In this post I will write about a couple SAT ‘power techniques’ learnt from experience.

One of my favorite stops every day is the ‘Sat question of the day’. It probably gives a boost to my estimated self-worth as I try to see how quickly I can solve their problems (one a day).

Today’s problem was particularly interesting that I had to write about it. Here’s the problem verbatim:

If half the people in a room leave at the end of every five-minute interval and at the end of twenty minutes the next to last person leaves, how many people were in the room to start with? (Assume that no one enters the room once the process begins.)
Answer Choices

* (A) 32
* (B) 28
* (C) 16
* (D) 12
* (E) 8

One look at the problem and I knew what I had to do: it would be simpler and more time would be saved if I used one time-honored technique. It is: work backwards from the answer choices.

After getting the answer right (the answer is (C)), I saw how they were recommending students approach the problem – as expected, they cannot tell you to ‘work backwards from the answers’ since they are expected to be formal, theoretical, erudite and didactic in content and tone. (as to how they recommend cracking problems like these). They wont tell you how to use ‘shortcuts’.

BUT it is a lot easier if you work backwards – first choose the answer that seems ‘most likely’. I chose to start with 28, becoz it sounded like a reasonably high number that could stand getting halved four times.

I started with 28, put out one finger in my right hand, thought ’14′, next finger out, ’7′, and then found 28 could not be the answer because 7 cannot be ‘halved’. So score out 28. Try next answer choice->16. Finger,16,Finger,8,Finger,4,Finger,2. So it must be the right answer. Click click submitted the answer (C) 16 and it came out right.

Morale of the story: Avoid a convoluted, theoretical path if your brain estimates ‘this will take longer’ (unless you have all the time in the world and are feeling instructional showing off your math skills).

Here’s a SAT sentence completion problem that came up a few days ago:

Demographers and anthropologists have corrected the notion that European explorers in North America entered a ——- territory by showing that the land in some areas was already as densely ——- as parts of Europe.
Answer Choices

* (A) fertile . . settled
* (B) colossal . . wooded
* (C) desolate . . populated
* (D) valuable . . exploited
* (E) hostile . . concentrated

As I read the question completely, I thought to myself that the person who set this question has essentially given it away by choosing to position the blank just after the word ‘densely’. I now knew I no longer needed to worry about the first blank as I quickly eyed over the five choices given, concentratin’ on the second word in all the choices provided. ‘densely populated’ is somethin’ like an overused phrase, so as soon as you see the word ‘densely’ you can be sure it goes with ‘populated’ more than any other answer choice. You dont have to worry about the first word in the answer choices.

Lesson: Sometimes you only have to fill one blank and the other ‘fills itself’.

IF you knew these already (from some test prep book or something) – think of it as ‘reinforcement’!