Is the average speed for the whole journey <span class="math-inline" data-latex-source="60" 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>60</mn></mrow><annotation encoding="application/x-tex">60</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">60</span></span></span></span></span> km/h? Statement I: The journey consists of equal distances covered at <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> km/h and <span class="math-inline" data-latex-source="60" 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>60</mn></mrow><annotation encoding="application/x-tex">60</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">60</span></span></span></span></span> km/h. Statement II: The harmonic mean of <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> and <span class="math-inline" data-latex-source="60" 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>60</mn></mrow><annotation encoding="application/x-tex">60</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">60</span></span></span></span></span> is <span class="math-inline" data-latex-source="48" 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>48</mn></mrow><annotation encoding="application/x-tex">48</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">48</span></span></span></span></span>. Choose the standard data-sufficiency option.
Practice this question from Chapter Mock 16: Data Sufficiency, with options and an explanation.
Question
Is the average speed for the whole journey <span class="math-inline" data-latex-source="60" 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>60</mn></mrow><annotation encoding="application/x-tex">60</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">60</span></span></span></span></span> km/h?
Statement I: The journey consists of equal distances covered at <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> km/h and <span class="math-inline" data-latex-source="60" 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>60</mn></mrow><annotation encoding="application/x-tex">60</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">60</span></span></span></span></span> km/h.
Statement II: The harmonic mean of <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> and <span class="math-inline" data-latex-source="60" 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>60</mn></mrow><annotation encoding="application/x-tex">60</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">60</span></span></span></span></span> is <span class="math-inline" data-latex-source="48" 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>48</mn></mrow><annotation encoding="application/x-tex">48</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">48</span></span></span></span></span>.
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 equal-distance average speed becomes the harmonic mean, which is $48$, so the answer to the question is "No". Statement II alone also directly gives the same result, so either alone is sufficient. Hence the answer is D.