$$x^2=y+5\ \ \ \ ---eqn\ \left(1\right)$$
$$y=z-2\ \ \ \ ---eqn\ \left(2\right)$$
$$z=2x\ \ \ \ ---eqn\ \left(3\right)$$
Substituting eqn (3) into eqn (2)
y = 2x - 2 - - - eqn (4)
Substituting eqn (4) into eqn (1)
$$x^2=2x-2+5$$
$$x^2=2x+3$$
$$x^2-2x-3=0$$
$$x^2-3x+x-3=0$$
$$x\left(x-3\right)+1\left(x-3\right)=0$$
x+1=0 or x-3=0
x=-1 or x=3
If x=-1, then z = 2(-1) = -2 and y = -2-2 = -4
If x=3, then z = 2(3) = 6 and y = 6-2 = 4
$$Target\ question=is\ x^3+y^2+z\ divisible\ by\ 7?$$
Statement 1: x>0
This means the value of x=3, y=4 and z=6.
$$\ x^3+y^2+z\ =>3^2+4^2+6=49$$
49 is divisible by 7. Hence, statement 1 is SUFFICIENT.
Statement 2: y=4
From the question stem, if y=4, then x=3 and z=6.
i.e if y=4, since y=z-2
z=y+2 = 4+2 = 6
And since z=2x, where z=6
x = 6/2 = 3
$$Therefore,\ \ x^3+y^2+z\ =>3^2+4^2+6=49$$
Also, 49 is divisible by 7, hence, statement 2 is SUFFICIENT.
Answer = option D
If \(x^2=y+5, y=z-2\) and \(z=2x,\) is \(x^3+y^2+z\) divisible by \(7?\)
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Source: Beat The GMAT — Data Sufficiency |
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deloitte247
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