CSAT Solved Papers/ 2022/Q35

2022 CSAT — Q35

Quant Arithmetic & numeracy 2.5 marks Medium

How many seconds in total are there in $x$ weeks, $x$ days, $x$ hours, $x$ minutes and $x$ seconds?

A 11580x
B 11581x
C 694860x
D 694861x Answer

Worked rationale

Convert every unit to seconds and factor out $x$ :

$x$ weeks $= x \cdot 7 \cdot 24 \cdot 3600 = 604800x$
$x$ days $= x \cdot 86400 = 86400x$
$x$ hours $= x \cdot 3600 = 3600x$
$x$ minutes $= x \cdot 60 = 60x$
$x$ seconds $= x$

Add the coefficients:

604800 + 86400 + 3600 + 60 + 1 = 694861.

Total $= 694861x$ seconds.

Answer: (d) 694861x.

Why the other options miss

A

an arithmetic slip: sums minutes-level conversions only ( $7\cdot 24\cdot 60 + \dots$ ), stopping short of seconds.
B

an arithmetic slip: the minutes-level sum plus the trailing $+1$ , still not in seconds.
C

off by one: drops the final ” $x$ seconds” term ( $+1$ ), the single most-missed unit.

Specialist insight

Factor $x$ out immediately so the problem becomes one integer sum of second-conversions. The deadly slip is forgetting the last ” $x$ seconds” contributes a bare $+1$ to the coefficient — that single unit separates $694860$ (trap c) from the correct $694861$ . List all five conversions before adding; do not eyeball.

The trap, in one line

$604800+86400+3600+60+1 = 694861$ — the final $+1$ (the bare seconds) decides it $\Rightarrow$ (d).

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