2
$\begingroup$

In a car park, there are 2 white car for every 3 blue cars and for every 2 blue cars there are 5 silver cars. What is the least number of cars in the park?

I am a bit confused about my approach to the question, according to my thinking...


enter image description here

But I still think that I am making a wrong approach. Need help.

Thanks in advance!

$\endgroup$
  • $\begingroup$ well if the cars are distinguishable then for the blue ones you need to have 15 silver ones, because you can pick 2 blue cars out of 3 in 3 ways if the order doesn't count. So over all 20. Hope this this is right. $\endgroup$ – randomname Jan 21 '14 at 18:11
  • 2
    $\begingroup$ I thought this was a simple question, but so far you have four different answers: $20$, $25$, $30$ and $36$. $\endgroup$ – Henry Jan 21 '14 at 18:19
3
$\begingroup$

If there are $w$ white cars, $b$ blue cars and $s$ silver cars then you know $$\frac{w}{2} =\frac{b}{3},$$ $$\frac{b}{2} =\frac{s}{5}.$$

If you are not allowed fractions of a car or striped cars, then $b$ must be a multiple of $3$ and a multiple of $2$, which means $b$ is a multiple of $6$. If $b=6$ then $w=4$ amd $s=15$ making a total of $25$ cars.

Or perhaps there are no cars at all.

$\endgroup$
  • 1
    $\begingroup$ agree with Henry, the LCM restriction applies to blue car relation between white and silver (which is LCM(2,3)=6. If you have 6 Blue cars, the minimum total number of cars is 25 $\endgroup$ – CAGT Jan 21 '14 at 18:41

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.