=4

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

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Senior Manager
Joined: 24 Nov 2006
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Re: Real Hard one from GMAT Club Challenges [#permalink]

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02 May 2007, 17:58
x^3 + (x^2-5)^2+2x = x^4 + x^3 - 10x^2 + 2x + 25 = A

(1) For x>0 there are infinite (integer) values of the expression above. Doing some calculations we have that, for x=1, A=19; x=2, A=13; x=3, A=49. So The expression could or could not be divisible by 7. Insuff =) B, C or E.

(2) y=4 =) x=3 =) The expression is divisible by 7. Suff =) B.

One thing to point out (and that I forgot to apply in this problem) is the need to start with the easiest looking btw (1) and (2). In this case, it was (2). Doing this could surely help save some precious time on exam day.

saurabhmalpani wrote:
if X^2=y+5 , y=z-2 , z=2x
Is x^3 + y^2 +z divisible by 7

(1) x>0
(2) y=4

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

Kudos [?]: 27 [0], given: 0

Senior Manager
Joined: 19 Sep 2004
Posts: 367

Kudos [?]: 6 [0], given: 0

Re: Real Hard one from GMAT Club Challenges [#permalink]

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02 May 2007, 18:17
Was a nice try but I think you forgot that only those values of X will be considered which satisfies X^2=Y+5

Thanks
Saurabh Malpani

Andr359 wrote:
x^3 + (x^2-5)^2+2x = x^4 + x^3 - 10x^2 + 2x + 25 = A

(1) For x>0 there are infinite (integer) values of the expression above. Doing some calculations we have that, for x=1, A=19; x=2, A=13; x=3, A=49. So The expression could or could not be divisible by 7. Insuff =) B, C or E.

(2) y=4 =) x=3 =) The expression is divisible by 7. Suff =) B.

One thing to point out (and that I forgot to apply in this problem) is the need to start with the easiest looking btw (1) and (2). In this case, it was (2). Doing this could surely help save some precious time on exam day.

saurabhmalpani wrote:
if X^2=y+5 , y=z-2 , z=2x
Is x^3 + y^2 +z divisible by 7

(1) x>0
(2) y=4

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

Kudos [?]: 6 [0], given: 0

Director
Joined: 26 Feb 2006
Posts: 900

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Re: Real Hard one from GMAT Club Challenges [#permalink]

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02 May 2007, 18:50
saurabhmalpani wrote:
if X^2 = y + 5, y = z - 2, and z = 2x,
Is x^3 + y^2 + z divisible by 7?

a) x> 0
b) y = 4

x^2 = y + 5, y = z - 2 , z = 2x
x^2 = z - 2 + 5
x^2 = 2x - 2 + 5
x^2 - 2x -3 = 0
x = -1 or 3

if x = -1, y = -4, and z = -2
if x = 3, y = 4, and z = 6

from a:
x is +ve, so x = 3.
x^3 + y^2 + z = 49. suff

from b:
y = 4 implies that x = 3.
x^3 + y^2 + z = 49. suff

So D............

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Senior Manager
Joined: 19 Sep 2004
Posts: 367

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02 May 2007, 19:01
Great Stuff. You are right on the money!!!

OA is D.

Saurabh Malpani

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Senior Manager
Joined: 03 May 2007
Posts: 270

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03 May 2007, 08:52
To Himalayan
Thanks for explanation
It makes sense now.

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Intern
Joined: 05 Jun 2003
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Re: Real Hard one from GMAT Club Challenges [#permalink]

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03 May 2007, 10:35
Thanks Himalaya. You turned a difficult question into a simple and easily- understood form.

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Intern
Joined: 01 Feb 2007
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03 May 2007, 17:42
Great Stuff Himalayan. Thanks

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03 May 2007, 17:42
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# if X^2=y+5 , y=z-2 , z=2x Is x^3 + y^2 +z divisible by 7 a)

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