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Solve GRE practice problems covering Quant (One answer choice and multiple answer choice), Data Interpretation, Text Completion, Sentence Equivalence, and Reading Comprehension Problems.
Solve GRE practice problems covering Quant (One answer choice and multiple answer choice), Data Interpretation, Text Completion, Sentence Equivalence, and Reading Comprehension Problems.
Re: Which of the following CANNOT be the greatest common divisor
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17 Aug 2020, 11:13
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1
Bookmarks
Carcass wrote:
Which of the following CANNOT be the greatest common divisor of two positive integers x and y?
(A) 1 (B) x (C) y (D) x - y (E) x + y
Key concept: Each divisor of integer N is less than or equal to N For example, here are the divisors of 15: {1, 3, 5, 15} Notice that every divisor is less than or equal to 15.
Similarly, if a number is a divisor of both x AND y, then that number must be less than or equal to x AND less than or equal to y. As such, the greatest common divisor of x and y cannot be greater than both x and y Since (x + y) > x and (x + y) > y, we can conclude that x+y cannot be the greatest common divisor of x and y.
Which of the following CANNOT be the greatest common divisor
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04 Aug 2022, 01:10
1
Theory
➡ GCD of two numbers is always smaller than or equal to the smaller of those two numbers ➡ GCD (a,b) <= Smaller (a,b)
Which of the following CANNOT be the greatest common divisor of two positive integers x and y
Let's take each option choice and evaluate
(A) 1 Now, we can take co-prime values of x and y (co-primes are numbers which have only 1 as as the common factor) and this will be true. Ex, x=2 and y=3 => GCD = 1 => TRUE
(B) x This can be true when one number is x and other number is a multiple of x Example: One number is 2 (which is x) and other number is 2*2 = 4 (which is a multiple of x). Making the GCD = 2 (which is x) => TRUE
(C) y This can be true when one number is y and other number is a multiple of y Example: One number is 2 (which is y) and other number is 2*2 = 4 (which is a multiple of y). Making the GCD = 2 (which is y) => TRUE
(D) x - y Take x = 4, y = 2. x - y = 4-2 = 2 GCD (4,2) = 2 => TRUE
(E) x + y Now, GCD of two numbers is always smaller than or equal to the smaller of those two numbers => GCD(x,y) <= Smaller of x and y So, GCD can never be x+y as x+y will be greater than both x and y. => FALSE
So, Answer will be E Hope it helps!
To learn more about LCM and GCD watch the following videos