•Whenever there appears any term of the type a3 + b3 + c3, do check for a + b + c being equal to zero. If a + b + c is indeed zero, then a3 + b3 + c3 = 3abc.
•The series 1, 3, 6, 10, 15 should immediately be recognized as series of sum of first n natural numbers.
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General Fundas of Algebra
1). If (32) ^ (x-2) = 64 / (8^x).
Find the value of x.
Options: (a) - 2 (b) 3 (c) 2 (d) - 3
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Quantitative Aptitude - Practice Exercise 1 (Number System)
•If the HCF of two numbers is H, the numbers can be assumed as H × a and H × b such that a and b are coprime.
•While finding the largest/smallest number that leaves particular remainders when divided by certain numbers, do not forget to first eliminate options based on the remainder and divisor combinations, e.g. a number leaving a remainder of 5 on division by 8 has to be odd; a number leaving a remainder of 3 on division by 15 has to have the unit digit as 3 or 8; etc.
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Factors, Multiples, HCF and LCM
•To find the highest power of x that divides N!, keep dividing N successively by x and the addition of all the quotients is your answer. (Successive division means dividing the quotient of the earlier division). While this is the process of getting the answer, do understand the concept behind find the highest power as it may be used in other application. The interpretation of the highest power of x that divides a factorial is that if from 1 × 2 × 3 × 4 × 5 × 6 × …… × N, if all the powers of x is segregated, how many will they amount to. E.g. From 19!, if we segregate all powers of 3 we will have something as follows:
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Highest power dividing a product/number
• Non-terminating but recurring nmubers are rational and hence can be expressed in the form p/q.
• Now, let us see how can we find thee recurring form of .4444444……
Let x=0.44444…..
Therefore, 10x=4.4444…
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Converting recurring number to p/q form
•Take any two numbers, say 39 & 47.
If they are multilplied, the last digit of the product is sameas the last digit of 9 x 7.
Hence, it is 3.
This concept could be extended to a host of situations. An interesting pattern emerges when we look at the exponents of the numbers. We would find conclusions as given below.
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Cyclicity
Speed in solving questions is of crucial importance if one wants to crack any entrance exam. In fact, the only two skills tested in the Data Interpretation section are those of understanding data or interpreting information from raw data and calculating fast.
For faster calculations
1.The first requirement is to mug up tables till 30, reciprocals with respect to percentage and decimals, squares & cubes till 30, square roots and cube roots till 7.
2. Practice various questions to become comfortable with the various types of problems and understand by which method you can solve a particular problem faster. Exposure to various types of questions is required.
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Calculating Faster
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