early-number-systems MCQs for UPSC Prelims

26 practice questions on early-number-systems from the A Story of Numbers section of the UPSC Prelims syllabus. 26 come with a written explanation. Try the sample set below - the answer stays hidden until you ask for it.

8 Easy 13 Medium 5 Hard

Sample questions

Q1
medium

In an additive system the signs are worth $1$, $10$, $100$ and $1000$, and each sign may be repeated as often as needed. Which of these numbers needs the most signs?

  1. A $110$
  2. B $505$
  3. C $999$
  4. D $1000$
Show answer and explanation

Correct answer: C - $999$

$999$ needs nine hundreds, nine tens and nine units, which is $27$ signs. $1000$ needs one sign only. $505$ needs five hundreds and five units, so $10$ signs, and $110$ needs one hundred and one ten, so $2$ signs. The largest number of signs is therefore for $999$.

Q2
hard

A clerk uses a positional system with digits but no zero. To write three hundred and six he puts a $3$, leaves a small gap for the empty tens place, then writes a $6$. Months later a second clerk copies the record. What is the most likely problem?

  1. A The gap may be overlooked, so the number is copied as $36$
  2. B The gap turns the number into $360$ every time
  3. C The number will always be copied as $3006$
  4. D The number cannot be read by anyone at all
Show answer and explanation

Correct answer: A - The gap may be overlooked, so the number is copied as $36$

A gap has no shape of its own, so it can easily be missed or closed up while copying, leaving $36$. Reading it as $3006$ would need two empty places, not one. The record is readable, just unreliable, and a gap between the digits does not push the $6$ into the tens place to give $360$.

Q3
easy

In the ancient Egyptian number system a single stroke stood for $1$ and an arch shape stood for $10$, so $34$ was drawn as three arches and four strokes. What kind of system is this?

  1. A An additive system, in which the symbol values are simply added up
  2. B A system that needs a symbol for zero to work
  3. C A system that uses only two symbols in total
  4. D A place-value system, in which position decides a symbol's value
Show answer and explanation

Correct answer: A - An additive system, in which the symbol values are simply added up

The value is found by adding what the symbols are worth, with no help from position, which is what additive means. It is therefore not a place-value system. The Egyptians also had signs for $100$, $1000$ and more, and an additive system needs no zero.

Q4
medium

A number system is positional but has no sign for zero. Which real difficulty does this create?

  1. A Only even numbers can be written
  2. B An empty place inside a number cannot be shown clearly
  3. C The system can never use more than four signs
  4. D Numbers cannot be added at all
Show answer and explanation

Correct answer: B - An empty place inside a number cannot be shown clearly

In a positional system a digit gets its value from its column, so an empty column must be marked; with no zero, a scribe could only leave a gap, and gaps are easy to misread. Addition still works, odd numbers are written as usual, and the number of signs has nothing to do with zero.

Q5
medium

How is $49$ written in Roman numerals?

  1. A IL
  2. B XLIX
  3. C XXXXIX
  4. D LIX
Show answer and explanation

Correct answer: B - XLIX

Split $49$ as $40+9$, where $40$ is XL and $9$ is IX, giving XLIX. IL is invalid, since I may only stand before V or X. XXXXIX repeats X four times, which the rules forbid. LIX means $50+9=59$.

Q6
medium

A museum label shows the Roman numeral LXXVII. What number is this in our system?

  1. A $67$
  2. B $72$
  3. C $77$
  4. D $87$
Show answer and explanation

Correct answer: C - $77$

L is $50$, the two X signs give $20$, V is $5$ and the two I signs give $2$, so the total is $50+20+5+2=77$. Counting only one X gives $67$ and counting three gives $87$. Missing the V gives $72$.

Q7
medium

Four Roman numerals are written below. Which one has the largest value?

  1. A CCC
  2. B XC
  3. C CD
  4. D CL
Show answer and explanation

Correct answer: C - CD

CD uses the subtractive rule, so it is $500-100=400$. CCC is $300$, CL is $100+50=150$ and XC is $100-10=90$. Comparing $400$, $300$, $150$ and $90$ shows CD is the largest of the four.

Q8
medium

Assertion (A): A positional number system needs a symbol for zero so that an empty place can be shown. Reason (R): In a positional system, a digit has the same value wherever it is written.

  1. A Both A and R are true, and R is the correct explanation of A
  2. B Both A and R are true, but R is not the correct explanation of A
  3. C A is true, but R is false
  4. D A is false, but R is true
Show answer and explanation

Correct answer: C - A is true, but R is false

A is true, because without a zero the empty tens place of $205$ cannot be marked and the number reads as $25$. R is false: in a positional system a digit's value depends entirely on its place, and that is exactly why an empty place must be shown. So A stands and R does not.

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