GMAT Club Math Book Facebook gmatclub.com/mathbook facebook.com/ gmatclubforum Table of Contents Number Theory ..................................................................................................................... 3 INTEGERS................................................................................................................................................... 3 IRRATIONAL NUMBERS ............................................................................
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Workbench 1. Design a module named timesTen. The module should accept an Integer argument. When the module is called‚ it should display the product of its argument multiplied times 10. Module Main () Call timesTen Module timesTen (Integer Value) Declare integerValue Set result = value*10 Display result End Module 5. Design a module named getNumber‚ which uses a reference parameter variable to accept an Integer argument. The module should prompt the user to enter a number and then
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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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of family member Age (as an integer variable array) State of family member State (as an string variable array) Derived Inputs: Number of family members will be derived by adding the number of times that the user enters the names of family members into the program. NumFamily (as an integer variable) Sum of ages will be derived from a loop that runs the same number of times as there are family members‚ adding together the ages as the loop runs. SumOfAges (as an integer variable) Calculation Approach:
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question paper. Each question carries 5 marks. • Answer all questions. • Time allotted: 2 hours. QUESTIONS 1. What is the smallest positive integer k such that k(33 + 43 + 53 ) = an for some positive integers a and n‚ with n > 1? n √ 2. Let Sn = k=0 1 √ . What is the value of k+1+ k 99 1 ? n=1 Sn + Sn−1 3. It is given that the equation x2 + ax + 20 = 0 has integer roots. What is the sum of all possible values of a? 4. Three points X‚ Y‚ Z are on a striaght line such that XY = 10 and XZ = 3. What
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(e) int i = 1000; char c = (char) i; (f) int i = 1000; boolean b = (boolean) b; 7. Write a statement or comment to accomplish each of the following: (a) state that this program will calculate the product of 3 integers. (b) name the class name as Calculate (c) declare the variable x‚ y and z to be of type int. (d) initialize the variable x and y to be 3‚ and 4. (e) assign the result of addition of x and y to variable z. (f) print out
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the user is a perfect number or not. (Note: A perfect number is the one whose all the divisors sum up the number itself. For example‚ number 28 is a perfect number as 1+2+4+7+14=28). 6. Write a program in C++ to read a set of 10 positive integers and display them all. If the number entered is zero‚ the program continues reading‚ but when the user input is a negative number‚ the program stops reading any further input and displays a message: “a negative number entered”. 7. Write a program
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a negative sign (-).These numbers are sometimes called directed numbers or signed numbers. e.g. 1.2 - FUNDAMENTAL OPERATIONS ON INTEGERS 1.2.1 – ADDITION OF INTEGERS To add integers with the same sign ‚add without regard to the signs.Then affix the common sign of the integers.To add two integers with different signs ‚consider the distance of each integer from zero (that is‚ consider the absolute value of each addend).Subtract the shorter distance from the longer distance. In the answer
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insufficient to argue that a mathematical statement is true simply by experiments and observations. For instance‚ Fermat (1601–1665) conjectured that when n is an integer greater than 2‚ the equation x n + y n = z n admits no solutions in positive integers. Many attempts by mathematicians in finding a counter-example (i.e. a set of positive integer solution) ended up in failure. Despite that‚ we cannot conclude that Fermat’s conjecture was true without a rigorous proof. In fact‚ it took mathematicians
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x[i] = x[i +1] ; x[i] - 1 = x[1] ; 3. Is the following legal? int x[5] = {1‚ 2‚ 3‚ 4‚ 5} ; int y[5] ; y = x; 4. Write prototype for the following. Do not write the functions. i) A function called largest that gets an array of integers and returns an integer. ii) A function called price that gets two double array names for input and a double array name for output. The function does not return a value. 5. Combine the following two statements into one statement. db1_arr[i] = data ; ++
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