he number theory or number systems happens to be the back bone for CAT preparation. Number systems not only form the basis of most calculations and other systems in mathematics, but also it forms a major percentage of the CAT quantitative section. The reason for that is the ability of examiner to formulate tough conceptual questions and puzzles from this section. In number systems there are hundreds of concepts and variations, along with various logics attached to them, which makes this seemingly easy looking topic most complex in preparation for the CAT examination. The students while going through these topics should be careful in capturing the concept correctly, as it’s not the speed but the concept that will solve the question here. …show more content…
Example: 2, 23,5,7,11,13 etc. Here are some properties of prime numbers:
• The only even prime number is 2
• 1 is neither a prime nor a composite number
• If p is a prime number then for any whole number a, ap – a is divisible by p.
• 2,3,5,7,11,13,17,19,23,29 are first ten prime numbers (should be remembered)
• Two numbers are supposed to be co-prime of their HCF is 1, e.g. 3 & 5, 14 & 29 etc.
• A number is divisible by ab only when that number is divisible by each one of a and b, where a and b are co prime.
• To find a prime number, check the rough square root of the given number and divide the number by all the prime number lower than the estimated square root
• All prime numbers can be expressed in the form 6n-1 or 6n+1, but all numbers that can be expressed in this form are not prime
Example: If a, a + 2 and a + 4 are prime numbers, then the number of possible solutions for a is: (CAT 2003)
(a) 1 (b) 2
(c) 3 (d) more than 3
Ans. (a) a, a + 2, a + 4 are prime numbers. The number fits is 1, 3, 5 and 3, 5, 7 but post this nothing will fit. Now 1, 3, 5 are not prime numbers as 1 is not prime number.
So, only one possibility is there 3, 5, 7 for a = 3.
Prime Factors: The composite numbers express in factors, wherein all the factors are prime. To get prime factors we divide number by prime numbers till the remainder is a prime number. All composite numbers can be
22. (15 points total, 3 points each) Choose True or False for each of the following:
Where the statement is true, mark T. Where it is false, mark F, and correct it in the space immediately below.
This is the result of solving an equation to find a value(s) for the variable(s) which make the equation true.
Find the number that 5 times itself is the same as 3 times that number plus 2.
numbers fit all of the rules that applied. I remembered that it could perfectly go into a group of
Also I still do not quit understand how this amounts to 8 ------> (1+1)**(5-2) = 8 why 2 * ? and what is the value?
Theorem 7. p0 + p1 + p2 + p3 + p4 + ·· · + pn = pn+3 — 1
1, 2, 4, 5, 6, 7, 8, 9, 10, 13, 14, 15, 18, 21, 19, 26
Choose the most correct answer. Where there is a conflict, the text is the final source. Please write letter next to number.
We will now take a look using the Prime Factorization formula which will aid us in finding the number
Choose 8-10 problems that are aligned to the domains of operations & algebraic thinking and numbers & operations in base ten.
Answer: True. The argument with the conclusion “Seven is greater than five” is valid but in some instances may not be sound. This is because we check that an argument is sound by if its first valid and then if all its premises are true. Thus, sound arguments are known to end up with true conclusions. Although in this case some arguments with the conclusion “seven is greater than five” may not be sound because if for instance, one of the premise states that everything seven is greater than everything 5. This premise will be false because seven centimeters is less than 5 meters/ seven ten dollar bills are less than 5 twenty dollar bills. Therefore, since the premise will not hold true, an argument as such will not be sound.
4 105 114 37 29 22 23 55 51 41 25 40 77 92 108 95 82 67 115 141 161 165 146 174 215 218 152 121 89 76 135 281 320 281 299 223 104
Teaching students effectively in areas of multiplicative thinking, fractions and decimals requires teachers to have a true understanding of the concepts and best ways to develop students understanding. It is also vital that teachers understand the importance of conceptual understanding and the success this often provides for many students opposed to just being taught the procedures (Reys et al., ch. 12.1). It will be further looked at the important factors to remember when developing a solid conceptual understanding and connection to multiplicative thinking, fractions and decimals.