Gmat_mission wrote:Is \(\left(\frac{a}{p}\right)\left(p^2+r^2+s^2\right)=ap+br+cs?\)
(1) \(\frac{c}{s}=\frac{a}{p}\)
(2) \(\frac{a}{p}=\frac{b}{r}\)
[spoiler]OA=C[/spoiler]
Source: Veritas Prep
Hi Gmat_mission.
Let's start by solving the parenthesis: $$\left(\frac{a}{p}\right)\left(p^2+r^2+s^2\right)=ap+\frac{a}{p}\cdot r^2+\frac{a}{p}\cdot s^2.$$ Now, let's take a loot at the given statements.
Statement 1:
(1) \(\frac{c}{s}=\frac{a}{p}\)
Replacing it into the expression above we get $$ap+\frac{c}{s}\cdot r^2+\frac{c}{s}\cdot s^2=ap+\frac{a}{p}\cdot r^2+cs$$ Since we don't know if \(\frac{a}{p}\cdot r^2\) is equal to \(br\) or not, this statment is
NOT SUFFICIENT.
Statement 2:
(2) \(\frac{a}{p}=\frac{b}{r}\)
Again, if we replace this into the expression at the beginning we will get $$ap+\frac{a}{p}\cdot r^2+\frac{a}{p}\cdot s^2=ap+br+\frac{a}{p}\cdot s^2.$$ Since we don't know if \(\frac{a}{p}\cdot s^2\) is equal to \(cs\) or not, this statment is
NOT SUFFICIENT.
Statement 1 + Statement 2:
In this case we get $$ap+\frac{a}{p}\cdot r^2+\frac{a}{p}\cdot s^2=ap+br+cs.$$ An this is what we needed to answer. So, the answer is YES.
Therefore, using both statements together is
SUFFICIENT.
Hence, the correct answer is the option
_C_.
I hope it helps you. <i class="em em---1"></i>
