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If 4x > y and y < 0 then which of the following...

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by BTGmoderatorLU » Tue Nov 28, 2017 6:12 pm
$$If\ \ \ 4x\ >\ y\ \ and\ y\ <\ 0,$$ then which of the following could be the value of x/y?

A)0
B)1/4
C)1/2
D)1
E)2

The OA is A.

I'm confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.
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by ErikaPrepScholar » Wed Nov 29, 2017 10:17 am
The question stem tells us that y is negative. We know that if we multiply or divide an inequality by a negative number, we must switch the direction of the sign. This means that we can rearrange the inequality from the question stem as follows:

$$4x\ >\ y$$ $$\frac{4x}{y}\ <\ 1$$ $$\frac{x}{y}\ <\ \frac{1}{4}$$

So x/y must be less than 1/4. The only answer that works is A, 0.
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If 4x > y and y < 0

by Harbans » Wed Nov 29, 2017 3:56 pm
All options are +ve so either both x and y are -ve or both are +ve
y < 0 so x < 0
Last edited by Harbans on Wed Nov 29, 2017 4:15 pm, edited 1 time in total.
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by ErikaPrepScholar » Wed Nov 29, 2017 4:11 pm
Hey Harbans,

Careful with your logic here! x can be negative, as long as its magnitude is more than 4 times smaller than y. For instance, if x = -1 and y = -5, then 4x = -4, which is greater than -5, making 4x > y and x/y = 1/5 (a positive number).

Unfortunately, all of our positive answer choices for x/y are too large: 1/4 makes 4x = y, and all of the other options make 4x > y. (You can test this out by plugging in numbers.)

Thus, 0 is the only answer that works here, but we could theoretically have a positive answer that is less than 1/4.
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by [email protected] » Wed Nov 29, 2017 6:53 pm
Hi LUANDATO,

We're told that 4X > Y and Y < 0. We're asked for a possible value of X/Y. This question can be solved by using the answer choices 'against' the prompt and TESTing VALUES.

Since Y < 0, we know that Y can be ANY NEGATIVE number....
IF... Y = -1
4X > -1
The 'easiest' value for X would be 0 (since 0 > -1). In this example, X/Y = 0/-1 = 0, which matches one of the answers.

Final Answer: A

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by Scott@TargetTestPrep » Mon Oct 07, 2019 6:53 pm
BTGmoderatorLU wrote:$$If\ \ \ 4x\ >\ y\ \ and\ y\ <\ 0,$$ then which of the following could be the value of x/y?

A)0
B)1/4
C)1/2
D)1
E)2

The OA is A.

I'm confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.
We are given that 4x > y and y < 0; dividing the first inequality by 4y (and remembering to switch the inequality sign), we have:

x/y < 1/4

The only choice that is less than 1/4 is 0, so x/y could be 0.

Answer: A

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