What is the ratio of milk to water in a mixture? Statement I: The mixture contains <span class="math-inline" data-latex-source="40" data-display-mode="false" contenteditable="false"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>40</mn></mrow><annotation encoding="application/x-tex">40</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">40</span></span></span></span></span> litres of milk and <span class="math-inline" data-latex-source="10" data-display-mode="false" contenteditable="false"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>10</mn></mrow><annotation encoding="application/x-tex">10</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">10</span></span></span></span></span> litres of water. Statement II: Milk forms <span class="math-inline" data-latex-source="80\%" data-display-mode="false" contenteditable="false"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>80</mn><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">80\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">80%</span></span></span></span></span> of the mixture. Choose the standard data-sufficiency option.
Practice this question from Chapter Mock 16: Data Sufficiency, with options and an explanation.
Question
What is the ratio of milk to water in a mixture?
Statement I: The mixture contains <span class="math-inline" data-latex-source="40" data-display-mode="false" contenteditable="false"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>40</mn></mrow><annotation encoding="application/x-tex">40</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">40</span></span></span></span></span> litres of milk and <span class="math-inline" data-latex-source="10" data-display-mode="false" contenteditable="false"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>10</mn></mrow><annotation encoding="application/x-tex">10</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">10</span></span></span></span></span> litres of water.
Statement II: Milk forms <span class="math-inline" data-latex-source="80\%" data-display-mode="false" contenteditable="false"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>80</mn><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">80\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">80%</span></span></span></span></span> of the mixture.
Choose the standard data-sufficiency option.
Option A
A
Option B
B
Option C
C
Option D — Correct answer
D
Correct choice.
Option E
E
Explanation
Statement I alone is sufficient because the ratio is $40:10=4:1$. Statement II alone is also sufficient because if milk is $80\%$, then water is $20\%$, giving ratio $80:20=4:1$. So the answer is D.