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# Data Sufficiency: Simultaneous Equations

What is the value of $$y$$? >(1) $$2.5z +2y +1.5x = 6$$ >(2) $$y - 3x - 5z = 13$$
Correct. [[snippet]] According to Stat. (1), $$\rightarrow 2.5z + 2y + 1.5x = 6$$. The number of unknowns (3) is greater than the number of equations (1), so you can't find the value of any of the unknowns, including $$y$$. Stat.(1) → IS → BCE. According to Stat. (2), $$\rightarrow y - 3x - 5z = 13$$. The number of unknowns (3) is greater than the number of equations (1), so you can't find the value of any of the unknowns, including $$y$$. Stat.(2) → IS → CE. According to Stat. (1+2), $$\rightarrow 2.5z + 2y +1.5x = 6$$ and $$\rightarrow y - 3x - 5z = 13$$. It seems as if the two statements together are insufficient. But multiplying the first equation by 2 reaches the desired outcome of equal coefficients for $$x$$ and $$z$$ in both equations. $$\rightarrow 5z + 4y + 3x = 12$$ Now add the first equation to this. $$\rightarrow (5z+4y+3x) + (y-3x - 5z) = 12 + 13$$ $$\rightarrow 5y = 25$$ $$\rightarrow y =5$$ Stat.(1+2) → S → C.
Incorrect. [[snippet]] According to Stat. (2), $$\rightarrow y - 3x - 5z = 13$$. The number of unknowns (3) is greater than the number of equations (1), so you can't find the value of any of the unknowns, including $$y$$. Stat.(2) → IS → ACE.
Incorrect. [[snippet]] According to Stat. (1), $$\rightarrow 2.5z + 2y + 1.5x = 6$$. The number of unknowns (3) is greater than the number of equations (1), so you can't find the value of any of the unknowns, including $$y$$. Stat.(1) → IS → BCE.
Incorrect. [[snippet]] According to Stat. (1), $$\rightarrow 2.5z + 2y + 1.5x = 6$$. The number of unknowns (3) is greater than the number of equations (1), so you can't find the value of any of the unknowns, including $$y$$. Stat.(1) → IS → BCE.
Incorrect. [[snippet]] According to Stat. (1+2), $$\rightarrow 2.5z + 2y +1.5x = 6$$ and $$\rightarrow y - 3x - 5z = 13$$. It seems as if the two statements together are insufficient. But multiplying the first equation by 2 reaches the desired outcome of equal coefficients for $$x$$ and $$z$$ in both equations. $$\rightarrow 5z + 4y + 3x = 12$$ Now add the first equation to this. $$\rightarrow (5z+4y+3x) + (y-3x - 5z) = 12 + 13$$ $$\rightarrow 5y = 25$$ $$\rightarrow y =5$$ Stat.(1+2) → S.
Statement (1) ALONE is sufficient, but Statement (2) alone is not sufficient to answer the question asked.
Statement (2) ALONE is sufficient, but Statement (1) alone is not sufficient to answer the question asked.
BOTH Statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.