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## TCS NQT Aptitude Test

Preparing properly for the TCS NQT aptitude test is very important. The questions can come in various forms and shapes. There is no fixed pattern to the type of questions that will be asked. However, most of the questions can be categorized into various topics. The TCS NQT aptitude questions can be categorized into Arrangements and Series, Permutation and Combination, Percentages, Mixtures, Probability. Ratio and Proportion, Work and Time, Speed and distance, Geometry, Clocks and Calendar, Series and Progression, Averages, Area and Perimeter, Fractions, Number System, LCM and HCF, Simplification, and Data interpretation.

## TCS NQT Percentage Problems

I would like to share some interesting problems that I came across while preparing for the TCS NQT exam. The problems on percentages can come regarding the population of a city. A certain percentage of men are married, and a certain percentage of women are married. What will be the percentage of the married adult population? Such a question requires us to assign a variable and accordingly calculate the number of married men and married woman. Then use that variable and compare it with the total population. In such cases you will see the variable cancels out and provides a percentage numeric figure. So even though there is no figure or number given regarding the population, we can find the fraction or percentage by using variables with respect to the overall population. The interesting feature of this type of problem is that it feels overwhelming at first. How can we solve it if there is no actual population given? What should we call the variable? What will the variable represent? Should we consider one variable or should we consider two variables? What will happen if the variables do not cancel out at the end? Because my answer cannot have a variable, how can I handle if I cannot eliminate a variable? I learned to tackle such problems after exhaustive practice. It is advisable not to consider too many variables if it is not required. Because the same variable can often be used in multiple different ways. Also, keeping the same variable helps to get it cancelled out at the end. If we have two variables, then eliminating both of them becomes a slightly larger task.

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## TCS NQT Fraction Problems

Problems with fractions are very important for the TCS NQT exam. Sometimes we will see fractions are having an exponential power. For example, when 1/3 is having an exponential of minus 4, its value is 81. Also, when 1/4 is having an exponential of minus 3, its value is 64. So, if we have to compare various fractions which have exponential, it is important to find out what their values are. It is almost impossible to find out the values of various fractions which have an exponential and compare them at the same time mentally. So, it is important to keep a note. If the fractions are combined with other mathematical operations, we need to complete those addition or subtraction or multiplication before starting the comparison. So, if we are given several options to choose from and find out the largest value, it should be clear to us in the simplest forms what exactly we are comparing.

## TCS NQT Fraction Comparisons

Another important scenario for fractions can come when we modify the numerator and denominator by equal amounts. If we add 5 to the numerator and denominator of 5/6 and 4/5, which will have the minimum change in its value? So first we have to add 5 to the numerator and denominator of both these fractions. Then subtract the original fractions from these new fractions to find out the change of each. And then to compare these, we have to get a common denominator. Finally, when we get the common denominator, we can see the difference is minimum for 5/6. Such questions seem very difficult at first. Because the fractions are always looking very tough. But when we know how to approach them, it becomes manageable. Most of the time, getting a common denominator helps us. When we get a common denominator, we can easily compare the numerators. Then we can find out which is the largest or smallest among the fractions.

## TCS NQT Mensuration, Geometry

We have various interesting problems in geometry and mensuration. If various points of a circle are connected with the center of the circle and forms angles with each other, it becomes interesting to see how the angles relate to each other in the overall picture. What if we are given one angle and asked to find another? We need to remember the radius of the circle is always constant. Thus, if we try to draw a triangle with the radius of the circle as the two sides, we will always have an isosceles triangle. So, if we are given an angle, we can easily find out what will be the opposite angle, because in an isosceles triangle two sides are equal, hence opposite angles will be equal. Based on this conclusion, we may further find out other angles that the question may ask us to find.

## Advanced Mensuration, Geometry

In mensuration finding the area of various shapes is important. The shapes may not be always a simple figure, like a square or triangle. It can have four sides and it can be any quadrilateral. In a quadrilateral, if two of the angles are 90 degree and the others aren’t, we can split that shape into one rectangle and one triangle. Then we can find the area of the rectangle separately, and the area of the triangle separately. On adding these two areas we can find the total area of the quadrilateral. It is important to remember the formula of some of the common shapes and sizes. Often these formulas will be used in some small steps of a much larger problem. But without these formulas, it will be very difficult to solve the problem. Remembering how to find the lengths of diagonals is also important. Often you will find in a Cartesian plane, a set of coordinates are given. In the TCS NQT exam, it is important to remember how to find out lengths of various lines using these coordinates. This can ultimately help in solving the problem question.

## Mensuration Tactical Questions

It is important to score good marks in the aptitude section of the TCS NQT exam. Geometry and mensuration forms are important part of it. One of the important type of questions is when shapes overlap each other. For example, if two circles overlap each other, what is the area of the overlapping portion? In such cases, we have to find the area of the arc and the area of the triangle formed by the arc. And then subtracting these two areas, we can find the overlapping area of one circle. And if both the circles have the same radius, we can multiply this area by 2 to get the total overlapping area of the two circles. Thus, we can see all the questions might not be straightforward. In some cases, we have to play around with the formulas we know. We also have to use our knowledge of basic geometry without being asked to find out various values and implement such logics. Thus, the more practice we do, the better we become at such indirect questions which uses hidden logics.

