represented in the form p/q where p and q are integers and q is not zero. Example: 2/3‚ 1/10‚ 8/3 etc. They can be finite decimal numbers‚ whole numbers‚ integers‚ fractions. Irrational numbers: A number that cannot be represented in the form p/q where p and q are integers and q is not zero. An infinite non recurring decimal is an irrational number. Example: √2‚ √5 ‚ √7 and Π(pie)=3.1416. The rational numbers are classified into Integers and fractions Integers: The set of numbers on the number line‚ with
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Section 4.1 Divisibility and Modular Arithmetic 87 CHAPTER 4 Number Theory and Cryptography SECTION 4.1 Divisibility and Modular Arithmetic 2. a) 1 | a since a = 1 · a. b) a | 0 since 0 = a · 0. 4. Suppose a | b ‚ so that b = at for some t ‚ and b | c‚ so that c = bs for some s. Then substituting the first equation into the second‚ we obtain c = (at)s = a(ts). This means that a | c‚ as desired. 6. Under the hypotheses‚ we have c = as and d = bt for some s and t . Multiplying
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CHAPTER 2 WHOLE NUMBERS What have we discussed? 1. The number 1‚ 2‚ 3… which use for counting are known as natural number. 2. If you add 1 to a natural number‚ we get its successor‚ if you subtract 1 from a natural number‚ you get its predecessor. 3. Every natural number has a successor. Every natural number except 1 has a predecessor. 4. If add the number zero to the collection of the natural numbers‚ we get the collection of whole numbers. Thus‚ the number 0‚ 1‚ 2‚
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The University of British Columbia CPSC 210 Midterm Examination February 8‚ 2012 - SOLUTIONS Time: 90 minutes Name (PRINT) (Last) (First) ____________________ Student No____________________________Signature _____________________ This examination has 12 pages. Check that you have a complete paper. Ensure you have access to the source repository that will be specified on the whiteboard. You may access this repository before you are told you can start the exam. We refer to the code in
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KSF 2013 – finalized problems Cadet 3 points # 1. In the picture‚ the big triangle is equilateral and has area 9. The lines are parallel to the sides and divide the sides into three equal parts. What is the area of the shaded part? (A) 1 # 2. It is true that (B) 4 1111 101 (C) 5 (D) 6 = 11. What is the value of (A) 5 (B) 9 3333 101 + (E) 7 6666 303 ? (D) 55 (C) 11 (E) 99 # 3. The masses of salt and fresh water in sea water in Protaras are in the ratio 7 : 193. How many kilograms of
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Damath Introduction: Damath comes from the Pinoys checker board game called “dama” and Mathematics. It blends local culture‚ education and digital technology that aim to make math teaching and learning child-friendly‚ challenging and interactive. DAMATH‚ a patent-pending mathematical board-game invented by five-time national awardees Jesus L. Huenda‚ is coined from the popular Filipino checkerboard game of dama‚ (or lady in Spanish) and mathematics. It started in a Sorsogon National High School
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are undetermined. Analysis – First I need to declare A‚ B‚ C‚ D‚ F and GPA as integers. A = 4‚ B = 3‚ C = 2‚ D = 1‚ F = 0. Each of these numbers will be floated The program will ask for the name of the user User Name: Stephen The program will then ask for the grades. Grades Entered: A‚A‚D The letters corresponding to the integers will be summed ex. A+A+D = 4+4+1 = 9 The program will then divide the sum of the integers by the amount entered. 9/3 = 3.0 = GPA The program will print the students name
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they are false. Assume x is of type int. A. Any bit of x equals 1. B. Any bit of x equals 0. C. Any bit in the least significant byte of x equals 1. D. Any bit in the most significant byte of x equals 0. Your code should follow the bit-level integer coding rules (page 120)‚ with the additional restriction that you may not use equality (==) or inequality (!=) tests. ◆SOLUTIONS◆ A. !!x B. !!~x C. !!(x & 0xFF) D. !!(~ & 0xFF) ------------------------------------------------- 2
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4. The first term of a sequence is 20 and the second term is 8. The third term and each term thereafter is the average (arithmetic mean) of the two terms immediately preceding it. What is the value of the first term in the sequence that is not an integer? (A) (B) (C) (D) (E) 22.6 1.23 24.7 12.5 6.8 5. a‚ 3a‚ ... The first term in the sequence above is a‚ and each term after the first is 3 times the preceding term. If the sum of the first 5 terms is 605‚ what is the value of a ? 6.
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GMAT Practice Questions | GMAT Study Guide | Free GMAT Prep www.platinumgmat.com | GMAT Practice Test Difficult Data Sufficiency Questions WXYZ Remainder If w‚ x‚ y‚ and z are the digits of the four-digit number N‚ a positive integer‚ what is the remainder when N is divided by 9? 1) w + x + y + z = 13 2) N + 5 is divisible by 9 A) Statement (1) ALONE is sufficient‚ but statement (2) alone is not sufficient. B) Statement (2) ALONE is sufficient‚ but statement (1) alone is not sufficient. C)
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