CAT aspirants typically make assumptions which mar their performance; most of these are perceptual barriers accumulated over the years. Following is an effort to address these issues.
Obvious may be devious
You need to be vigilant with respect to responding to vibes which are a bit too obvious. In fact, most of the times it has been observed that the obvious needs to be explored further to arrive at the answer or in other words, the obvious may be too good to be true! Consider the following question:-
Q 1. If a/(b+c) = b/(c+a)= c/(a+b) = r, then "r" cannot take any value except :
1. ½
2. -1
3. ½ or -1
4. -1/2 or -1
A quick visual inspection of the question is good enough to conclude that ½ is surely satisfying the equation, as this is the result when a, b and c are equal. Further, this gets corroborated by the law of equality of ratios, where the sum of numerators will be equal to the sum of denominators, thus a/(b+c) = b/(c+a) = c/(a+b) = (a+b+c)/(2 (a+b+c) = ½
Now you must be tempted to mark option 1 as the answer, which projects the value of "r" as ½ . However, a timely adherence to the principle 'obvious may be devious' can help you from landing at the wrong option. In fact, there is more than one option which has ½ as a part of the answer--- option 3. The other value in this option is -1; so it is advisable to verify this as a possible value of "r" - if it satisfies, then option 3 is the answer, else the answer is option 1.
To validate this, proceed in the reverse direction- assume that -1 is a possible value of "r". Thus a/(b+c)= b/(a+c)= c/(a+b) = -1
Now this implies that b+c=-a, a+c= -b and a+b=-c or a+b+c=0. In other words when a+b+c=0, then the value of "r" is -1.
So there are two possible values for "r": 0 and -1. Hence the answer is option 3.
Long may not prolong
It has been seen that students have an inherent dislike for lengthier questions. The sheer bulk of the question is a huge deterrent and keeps the student at bay from approaching such questions. Consider the following question:
Q2. A train enters a tunnel AB. Inside the tunnel is a cat located at a point that is 3/8 of the distance AB measured from the entrance A. When the train whistles, the cat runs. If the cat moves to the entrance of the tunnel, A, the train catches the cat exactly at the entrance. If the cat moves to the exit, B, the train catches the cat exactly at the exit. What is the ratio of the speed of the train to that of the cat?
1. 1:4
2. 1:8
3. 4:1
4. 1:16
The question assumes the proportions of a short story around a cat, a train and the tunnel, which spans across a disproportionate number of words, when measured against the "time challenge"! Not many students will attempt this question because of this very reason, and even more so if it is followed by a shorter/ more inviting question. However, if the principle "long may not prolong" guides you judiciously, then you may arrive at the correct answer in a split second after having read the question. The question asks you the ratio of the speed of the train to that of the cat, and in the given scenario the train is faster than the cat as it is able to catch the latter at point B when coming from the opposite side. The only option in which the speed of the train is greater than that of the cat is option 3, and hence it qualifies as the answer!
In case there are more such options where the speed of the train is greater than that of the cat, then you need to graduate to the next step, which is as follows:
Assume the length of the tunnel as 8 km, as a multiple of 8 will facilitate faster calculations, given the distance of the cat from point A as 3/8. Thus, the cat is at a distance of 3 km from point A. When the train whistles, the cat runs towards A and the train catches it exactly at A. This implies that during the time the cat covers a distance of 3 km, the train reaches point A from wherever it is. Now if the cat runs towards B, when it covers a distance of 3 km towards B, the train enters the tunnel and is at point A. At this instant, the cat is at distance of 2 km from B and the train is at a distance of 8 km from B. If the train catches the cat at B, then during the time the cat covers 2 km, the train has to cover 8 km. In other words, the ratio of the speed of the train to that of the cat is 4:1.
Abundant may be redundant
Many a time it has been seen that students feel a compulsion to use every bit of data given in the question. You need to be wary of this habit, as the redundant data has been given merely to enmesh and mislead you, leading to an increased opportunity cost. Consider the following question:
Q3. Two boats travelling at 5 and 10 km/hr head directly towards each other. They begin at a distance of 20 km from each other. How far apart are they (in km) one minute before they collide?
1. 1/8
2. ¼
3. ½
4. Can't be determined
The question simply requires you to find the distance travelled by the two boats in one minute, and can be reached by a quick application of the age old mathematical wisdom of distance being a product of speed and time. Since the boats are travelling in opposite directions (towards each other), their relative speed is 15 km/hr (5+10). In one minute (or 1/60 of an hour) the distance covered will be 15 * (1/60) = ¼ km. Hence option 2 is the answer. There is no need to use the initial distance of separation between the two boats (20 km); this is bait and will unnecessarily complicate the calculations. It is therefore advised not to process every piece of information coming your way, but to prudently filter out the relevant one from the overall data heap!
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Quicker can avoid flicker
As a CAT test taker you need to appreciate the relevance of accomplishing the task in the minimum possible time. In other words, the efficiency syndrome plays a critical part in your success. It is in this context that a quicker approach to solving questions may help you to gain the vital competitive edge. Consider the following question:
Q4. If a+b+c=0, find the value of (a^4+b^4+c^4)/(a^2*b^2+b^2*c^2+c^2*a^2)
1. 0
2. 1
3. 2
4. Can't be determined
This question prima facie links you to the application of the expansion of the algebraic expression (a+b+c)^2 and you mechanically tend to go in that direction. However a careful scrutiny of the expression reveals the symmetrical nature of the function. Each variable in the expression goes through a similar treatment which implies that you can assign random values to these variables while satisfying the condition that their sum is zero. Further, plug in values which keep your calculations lean. For example, put 1, -1, 0 as the three values (irrespective of which variable is assigned which value) in the given expression; the outcome is 2. Hence option 3 is the correct answer.
Rough may not be tough
We are an opinionated lot; we tend to form perceptions based on our previous experiences. While this may be helpful in certain situations, it may also create a perceptual barrier while selecting questions to attempt. This has been particularly noticed with respect to topics which the questions are sourced from. Consider the following question:
Q5. Three labeled boxes containing red and white cricket balls are all mislabeled. It is known that one of the boxes contains only white balls and the other one contains only red balls. The third one contains a mixture of red and white balls. You are required to correctly label the boxes with the labels red, white and red & white by picking a sample of one ball from only one box. What is the label on the box you should sample?
1. White
2. Red
3. Red & White
4. We need to take more than one sample to determine
A preliminary look at the question makes you opine that it is based on an application of "Probability & Permutations/Combinations". The generous usage of "boxes and balls" further strengthens your belief, as this parlance is typical of questions from these topics. The minute you sense this signal (incorrectly so), your behavior towards the question gets stereotypically decided --- a previous discomfort level with these topics keeps you away from attempting this question and vice versa. It is therefore advised that you approach the questions with an open mind and not breed a bias based on overt parameters. For example, the above question is a basic application of logic and you can easily conclude that options 1 and 2 are equally good or bad with respect to qualifying as potential answers; and since only one option is to be marked, these two can be eliminated, thus narrowing down the decision to options 3 and 4. Assuming that option 3 is the answer, if you withdraw a ball from this box and it happens to be red, it implies that this box has only Red balls and can be labeled accordingly. This means that the box which is mislabeled as White can be correctly labeled as the "Red & White " box, since the possibility of this having only Red balls has been discarded, as also the possibility only White balls (since its mislabeled). Consequently the box mislabeled as Red can now be correctly labeled as the White box. A similar treatment is required if the ball withdrawn from the box which is mislabeled as "Red & White" is White. Hence option 3 is the answer.
###### Bell the CAT: Key Learning
• These five principles do not cover the entire gamut of possibilities, but they can surely make a difference on the day of the CAT!
• While solving the questions focus more on the weak areas as it is extremely important to clear individual section cut offs.