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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Institute of Engineering‚ Information and Technology Structure of Programming Language “C++ Programming Language” INSTRUCTOR: SCLP SUBMITTED BY: UC HISTORY OF C++ In the early 1970s‚ Dennis Ritchie of Bell Laboratories was engaged in a project to develop a new operating system. Ritchie discovered that in order to accomplish his task he needed the use of a programming language that was concise and that produced compact and speedy programs. This need led Ritchie to develop the
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world of data structures and algorithms Bit-Sum Prime Difficulty level: moderate Every student‚ who has learned programming‚ must have written a program to determine whether a given positive integer is a prime number. Basically in order to determine whether a positive integer n is prime‚ we search for any number in the range [2‚ n − 1] which can divide n. Some of you would have designed a slighly better implementation where you search √ for any divisor of n from the range [2‚ n ]
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the hands of a clock at 4:00? A. 50 B. 60 C. 75 D. 120 E. 150 13. If two angles are supplementary‚ then their sum is A. 60 degrees B. 90 degrees C. 180 degrees D. 270 degrees E. 360 degrees 14. Suppose x‚y > 0 and x‚y are both integers. If x+ y=2‚ then x-y=? A. -1 B. 0 C. 1 D. 2 E. cannot be determined 15. If x‚ y‚ w and z correspond to four numbers -3‚ ½‚ -4 and 2 but not necessarily in the same order‚ what is the largest possible value of the
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(osler@rowan.edu) Rowan University‚ Glassboro‚ NJ 08028 Fermat’s Little Theorem [1] states that n p −1 − 1 is divisible by p whenever p is prime and n is an integer not divisible by p. This theorem is used in many of the simpler tests for primality. The so-called multinomial theorem (described in [2]) gives the expansion of a multinomial to an integer power p > 0‚ (a1 + a2 + ⋅⋅⋅ + an ) p = p k1 k2 kn a1 a2 ⋅⋅⋅ an . k1 ‚ k2 ‚ ⋅⋅⋅‚ kn k1 + k2 +⋅⋅⋅+ kn = p ∑ (1) Here the multinomial
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Java Problems SEQUENCE PROBLEMS: 1. Create a Java program that will print the sum of two integers. 2. Print the sum and product of three integers. 3. Print the perimeter and area of a rectangle. 4. Given the number of a baseball team’s wins and losses‚ compute its winning percentage. Assume that there are no ties. 5. Input the number of a team’s wins‚ losses‚ and ties‚ and print its winning percentage. Assume that a tie game counts as a full game played and a half-game won. 6. Given the
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Linear Application and Hill Cipher. Cryptography has played an important role in information and communication security for thousand years. It was first invented due to the need to maintain the secrecy of information transmitted over public lines. The word cryptography came from the Greek words kryptos and graphein‚ which respectively mean hidden and writing (Damico). Since the ancient days‚ many forms of cryptography have been created. And in 1929‚ Lester S. Hill‚ an American mathematician and
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as the specific topic I would like to go deep into. Fermat ’s Last Theorem states that if n is a positive integer greater than 2‚ then the Diophantine equation x^n+y^n=z^n has no nontrivial solutions. Diophantine equation is an equation together with the restriction that the only solutions of the equation of interest are those belonging to a specified set‚ often the set of integers or the set of rational numbers. Fermat ’s last theorem has its origins in the mathematics of ancient Greece; two
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variables result‚ w‚x‚ y‚ and z are all integers‚ and that w= 5‚ x= 4‚ y=8 and z=2. What will the values be stored in result in each of the following statements? a. set result= x+y= 4+8 b. set result=z*2= 2*2 c. set result= y/x= 8/4 set result= y-z= 8-2 5. Write a pseudocode statement that declares the variable cost so it can hold real numbers. Floating-point variable cost 6. Write a pseudocode statement that declares the variable total so it can hold integers. Initialize the variable with the
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