CSAT Solved Papers/ 2024/Q60

2024 CSAT — Q60

Quant Data sufficiency 2.5 marks Medium

A Question is given followed by two Statements I and II. Consider the Question and the Statements.

Question: What is the time required to download the software?

Statement-I: The size of the software is 1212 megabytes.

Statement-II: The transfer rate is 2⋅42{\cdot}4 kilobytes per second.

Which one of the following is correct in respect of the above Question and the Statements?

  1. A The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
  2. B The Question can be answered by using either Statement alone
  3. C The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone Answer
  4. D The Question cannot be answered even by using both the Statements together

Worked rationale

Time == (size) ÷\div (rate). This needs both a size and a rate.

Statement-I alone (size =12= 12 MB): no rate given, so the time is undetermined. Insufficient.

Statement-II alone (rate =2.4= 2.4 KB/s): no size given, so the time is undetermined. Insufficient.

Both together. With size and rate both fixed, the time is a single computable value: time=12 MB2.4 KB/s\text{time} = \dfrac{12\ \text{MB}}{2.4\ \text{KB/s}} — a definite number once the MB→\toKB conversion is applied. The question is answerable.

Answer: (c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.

Why the other options miss

  • A
    thought a statement was enough when it wasn’t: imagines a “default” size or rate, treating one statement as enough.
  • B
    thought either statement was enough when neither is: the same error applied symmetrically — neither a bare size nor a bare rate yields a time.
  • D
    over-read the unit gap as unanswerable: over-worries the MB-vs-KB unit gap and declares it unanswerable; the conversion factor is standard, so size÷\divrate is perfectly determinate.

Specialist insight

This is the textbook both-needed DS shape: a rate problem (time=quantity/rate\text{time}=\text{quantity}/\text{rate}) where each statement supplies exactly one of the two ingredients. Neither alone can answer; together they do. The only thing that could look like a (d) is the unit mismatch (megabytes vs kilobytes), but data sufficiency asks “can it be answered,” not “what is the number” — and with a fixed conversion the time is a single value. Resist inventing a missing quantity (the (a)/(b) trap) and resist over-reading the unit wrinkle as indeterminacy (the (d) trap).

The trap, in one line

A rate problem needs both quantity and rate: size alone or rate alone can't give a time, but together they do — the MB/KB conversion is fixed, so it's (c)(c), not (d)(d).

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