How do you solve this question?

A cookie jar contains only two types of cookies - macaroons and ginger snaps. The ratio of macaroons to ginger snaps is $2:5$. Which of the following could be the total number of cookies in the cookie jar?

[X] 42
[ ] 45
[ ] 48
[ ] 52
[ ] 57

Why is the answer $42$?

  • 2
    $\begingroup$ It's the only option that is divisible by $2+5=7$, since the question assumes that we can't break the cookies into halves or fifths and so on. $\endgroup$ – Adriano Apr 19 '14 at 0:07
  • $\begingroup$ "Why is the answer 42?" Yes, this confused the Magratheans too. $\endgroup$ – naslundx Apr 24 '14 at 17:45
  • $\begingroup$ For those of us needing a refresher on the Magratheans and the number 42: aliens.wikia.com/wiki/Magrathean $\endgroup$ – Alex Apr 25 '14 at 4:11

Because it is the only multiple of $7=2+5$: $2$ parts of macaroons and $5$ parts of gingers.

The total number of biscuits must be $2n+5n=7n$, with $n$ integer, and $42$ is the only multiple of $7$ in your list.


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