## mathmath333 one year ago There are 4 qualifying examinations to enter into Oxford University: RAT, BAT, SAT, and PAT. An enginner cannot go to Oxford University through BAT or SAT . A doctor on the other hand can go to Oxford University through the RAT ,BAT and PAT but not through SAT. Further there are 3 ways to become a doctor (viz. Foundation, Inter and Final).Find the ratio of number of ways in which an engineer can make it to Oxford University to the number of ways a doctor can make it to oxford university?

1. mathmath333

\large \color{black}{\begin{align} & \normalsize \text{There are 4 qualifying examinations to enter into Oxford University: }\hspace{.33em}\\~\\ & \normalsize \text{RAT, BAT, SAT, and PAT. An enginner cannot go to Oxford University }\hspace{.33em}\\~\\ & \normalsize \text{ through BAT or SAT . A doctor on the other hand can go to Oxford}\hspace{.33em}\\~\\ & \normalsize \text{ University through the RAT ,BAT and PAT but not through SAT. }\hspace{.33em}\\~\\ & \normalsize \text{ Further there are 3 ways to become a doctor (viz. Foundation, }\hspace{.33em}\\~\\ & \normalsize \text{ Inter and Final).Find the ratio of number of ways in which an engineer}\hspace{.33em}\\~\\ & \normalsize \text{ can make it to Oxford University to the number of ways a doctor can}\hspace{.33em}\\~\\ & \normalsize \text{ make it to oxford university?}\hspace{.33em}\\~\\ & a)\ 3:2 \hspace{.33em}\\~\\ & b)\ 2:3 \hspace{.33em}\\~\\ & c)\ 2:9 \hspace{.33em}\\~\\ & d)\ 9:2 \hspace{.33em}\\~\\ \end{align}}

2. ganeshie8

too much data haha

3. mathmath333

yes look tough at first sight , deceptive

4. ganeshie8

we need to find a clever way to organize so that it helps in interpreting easily

5. mathmath333

yes

6. ganeshie8

|dw:1441157718151:dw|

7. ganeshie8

idk if it is useful yet but may be start by filling in that table just put a "ticks" in the corresponding cells if each of engg/doc are allowed

8. mathmath333

|dw:1441157912927:dw|

9. ganeshie8

right lets read the problem again

10. mathmath333

|dw:1441158032672:dw|

11. ganeshie8

see, suddenly the problem became simpler! I think its eithr 2:3 or 2:9

12. mathmath333

what about the 3 ways to become doctor , can an engineer become a doctor and then go to oxford

13. ganeshie8

I don't think engineer can become a doctor, so for engineer there are just 2 ways to go to oxford

14. ganeshie8

for doctor, he can write any one of the 3 tests(RAT, BAT, PAT), then pick any one of the available 3 programs(Foundation, Inter, Final) therefore there are 3*3 = 9 ways for doctor

15. ganeshie8

depends on how we interpret the problem

16. mathmath333

but foundation , inter and final are the ways for becoming a doctor not program after BAT,RAT etc

17. mathmath333

answer given in book is 2:3

18. ganeshie8

sounds good to me!