IPMAT Indore 2024 · Quantitative Ability · Question 17

Step 1 — a sum of non-negatives equal to zero. Both \left| x+1 \right|\ge 0 and {\left( y+2 \right)}^{2}\ge 0. Their sum is zero only if each is zero:

\left| x+1 \right|=0 \Rightarrow x=-1

{\left( y+2 \right)}^{2}=0 \Rightarrow y=-2

Step 2 — substitute into the second equation.

a\left( -1 \right)-3a\left( -2 \right)=1

-a+6a=1 \Rightarrow 5a=1 \Rightarrow a=\frac{1}{5}

Answer: Option 1 — \frac{1}{5}

Shortcut. “Non-negatives summing to zero” is a gift. It hands you both variables at once: x=-1, y=-2. Then ax-3ay=a\left( x-3y \right)=a\left( -1+6 \right)=5a=1. Factor out a before substituting and the arithmetic is a single step: a=1/5. Watch the double negative — dropping it gives -7a=1 and tempts you toward option (c).