What is the rate of interest per annum? Statement I: Rs. <span class="math-inline" data-latex-source="2000" 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>2000</mn></mrow><annotation encoding="application/x-tex">2000</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">2000</span></span></span></span></span> becomes Rs. <span class="math-inline" data-latex-source="2420" 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>2420</mn></mrow><annotation encoding="application/x-tex">2420</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">2420</span></span></span></span></span> in <span class="math-inline" data-latex-source="2" 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>2</mn></mrow><annotation encoding="application/x-tex">2</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">2</span></span></span></span></span> years at compound interest compounded annually. Statement II: Rs. <span class="math-inline" data-latex-source="2000" 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>2000</mn></mrow><annotation encoding="application/x-tex">2000</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">2000</span></span></span></span></span> fetches an interest of Rs. <span class="math-inline" data-latex-source="400" 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>400</mn></mrow><annotation encoding="application/x-tex">400</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">400</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
What is the rate of interest per annum?
Statement I: Rs. <span class="math-inline" data-latex-source="2000" 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>2000</mn></mrow><annotation encoding="application/x-tex">2000</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">2000</span></span></span></span></span> becomes Rs. <span class="math-inline" data-latex-source="2420" 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>2420</mn></mrow><annotation encoding="application/x-tex">2420</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">2420</span></span></span></span></span> in <span class="math-inline" data-latex-source="2" 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>2</mn></mrow><annotation encoding="application/x-tex">2</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">2</span></span></span></span></span> years at compound interest compounded annually.
Statement II: Rs. <span class="math-inline" data-latex-source="2000" 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>2000</mn></mrow><annotation encoding="application/x-tex">2000</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">2000</span></span></span></span></span> fetches an interest of Rs. <span class="math-inline" data-latex-source="400" 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>400</mn></mrow><annotation encoding="application/x-tex">400</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">400</span></span></span></span></span>.
Choose the standard data-sufficiency option.
Option A — Correct answer
A
Correct choice.
Option B
B
Option C
C
Option D
D
Option E
E
Explanation
Statement I alone is sufficient because $2420/2000=1.21=(1.1)^2$, so the rate is $10\%$ per annum. Statement II alone is insufficient because the time period is not given. Hence the answer is A.