Mixture

In a mixture problem, the amount (or value) of an ingredient in a substance before mixing equals the amount (or value) of that ingredient in the substance after mixing:

Amount of Ingredient Before Mixing = Amount of Ingredient After Mixing

Here’s how you’d apply this concept in a GMAT mixture problem.

What amount (in milliliters) of a 1% hydrogen peroxide solution must be added to 60 milliliters of a 6% hydrogen peroxide solution to yield a 5% hydrogen peroxide solution?

• (A) 12
• (B) 15
• (C) 18
• (D) 20
• (E) 45

Let x = the amount (in milliliters) of the 1% hydrogen peroxide solution that must be added. Then, the total volume of the final hydrogen peroxide solution is x + 60.

1. Determine the amount of hydrogen peroxide before mixing: $1\% \times x + 6\% \times 60$
2. Determine the amount of hydrogen peroxide after mixing: $5\% \times (x + 60)$
3. Set the two amounts equal and solve the resulting equation:

Amount of Ingredient Before Mixing = Amount of Ingredient After Mixing

$1\% \times x + 6\% \times 60 = 5\% \times (x + 60)$

Now, solve the equation step by step:

• $0.01x + 0.06 \times 60 = 0.05 \times (x + 60)$
• $0.01x + 3.6 = 0.05x + 3$
• $3.6 - 3 = 0.05x - 0.01x$
• $0.6 = 0.04x$
• $x = \frac{0.6}{0.04} = 15$

The amount of the 1% hydrogen peroxide solution to be added is 15 milliliters.