To break into the 720+ it is imperative that you have to solve tougher higher difficulty problems. (This is true for the verbal section also)

**What is a higher order problem?**

A higher order problem is problem which has

• A situation which can otherwise be solved by identifying the concept/formula and applying the same directly

• A complexity present in the problem which acts as a stumbling block, thereby preventing you from getting an answer directly.

When approaching a higher problem first

- Identify the concept involved
- Identify the complexity in the problem
- Remove the complexity and if possible arrive at a result
- Modify the complexity in such a manner the complexity gets integrated into the problem and this results in a newer problem
- Solve the new problem by directly applying the concept.

A car moving at 45 kmph and is chasing a two wheeler that is moving at 30 kmph. The distance between the car and the two wheeler at 10:00 am is 48 kms. The car stops at 11:30 am for 15 mins to fill fuel and moves at 45 kmph. When will the car meet the two-wheeler?

1.12.42 pm 2.1:42 pm 3.1:57 pm 4. 1:47 pm 5. 1:30pm

Try this problem independently first, then read further.

Let me take you through the problem in the science of thinking* approach toward higher order problem solving.

**The concept –**Time, speed and distance, Relative velocity involving two bodies moving towards each other.

**The complexity**– The stoppage time of the car. At 11:30 am the car stops for 15 mins.

Eliminate the complexity first

If the car didn’t stop at 11:30 then the time taken by both the bodies to meet is determined using the relationship

Time taken to meet = Initial distance between the bodies/ relative velocity

= 48/(45 -30) { Relative velocity when two bodies move in the same direction = difference of their speeds, hence 45-30 =15)

= 48/15= 3.2hrs

**Modification of the complexity**

As you would have observed if the complexity is eliminated the problem can be solved directly. As per the problem. The car travels till 11:30 and then stops for 15mins. So you might calculate the distance travelled by each body from 10:00 till 11:30 and then calculate the distance travelled by the two wheeler for that extra 15mins and then proceed. This complicates the problem.

Instead you can restructure the problem in such a way that the complexity gets integrated into the problem and doesn’t get noticed.

Here you can shift the 15min time interval from 11:30 to 10:00 such that the car starts only at 10:15 instead of 10:00. Hence the initial distance increases from 48 to 48 + (distance travelled by two wheeler for 15mins) = 48 + 7.5 =55.5kms

Hence now there is no stoppage time at 11:30.

Time taken to meet = Initial distance between the bodies/ relative velocity

= 55.5/(45 -30) = 55.5/15= 3.7hrs = 3hrs 42minutes

Meeting time =10:15 + 3 : 42 = 13: 57

You would get higher order problems only if the adaptive algorithm decides that you deserve questions of this difficulty.

So for those of you who aim to crack the 720+ barrier. Practice on higher order problems.

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