I saw a question on this website: 4 < x < y < 8 : Quant

Question:

4<x<y<8. The ratio of x to y is 4 to 7.

Quantity A: y-x

Quantity B: 3

I get the answer as D (relationship can’t be determined) as I did the following:

I chose numbers like 4.4, 7.7, and 4.2, 7.35 - as both adhere to the ratio of 4:7. For one set of values I got the difference as 3 and for another set, less than 3. Hence, I went with option D. But, it seems that a few people claim that the answer is A.

I’m not sure if it is A, but can someone justify me with one answer for this question?

Thanks in Advance.

I understand that the answer can be D. But I don’t understand why this is a bad question. Any idea?

I still don’t understand why the answer is not A.

X/Y = 4/7

Y = 7X/4

Y-X = 7X/4 - X = 3X/4

When X = 4, Y-X = 3, Since X > 4, Y-X > 3

So A is more than B

Trying to look at the question in term of Y:

x/y = 4/7

x = 4y/7

y - x = 3y/7

When y is 7, x - y = 3, which would make the answer D.

Except that when Y = 7, X = 4 which it cannot be. Thus, y > 7 and 3y/7 > 3 so the answer is also A.

Why is the answer to this question D?

x:y = 4:7.

I took two multiplication factors: 1.1 and 1.05.

If you take 1.1, then x = 4.4 and y = 7.7 which is between 4 and 8 as per the question. The difference is 3 right?

Also, if you take 1.05, then x = 4.2 and y = 7.35, which is again between 4 and 8 as per the question. The difference in this case is not 3 right?

@hundreddays Can you please let me know what mistake I have done here?

One I see is:

If x = 4.4 and y = 7.7 then y - x = 3.3 not 3

So that would mean answer choice C is not an option yet.

That was a terrible arithmetic mistake. Apologies.

“Except that when Y = 7, X = 4 which it cannot be. Thus, y > 7 and 3y/7 > 3 so the answer is also A.”

How can y > 7 here? It is given that y < 7 right?

y - x compared with 3

=> 3y/7 compared with 3

After canceling 3 on both sides and multiplying by 7 on both sides,

y compared with 7.

In this case, B is greater right?

Hmmm how I see it is:

The given is that y < 8 but the more limiting factor is x > 4

Since, x = 4y/7, if y =< 7 then x =< 4 which breaks the rule. Thus, y must be more than 7

Now, y - x = 3y/7

If y > 7 then 3y/7 is always more than 3 so it is A.

From the same logic that y > 7, comparing y and 7 like you have shown means that y is bigger and the answer is A