If y < 0 and 4x > y, Which of the Following could be Equal to \(\frac{x}{y}\) GMAT Problem Solving

Question: If y < 0 and 4x > y, which of the following could be equal to\(\frac{x}{y}\)?

1. 0
2. \(1\over4\)
3. \(1\over2\)
4. 1
5. 4

Answer:
Approach Solution (1):
4x > y
Divide both the sides by y, we get:
\({4x\over{y}}<1\)[Since y is negative so we will have to reserve the inequality sign]
Divide both sides by 4, we get:
\({4x\over{y}}<{1\over4}\)
\(\Rightarrow{x\over{y}}<{1\over4}\)
Only option choice which is less than\(1\over4\)is 0
Correct option: A

Approach Solution (2):
We can see we can create\(x\over{y}\)on the left side but that requires you to divide both the sides by y. since y is negative that will flip the inequality sign.
Hence we start with 4x > y and divide both sides by y to get\({4x\over{y}}<1\). Then move 4 over to get
\(\Rightarrow{x\over{y}}<{1\over4}\)
Correct option: A

Approach Solution (3):
Since y < 0, let us divide both sides by y. inequality sign gets changed since y < 0.
4x > y…\(\Rightarrow{x\over{y}}<{1\over4}\)
Only 0 is possible
Correct option: A

“If y < 0 and 4x > y, which of the following could be equal to\(x\over{y}\)?”- 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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