If x and y are Positive Integers, Which of the Following GMAT Problem Solving

Question: If x and y are positive integers, which of the following cannot be the greatest common divisor of 35x and 20y?

1. 5
2. 5(x – y)
3. 20x
4. 20y
5. 35x

Answer:

Approach Solution (1):

Greatest common divisor (GCD) of 35x and 20y obviously must be a divisor of both 35x and 20y, which means that \(\frac{35x}{GCD}\) and \(\frac{20y}{GCD}\)must be an integer.

If GCD = 20x (option C), then \(\frac{35x}{20x} = \frac{7}{4} \neq integer\), which means that 20x cannot be GCD of 35x and 20y as it is not a divisor of 35x.

Correct Option: C

Approach Solution (2):

1. 5 --- if x = y = 1 --- 35x = 35 and 20y = 20 --- GCD (35, 20) = 5. Answer is YES, 5 can be GCD of 35x = 35 and 20y;
2. 5(x – y) --- if x = 3 and y = 2 --- 35x = 105 and 20y = 40 --- GCD (105, 40) = 5 = 5 (x – y). Answer is YES, 5 (x – y) can be GCD of 35x and 20y;
3. 20y --- if x = 4 and y = 1 --- 35x = 140 and 20y = 20 --- GCD (140, 20) = 20 = 20y. Answer is YES, 20y can be GCD of 35x and 20y;
4. 35x --- if x = 1 and y = 7 --- 35x = 35 and 20y = 140 --- GCD (35, 140) = 35 = 35x. Answer is YES, 35x can be GCD of 35x and 20y.

Correct Option: C

“If x and y are positive integers, which of the following cannot be the greatest common divisor of 35x and 20y?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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