## Mensuration Formula Questions

In another scenario, we can have a square inside a circle. We can be asked in the TCS NQT exam, if we want to enlarge a square pond into a circular pond, how much earth has to be removed? The length of each side of the square is given. So, from there we can find out the length of the diagonal of the square. Dividing the diagonal by 2 will give us a radius of the circle. And now we can find out how much volume of earth needs to be removed. We subtract the volume of the square from the volume of the circle. In such a question, if multiple options are given in the answer, it can further confuse the candidate. Often a candidate can forget to divide the length of the diagonal by 2 to get the radius. In such cases, one of the answers is often given to confuse the candidate. So, if the candidate chooses the option from the answer of the volume of earth to be removed by calculating using the diameter of the circle, that answer will be wrong. In a limited time of the TCS NQT exam, it is important not to do calculations too fast. It is also advisable to review your calculations one more time before choosing an option in the answer.

## Mensuration Real-life

In another example, we can be asked to find how many small pieces of an object can be obtained from a larger piece of the same object. Let’s say a big cake has a length of 30 centimeters, a width of 30 centimeters, and a height of 5 centimeters. We want to cut small pieces of length 5 centimeters, width 5 centimeter, and height 10 centimeters. If we divide the volume of the big cake by the volume of each small piece, we get 18 as the answer. Now imagine how complex the problem would get if instead of a rectangle, we are using some other shape of the cake. Or maybe we are using a rectangle shape of the large cake, but cutting out different sizes, which is not a square or rectangle. In such cases, it is important to remember the formula to calculate volume of different shapes. This will allow us to easily find out the volumes and solve such questions. If we are not sure of the formula, we will have a tough time solving the problem. Different types of such problems can be framed with water flowing through a cylindrical pipe as well. We have seen candidates struggle with some of these problems in the TCS NQT exam.

## TCS NQT Number System

In another example, we can be asked to evaluate numbers raised to an exponential number. For example, for what value of n the sum of the digits in the number 10ⁿ + 1 is 2? Here we have to replace the value of n by various values and see what happens. What happens when n is 2? The sum value is 101. What happens when n is 3? The sum value is 1001. So we can see the sum of the digits of the number is always 2. Hence for any whole number value of n the sum of the digits will be 2. In such cases where the answer is not apparent, we have to replace the value and see what happens. We have to be careful enough so that the options in the answers do not confuse us. Sometimes we may forget to test with a particular value and that may give us the wrong answer. Sometimes we may test too much and confuse ourselves when the answer is actually simple. So it is important to do a balanced analysis. In the TCS NQT exam, there can be longer equations than this as well. However, the method to solve these is more or less the same.

## TCS NQT Shape Formulas

In the TCS NQT exam, we can be asked various questions on shapes adjacent to each other. If we have three squares with areas of 100, 16 and 49 sq units placed side by side, how much should the area of the square with area 16 sq units be reduced so that the total length of the sides of the 3 squares when placed side by side is 19? Here we have to assume the new length of the middle square as a variable. Then we take a square root of the areas of each of the squares to find out the length of a single side of them. This will give us the new side length of the middle square. Using the new length, we can find out the new area. Then we can compare the new area and the old area to find out the answer. Hence the area of the middle Square should be reduced by 12 sq units. In some cases, the square root of the numbers may not be exactly possible. We can hope that these numbers cancel out in some way at the end. If not, it is better to remember the decimal values of some of the common square root numbers. It is also advisable to be familiar with the multiplication tables of most of the natural numbers as much as possible.

## Mensuration Aptitudes

A complete knowledge of the various formulas of a cube are important for the TCS NQT exam. If the numbers representing volume and surface area of a cube are equal, then what will be the length of the edge of the cube in terms of the unit of measurement? If we assume the edge of the cube as a, then a x a x a = 6 x a x a, or a = 6. A similar question can be poised with the diagonal of the cube. Or the question asks to compare the cube with a similar side-by-side sphere. What can happen if the volume of the cube and the volume of a cylinder are same? What will be the radius of the cylinder if its height is given? How much water can be stored in the cylinder? In such cases, we see it is relevant to know the formula of a cylinder. Tougher questions for the TCS NQT can often include several parts in the same question. The answer of one part of the question can be used in the second part. The options given will most likely be from the second part question. So even if you are able to solve the first part, you will not be able to answer the question without solving the second part. Knowing these formulas can thus help a lot in the TCS NQT exam.

## TCS NQT Probability

Questions on probability are important for the TCS NQT exam. For example, let’s say a complete cycle of a traffic light take 60 seconds. During each cycle the light is green for 25 seconds, yellow for 5 seconds and red for 30 seconds. At a randomly chosen time, what will be the probability that the light is not green? To find the probability that the light is not green, we have to find the time during which the light is not green, and divide it by the total time. Hence, we add 5 and 30, and divided by 60. Hence the answer is 7/12. Having a clear idea of the different formulas of probability calculation is important for the TCS NQT exam. This is a simple example of probability, but it can also be combined with various other scenarios. Most of the problems on probability can be easily solved by having a knowledge of the probability formulas. Usually by replacing the variable values we can find the answers. In some cases, the answer can be in fraction as we just now saw. Continuous practice of various quantitative aptitude questions can thus accelerate learning and help during the TCS NQT exam.

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