Number Series, Coding and DecodingMCQMTP Sep 24 Series IQuestion 2079 of 217

Find the missing value in the series: $51, 52, 60, 87, 151, ______. 492.$

Select Your Answer (Keyboard: A, B, C, D)

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Correct Answer

✅ Option b — $276$

To find the missing value in the series $51, 52, 60, 87, 151, ?, 492

\displaystyle , let us analyze the differences between consecutive terms:<br><br>- 1st to 2nd term: &#36;52 - 51 = 1 = 1^3

- 2nd to 3rd term: $60 - 52 = 8 = 2^3

\displaystyle <br>- 3rd to 4th term: &#36;87 - 60 = 27 = 3^3

- 4th to 5th term: $151 - 87 = 64 = 4^3

\displaystyle <br><br>We observe that the difference between terms is the sequence of consecutive perfect cubes (

1^3, 2^3, 3^3, 4^3, \dots

\displaystyle ).<br>Following this logical pattern, the next difference must be

5^3 = 125$. We add $125$ to the 5th term ($151

\displaystyle ):<br><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mn>151</mn><mo>+</mo><mn>125</mn><mo>=</mo><mn>276</mn></mrow><annotation encoding="application/x-tex">151 + 125 = 276</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">151</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">125</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">276</span></span></span></span></span><br>Let us verify the final step by adding

6^3 = 216

\displaystyle to our result:<br><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mn>276</mn><mo>+</mo><mn>216</mn><mo>=</mo><mn>492</mn></mrow><annotation encoding="application/x-tex">276 + 216 = 492</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">276</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">216</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">492</span></span></span></span></span><br>This perfectly matches the last term in the sequence, mathematically proving that the missing term is &#36;276

.

Hence, **Option B** is the correct answer.

Paper

Paper 3: Quantitative Aptitude

Weightage

5 Marks

Key Topics

Number series, Coding & Decoding, Odd man out

This chapter covers Number series, Coding & Decoding, Odd man out and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

Exam Strategy Tip

This topic carries 5 Marks weightage. Focus on understanding core concepts rather than memorizing.

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