How about this one in 2 mins?

[netigen]

This one took me 5 min in the CAT. Please point out a quick approach

[punit.kaur.mba]

how did u even solve it. i took 10 minutes but couldnt even solve this one... just realised how poor im in geometry.

[hema123]

Solved it in 2 min.

From the question, we can deduct that its asking for the ratio of PS/RS

Also we know that PQ+QR+PS=60 and PQ>QR

Now consider the sides as 3*5 ,4*5,5*5 or 15,20,25. They all add up to 60.

From the daigram , we can deduce that -

PS^2=PQ^2-144 = 400-144=256
RS^2=QR^2-144 = 225 -144=81.

Hence PS/RS=16/9.

[hema123]

Solved it in 2 min.

From the question, we can deduct that its asking for the ratio of PS/RS

Also we know that PQ+QR+PS=60 and PQ>QR

Now consider the sides as 3*5 ,4*5,5*5 or 15,20,25. They all add up to 60.

From the daigram , we can deduce that -

PS^2=PQ^2-144 = 400-144=256
RS^2=QR^2-144 = 225 -144=81.

Hence PS/RS=16/9.

[simplyjat]

The important point to understand is that you do not need to solve every question under two minutes. There are question that are too obvious and take 15 seconds. And the rest of time is added for the tough questions.

I remember giving one MGMAT exam. There was a tough Permutation and Combination problem; I took 11 mins and 58 secs to solve the problem (though I got that one wrong) and still managed to finish the maths section in time.

The motto of the story is "Premature optimization is root cause of all evil". Do not consider time as a factor until and unless you have a serious time crunch in the practice test (such as missing 5-7 questions).

[wawatan]

i disagree with simplyjat. someone who scored 780 told me that i should spend no more than 2 minutes on a question. it makes sense b/c if you spend more then 2 min on 1 question, you will keep doing it on the other questions, before you know it, you won't be able to finish the test on time. simplyjat probably practiced alot of cat exams, so he knows that he is able to finish quant on time. but for normal people like us who need to take the exam within a time constraint, you have to try to finish the problem within 2 min. hope this helps!

[simplyjat]

There are personal opinions, something works from someone and not for someone else. One has to identify what works for him or her.

If I look it from math perspective; You need to spend, on an average, two minutes per question. And there is a difference between average and actual numbers. If average of some list is 5, it does not mean that every entry in the list has to be five; some entries will be less than 5 and some will be more than 5.

Take it other way as well; if you spend less than 2 mins on every question, then on average time spent on each question is going to be less than 2. Eventually you will end up under-utilizing you time; you will end the section before 75 minutes and may commit some silly mistakes. And some time (couple of seconds) is also lost when you keep looking at the time continually.

[chidcguy]

Solved it in 2 min.

From the question, we can deduct that its asking for the ratio of PS/RS

Also we know that PQ+QR+PS=60 and PQ>QR

Now consider the sides as 3*5 ,4*5,5*5 or 15,20,25. They all add up to 60.

From the daigram , we can deduce that -

PS^2=PQ^2-144 = 400-144=256
RS^2=QR^2-144 = 225 -144=81.

Hence PS/RS=16/9.

I went the same route, How ever I picked 12,13,5 to start with and considered sides (24,26,10) which also add up to 60, just like 15,20,25. I should have realized that I should try another set of right angle triangles. Thats why this method is NOT fool proof, while it can help us to get the solution. There should be some other concrete way of doing this problem, which will help us identify and learn another testing concept. We just learnt one on using the numbers of right triangle