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# ds -divisble

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SVP
Joined: 07 Nov 2007
Posts: 1738
Location: New York

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04 Sep 2008, 13:02
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if $$x^2=y+5$$ and $$y=z-2$$ and 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
If we substitute z and y with x in the three equations we have

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Manager
Joined: 22 Jul 2008
Posts: 140

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04 Sep 2008, 13:18
St.1 By substitutions one can get the equation,
x^2 - 2x-3 =0
Solving for x, x= +3 or -1; If x=3, then y=4 and z=6
Putting these values in, we get the result of 49 which is divisible by 7. However, if x= -1, we get 13 as the result and it is not divisible by 7. Therefore, St.1 is required and sufficient.

St. 2 By putting the values in, we get 49 that is divisible by 7. So, sufficient.
Intern
Joined: 29 Jul 2008
Posts: 7

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04 Sep 2008, 13:48
i'd go for b.

The stem's equations can be used to put the equation of the question in terms of x onl. So x^3+4X^2-6X+4.

St 1) insuff try x=1 answer no x=3 ans yes
St 2) we can get the value of x using one of the eq in the stem and replace. Suff.
Senior Manager
Joined: 31 Jul 2008
Posts: 270

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04 Sep 2008, 14:19
will go for B

for 1 reduce equation in terms of x

for 2 reduce the equation in terms of y
Manager
Joined: 15 Jul 2008
Posts: 205

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04 Sep 2008, 17:34
x2suresh wrote:
if $$x^2=y+5$$ and $$y=z-2$$ and 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
If we substitute z and y with x in the three equations we have

What is the OA dude ?
B is very tempting.. but when i try stem 1 with x=1,2,3,4, and 5.. only x=3 seems to satisfy all the 3 equations in the question. So D is looks realistic.
what is the source and OE ?
Intern
Joined: 06 Aug 2007
Posts: 37

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04 Sep 2008, 18:06
I vote for D.

X^2=Y+5, Y=Z-2, Z=2X

A. X>0

X^2=2X-2+5
X^2-2X+3=0, solving for X gives X=3

Solving for Y and Z gives, Y=4, Z=6... Sufficient

B. Y=4

Solving for X and Z gives, X=3, Z=6... Sufficient
SVP
Joined: 07 Nov 2007
Posts: 1738
Location: New York

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04 Sep 2008, 20:04
OA is D

This is from GMATCLUB challenges.
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VP
Joined: 17 Jun 2008
Posts: 1289

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05 Sep 2008, 22:14
x2suresh wrote:
if $$x^2=y+5$$ and $$y=z-2$$ and 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
If we substitute z and y with x in the three equations we have

(1)here solving eqns we get x=-1,3 => 3 gives div by 7 but when x=-1 the expr is noit div => INSUFFI
(2)gives x=3 and hence when substituted the expr is div by 7 SUFFI

IMO B
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VP
Joined: 17 Jun 2008
Posts: 1289

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05 Sep 2008, 22:16
spriya wrote:
x2suresh wrote:
if $$x^2=y+5$$ and $$y=z-2$$ and 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
If we substitute z and y with x in the three equations we have

(1)here solving eqns we get x=-1,3 => 3 gives div by 7 but when x=-1 the expr is noit div => INSUFFI
(2)gives x=3 and hence when substituted the expr is div by 7 SUFFI

IMO B

i made silly mistake overlooked x>0
oh god!!!
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Its Now Or Never

Manager
Joined: 04 Jan 2008
Posts: 116

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06 Sep 2008, 02:47
IMO D

x^2=y+5, y=z-2, z=2x
Now,
y=z-2 => z=2+y
but, z=2x, means 2x=2+y => x=1+y/2
Putting x in x^2=y+5 => (1+y/2)^2=y+5
Solving further gives y=4 or -4

Now eliminating y from x^2=y+5 and y=z-2 gives x^2=z+3
putting z=2x gives, x^2=2x+3
Solving further gives x=-1 or 3

Now Option (1) says x>0, means x=3
and z=6 & y=4 => SUFFI to answer

Option (2) says y=4, thus gives z=6 & x=3 again => SUFFI to answer

thus D

--== 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: ds -divisble   [#permalink] 06 Sep 2008, 02:47
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