100 practice questions covering A Story of Numbers, organised into 2 topics.
100 questions include a written explanation.
Pick a topic below, or try the samples first.
Consider these statements about whole numbers. (i) A zero written at the left end, as in $047$, changes the value of the number. (ii) A zero written inside, as in $407$, changes the value of the number. Which statement(s) are correct?
AOnly (ii)
BBoth (i) and (ii)
COnly (i)
DNeither (i) nor (ii)
Show answer and explanation
Correct answer: A - Only (ii)
A leading zero marks a place above the highest digit, and that place holds nothing, so $047$ is still $47$ and (i) is false. A zero inside pushes every digit on its left into a higher place, so $407$ is far larger than $47$ and (ii) is true. Only (ii) stands.
Q2
easy
In a tally record, marks are usually made in groups of five, with the fifth mark drawn across the first four. Why are the marks grouped like this?
AGrouping is the only way to add two numbers
BGrouping makes the marks look neater on the page
CGrouping makes a long row of marks much quicker to count
DGrouping changes the value of each single mark
Show answer and explanation
Correct answer: C - Grouping makes a long row of marks much quicker to count
Counting a long row one mark at a time is slow, but counting in fives is fast, so grouping saves time and reduces mistakes. Neatness is not the reason. Addition can be done without grouping, and each mark still stands for one, so its value never changes.
Q3
medium
A merchant sends $8$ boxes of spice to another town and wants the buyer to confirm that nothing was lost on the way. Which practice helps most?
ASending the boxes in a larger cart
BSending a written note of the number of boxes along with the load
CSending the boxes on a different day
DPainting all the boxes the same colour
Show answer and explanation
Correct answer: B - Sending a written note of the number of boxes along with the load
The buyer can only check for a loss if he knows how many boxes were sent, so the count must travel with the goods. A bigger cart, matching paint and a change of day do not tell the buyer the number that left, so none of them can reveal a missing box.
Q4
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?
A$1000$
B$110$
C$505$
D$999$
Show answer and explanation
Correct answer: D - $999$
$999$ 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 $999$.
Q5
hard
Read these two statements about early record keeping. (i) A record of quantity is useful only if the same record can be read again later, by the maker or by someone else. (ii) A count kept only in a person's memory is as trustworthy as a count marked on a stick. Which statement(s) are correct?
AOnly (ii)
BBoth (i) and (ii)
COnly (i)
DNeither (i) nor (ii)
Show answer and explanation
Correct answer: C - Only (i)
A record has value because it lasts and can be checked again, which is why marks were cut into sticks and bones. Statement (ii) fails because memory fades and cannot be shown to another person as proof. So (i) alone is correct, and every option that accepts (ii) is wrong.
Q6
medium
A student adds $407+186$ and writes $583$. Which mistake produced that answer?
AThe zero was treated as a one
BThe carry from the ones column was never added into the tens
CThe hundreds were added twice over
DThe numbers were subtracted instead of added
Show answer and explanation
Correct answer: B - The carry from the ones column was never added into the tens
The ones give $7+6=13$, so $3$ is written and $1$ is carried. Ignoring that carry leaves the tens as $0+8=8$ and produces $583$ instead of the correct $593$. The hundreds were added once, the zero was used correctly, and subtracting would have given $221$.
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