Is the triangle equilateral? Statement I: All three sides are equal. Statement II: Each angle of the triangle is <span class="math-inline" data-latex-source="60^\circ" data-display-mode="false" contenteditable="false"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mn>60</mn><mo>∘</mo></msup></mrow><annotation encoding="application/x-tex">60^\circ</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6741em;"></span><span class="mord">6</span><span class="mord"><span class="mord">0</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6741em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">∘</span></span></span></span></span></span></span></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 triangle equilateral?
Statement I: All three sides are equal.
Statement II: Each angle of the triangle is <span class="math-inline" data-latex-source="60^\circ" data-display-mode="false" contenteditable="false"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mn>60</mn><mo>∘</mo></msup></mrow><annotation encoding="application/x-tex">60^\circ</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6741em;"></span><span class="mord">6</span><span class="mord"><span class="mord">0</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6741em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">∘</span></span></span></span></span></span></span></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 by definition. Statement II alone is also sufficient because a triangle with all angles $60^\circ$ is equilateral. Either statement alone is sufficient, so the answer is D.