Number Series, Coding and DecodingMCQMTP March 22Question 2129 of 217
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If E=5\displaystyle E = 5 and READ=7\displaystyle READ = 7, then what is the code of 'DEAR'?

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

✅ Option b — 7

All Options:

  • A6
  • B7
  • C8
  • D9

Detailed Solution & Explanation

Let's find the coding rule using standard alphabetical positions (A=1,B=2,…,Z=26\displaystyle A=1, B=2, \dots, Z=26):
1. For the letter E\displaystyle E, the position is 5\displaystyle 5. The code is 5\displaystyle 5. Since there is 1\displaystyle 1 letter, the average position is 5/1=5\displaystyle 5/1 = 5.
2. For the word READ\displaystyle READ (number of letters, n=4\displaystyle n = 4):
Alphabetical values: R=18\displaystyle R = 18, E=5\displaystyle E = 5, A=1\displaystyle A = 1, D=4\displaystyle D = 4
Sum of values = $18 + 5 + 1 + 4 = 28<br>Calculatingtheaverageposition:<br><spanclass="katex−display"><spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"display="block"><semantics><mrow><mtext>Code</mtext><mo>=</mo><mfrac><mtext>Sum of positions</mtext><mi>n</mi></mfrac><mo>=</mo><mfrac><mn>28</mn><mn>4</mn></mfrac><mo>=</mo><mn>7</mn></mrow><annotationencoding="application/x−tex">Code=Sum of positionsn=284=7</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.6944em;"></span><spanclass="mordtext"><spanclass="mord">Code</span></span><spanclass="mspace"style="margin−right:0.2778em;"></span><spanclass="mrel">=</span><spanclass="mspace"style="margin−right:0.2778em;"></span></span><spanclass="base"><spanclass="strut"style="height:2.0574em;vertical−align:−0.686em;"></span><spanclass="mord"><spanclass="mopennulldelimiter"></span><spanclass="mfrac"><spanclass="vlist−tvlist−t2"><spanclass="vlist−r"><spanclass="vlist"style="height:1.3714em;"><spanstyle="top:−2.314em;"><spanclass="pstrut"style="height:3em;"></span><spanclass="mord"><spanclass="mordmathnormal">n</span></span></span><spanstyle="top:−3.23em;"><spanclass="pstrut"style="height:3em;"></span><spanclass="frac−line"style="border−bottom−width:0.04em;"></span></span><spanstyle="top:−3.677em;"><spanclass="pstrut"style="height:3em;"></span><spanclass="mord"><spanclass="mordtext"><spanclass="mord">Sum of positions</span></span></span></span></span><spanclass="vlist−s">​</span></span><spanclass="vlist−r"><spanclass="vlist"style="height:0.686em;"><span></span></span></span></span></span><spanclass="mclosenulldelimiter"></span></span><spanclass="mspace"style="margin−right:0.2778em;"></span><spanclass="mrel">=</span><spanclass="mspace"style="margin−right:0.2778em;"></span></span><spanclass="base"><spanclass="strut"style="height:2.0074em;vertical−align:−0.686em;"></span><spanclass="mord"><spanclass="mopennulldelimiter"></span><spanclass="mfrac"><spanclass="vlist−tvlist−t2"><spanclass="vlist−r"><spanclass="vlist"style="height:1.3214em;"><spanstyle="top:−2.314em;"><spanclass="pstrut"style="height:3em;"></span><spanclass="mord"><spanclass="mord">4</span></span></span><spanstyle="top:−3.23em;"><spanclass="pstrut"style="height:3em;"></span><spanclass="frac−line"style="border−bottom−width:0.04em;"></span></span><spanstyle="top:−3.677em;"><spanclass="pstrut"style="height:3em;"></span><spanclass="mord"><spanclass="mord">28</span></span></span></span><spanclass="vlist−s">​</span></span><spanclass="vlist−r"><spanclass="vlist"style="height:0.686em;"><span></span></span></span></span></span><spanclass="mclosenulldelimiter"></span></span><spanclass="mspace"style="margin−right:0.2778em;"></span><spanclass="mrel">=</span><spanclass="mspace"style="margin−right:0.2778em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.6444em;"></span><spanclass="mord">7</span></span></span></span></span>Thismatchesthegivencode.<br><br>Now,let′sapplythesameruletotheword\displaystyle <br>Calculating the average position:<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><mtext>Code</mtext><mo>=</mo><mfrac><mtext>Sum of positions</mtext><mi>n</mi></mfrac><mo>=</mo><mfrac><mn>28</mn><mn>4</mn></mfrac><mo>=</mo><mn>7</mn></mrow><annotation encoding="application/x-tex">\displaystyle \text{Code} = \frac{Sum of positions\displaystyle \text{Sum of positions}}{n} = 284=7\displaystyle \frac{28}{4} = 7</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord text"><span class="mord">Code</span></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:2.0574em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3714em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">n</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">Sum of positions</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></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:2.0074em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">4</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">28</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></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">7</span></span></span></span></span> This matches the given code.<br><br>Now, let's apply the same rule to the wordDEAR$ (which consists of the exact same letters as $READinadifferentorder):<br>Alphabeticalvalues:\displaystyle in a different order):<br>Alphabetical values:D = 4,\displaystyle ,E = 5,\displaystyle ,A = 1,\displaystyle ,R = 18<br>Sumofvalues=\displaystyle <br>Sum of values =4 + 5 + 1 + 18 = 28$
Calculating the average position:
Code=Sum of positionsn=284=7\displaystyle \text{Code} = \frac{Sum of positions\displaystyle \text{Sum of positions}}{n} = 284=7\displaystyle \frac{28}{4} = 7

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

About This Chapter: Number Series, Coding and Decoding

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.

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Exam Strategy Tip

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

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