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Re: Que : If n is an even integer, which of the following MUST BE an integer?

Solution: Multi-Choice questions: ‘Must be’ VS ‘Could be’ We have to find the options that must be true ‘MUST BE’: Choose only the options that are absolutely true in ALL cases => ‘n’ is an even integer, Always an integer => n=even=2m (m is always an integer) Option I: \(\frac{n^2-1}{2}=\frac{\left...


Re: Que : When the equation \(x^2+ax+b=0\) has roots p and q, what is the value of p + q?

Solution: To save time and improve accuracy on DS questions in GMAT, learn and apply the Variable Approach. Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem....


Que : If n is an even integer, which of the following MUST BE an integer?

Que : If n is an even integer, which of the following MUST BE an integer? I. \(\frac{\left(n^2-1\right)}{2}\) II. \(\frac{\left(n-1\right)}{2}\) III. \(\frac{n}{2}\) A. I only B. II only C. III only D. I & III only E. I, II, & III


Re: Que: How many different prime factors of \(3^5+3^6+3^7\) are there?

Solution: Factors of M are the integers dividing M without a remainder => If M=ab (a and b are positive integers) => a and b are factors of M => When M is expressed as a product of its prime factors only => We have prime factorized M =>If we prime factorize a positive integer M => M= \(\left(p_1\ri...


Re: Que: If a certain machine produces toys at a constant rate, how many minutes will it take the machine.......

Solution: To save time and improve accuracy on DS questions in GMAT, learn and apply the Variable Approach. Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem....


Que: If a certain machine produces toys at a constant rate, how many minutes will it take the machine.......

Que: If a certain machine produces toys at a constant rate, how many minutes will it take the machine to produce 1,200 toys?

(1) It takes the machine 75 minutes to produce 40 toys.
(2) It takes the machine 2.25 minutes to produce 2 toys.


Re: Que: If n is positive integers, what is the unit digit of \(\left(3^{4n+1}\right)\left(4^{19}\right)\)?

Solution: Powers that repeat every 4th power: Ex) Units digit: The digit 3 repeats after every fourth power => ~\(3^1\)= ~3, ~\(3^2\)= ~9, ~\(3^3\) = ~7, ~\(3^4\)= ~1, ~\(3^5\)= ~3, ... => Pattern: 3, 9, 7, 1, 3, 9, 7, 1 …. Ex) Units digit: The digit 4 repeats after every second power => ~\(4^1\) =...


Re: Que: If x and y are different prime numbers greater than 30 but less than 40, what is the value of x + y?

Solution: Prime number: An integer that has two positive factors = only 1 and itself => ex) 2, 3, 5, 7… We have to find the value of x + y If x and y are different prime numbers greater than 30 but less than 40 Prime numbers between 30 and 40: 31 and 37 => ∴ x + y = 31 + 37 = 68 Therefore, E is the...


Re: Que: If the ratio of the numbers of men to women to children in a certain room is 5 to 3 to 7.....

Solution: To save time and improve accuracy on DS questions in GMAT, learn and apply the Variable Approach. Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem....


Re: Que: Machine A and machine B produce toys at their constant rates, respectively. In how many hours......

Solution: To save time and improve accuracy on DS questions in GMAT, learn and apply the Variable Approach. Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem....