## If $$x$$ is a positive integer, what is $$x?$$

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### If $$x$$ is a positive integer, what is $$x?$$

by Gmat_mission » Wed Sep 23, 2020 5:27 am

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## Global Stats

If $$x$$ is a positive integer, what is $$x?$$

(1) $$x^2 + 7x - 18 = 0$$

(2) $$x^2 - 7x + 10 = 0$$

Source: Manhattan GMAT

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### Re: If $$x$$ is a positive integer, what is $$x?$$

by deloitte247 » Sat Oct 03, 2020 9:59 am

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## Global Stats

$$Statement\ 1\ =>\ x^{^2}+7x-18=0$$
$$\ x^{^2}-2x+9x-18=0$$
$$x\left(x-2\right)+9\left(x-2\right)=0$$
$$x+9=0\ or\ x-2=0$$
$$x=-9\ or\ x=2$$
Since x is a positive integer, x is not = -9 but definitely x = 2. Hence, statement 1 is SUFFICIENT

$$Statement\ 2\ =>x^2-7x+10=0$$
$$x^2-5x-2x+10$$
$$x\left(x-5\right)-2\left(x-5\right)$$
$$x-2=0\ or\ x-5=0$$
$$x=2\ or\ x=5$$
Both answers are positive integers so the information provided was not enough to arrive at a definite answer so statement 2 is NOT SUFFICIENT

Since only statement 1 is SUFFICIENT,