Multiply both sides by 5 and then subtract 3y. You get 2 vs 2y, and since y > 4, quantity B will always be bigger

Explanation

Tricky question.

The stem says that y > 4 but it does not mention the fact that it could be an integer such as 5 or a fraction such as \(\frac{6}{1.4} = 4.2\)

If you substitute 5 to A the result is 3.4 that is less than 4. OR 4.2 the result is 2.92 that is less than 4.

So, no matter what quantity B is > than quantity A

B is the answer

We can solve this question using matching operations

Given:
Quantity A: \(\frac{3y+2}{5}\)
Quantity B: \(y\)

Multiply both quantities by 5 to get:
Quantity A: \(3y+2\)
Quantity B: \(5y\)

Subtract 3y from both quantities to get:
Quantity A: \(2\)
Quantity B: \(2y\)

Divide both quantities by 2 to get:
Quantity A: \(1\)
Quantity B: \(y\)

Since we're told that y > 4, we know that Quantity B is greater.

Answer: B

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One can solve using graph
as below
both function meet at (1,1) ~ (y,f(y))
from point (1,1) f(y)=y is grater then f(y) = 3y+2 / 5

check attachment/picture

Great graph solution.

Thank you

Interesting approach!

Thanks! I think it's one of the most useful strategies for solving Quantitative Comparison questions.
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If y = 5, we get:
Quantity A: [3(5) + 2]/5
Quantity B: 5

Simplify to get:
Quantity A: 3.4
Quantity B: 5

So, Quantity B is greater (not Quantity A).
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Substitute 4.1

we get LHS = 2.86 < 4.1

ans B

Then we take y = 5

RHS --> 3(5) + 2 / 5 = 17/5 = its ~3.4 and RHS = 5

Ans B

You can simplify the expression by
1) multiply both sides by 5
2) subtract 3y from both sides
3) then you are left with '2' on the left and '2y' on the right.

You compare '2' to '2y'

Substitute any number bigger than 4, B is always bigger than '2'

Seeing if the 2 columns can be simplified will make your life so much easier. Just be careful not to divide by x if x can be zero. In this case with just variable add/sub, the 'x is zero' is irrelevant. So simplify to your heart's content in this problem.

y>4 multiply both sides by 3 we get : 3y>12 then add both sides with 2 we get 3y+2>15 then divide both side by 5 we get

(3y+2)/5>3 thus B holds true for every value of y

it would be D, because it is not mentioned the integer of y.
If y=1/3, A>B
If y=5, A<B