CSAT Solved Papers/ 2024/Q30

2024 CSAT — Q30

Quant Arithmetic & numeracy 2.5 marks Easy

Consider the following:

$1000$ litres $= 1\ \text{m}^3$
$1$ metric ton $= 1000\ \text{kg}$
$1$ hectare $= 10000\ \text{m}^2$

Which of the above are correct?

A 1 and 2 only
B 2 and 3 only
C 1 and 3 only
D 1, 2 and 3 Answer

Worked rationale

Check each metric equivalence against its definition.

$1000$ litres $= 1\ \text{m}^3$ . A litre is $1\ \text{dm}^3 = (0.1\,\text{m})^3 = 10^{-3}\ \text{m}^3$ , so $1000$ litres $= 1\ \text{m}^3$ . Correct.
$1$ metric ton $= 1000\ \text{kg}$ . The metric (tonne) is defined as $1000\ \text{kg}$ . Correct.
$1$ hectare $= 10000\ \text{m}^2$ . A hectare is $100\,\text{m}\times100\,\text{m} = 10^4\ \text{m}^2$ . Correct.

All three are valid.

Answer: (d) 1, 2 and 3.

Why the other options miss

A

a convention slip: doubts the hectare, confusing it with an acre (which is $\approx 4047\ \text{m}^2$ ) and wrongly rejecting statement 3.
B

a convention slip: misremembers $1\ \text{m}^3 = 100$ litres (a factor-of-ten slip on $\text{dm}\to\text{m}$ ), rejecting statement 1.
C

the wrong ton: confuses the metric tonne ( $1000\ \text{kg}$ ) with the US/short ton, wrongly rejecting statement 2.

Specialist insight

This is a pure recall-and-verify item, but each conversion hides a classic confusion: litre $\leftrightarrow$ $\text{dm}^3$ (so $1\ \text{m}^3 = 1000$ L, since the linear factor $10$ cubes to $1000$ ); the metric tonne $=1000$ kg (not the short ton); and the hectare $=10^4\,\text{m}^2$ (not the acre). Anchor each on its definition rather than a half-remembered figure — the linear-to-volume cube ( $10^3$ ) and the are/hectare ( $100\times$ ) factors are where careless candidates drop a statement.

The trap, in one line

All three are standard SI equivalences; the bait is confusing hectare with acre or $1\ \text{m}^3$ with $100$ litres — verify by definition and all hold, $(d)$ .

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