Venture Capital puzzles, solved step by step

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096A timed cognitive test item: if 4 associates screen 60 pitch decks in 3 hours, how many decks do 6 associates screen in 5 hours, working at the same rate?Mental maths and speed testsWarm upSeed and early-stage VCMulti-stage VC
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Answer in under thirty seconds.
Show the worked solution
150 decks. Reduce everything to one unit first: 4 associates working 3 hours is 12 associate-hours, and 60 decks over 12 is 5 decks per associate-hour. Six associates for five hours is 30 associate-hours, so 30 x 5 = 150. As a check, scale the original: 60 x 6/4 x 5/3 is also 150. This assumes everyone works at the same steady rate.
Why reduce to a rate per associate-hour?
If 2 cooks make 40 rotis in an hour, one cook makes 20 an hour, and any kitchen size or shift length follows from that one number. Work problems become simple once you find the output of one worker in one unit of time, because the total is then that rate times workers times hours. Here 60 decks came from 4 x 3 = 12 associate-hours, so the rate is 5 decks per associate-hour. Everything else is multiplication.
Four associates working three hours make 12 associate-hours, and 60 decks over 12 cells is 5 decks per associate-hour; six associates working five hours make 30 such cells, so they screen 30 x 5 = 150 decks.
The relationship
$D = r \times a \times h \qquad r = \frac{60}{4 \times 3} = 5 \qquad D = 5 \times 6 \times 5 = 150$
D decks screened
r decks per associate-hour
a number of associates
h hours worked
What it says in wordsOutput is the rate of one person for one hour, times the people, times the hours.
How do you avoid the slip under time pressure?
Ask which way each change pushes the answer before you multiply. More associates and more hours both raise output, so both ratios must be greater than one: 6/4 and 5/3, never 4/6 or 3/5. The fast wrong answer, 90, applies the 6/4 and stops. On a timed test the danger is not hard arithmetic but a missed step, so a five-second check that the answer moved in the right direction by roughly the right amount is worth it: one and a half times the people for two thirds more time should give about two and a half times the output, and 60 x 2.5 is 150.
Where would this break down in a real deal team?
The model assumes every associate screens at the same steady pace and that output scales with hours. Real screening slows late in a long day, and a bigger team spends time coordinating and avoiding duplicate work. Saying so is unnecessary on the test itself, but it is the right instinct if the same question comes up in an interview: the arithmetic answer is the ceiling, and the real number is usually lower.
Where candidates lose it
The common slip is to scale for only one of the two changes, giving 90 from the associates alone or 100 from the hours alone. Under a clock, candidates grab the first ratio they see and move on.
The other loss is inverting a ratio, as if more associates meant fewer decks. Find the unit rate first and the direction takes care of itself.
What the interviewer asks next
How many associates are needed to screen 300 decks in 4 hours?
If two of the six associates work at half speed, how many decks are screened in 5 hours?
A partner reviews 20% of screened decks at 3 decks an hour. How many partner-hours does the 5-hour session create?

D	decks screened
r	decks per associate-hour
a	number of associates
h	hours worked

Try it first

Why reduce to a rate per associate-hour?

How do you avoid the slip under time pressure?

Where would this break down in a real deal team?

Where candidates lose it

What the interviewer asks next