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Bunuel
If x and y are positive integers, is \(\frac{x}{y} > 1\)?

(1) \(x + 3 = y\)

(2) \(\frac{x + 5}{y} > 1\)


we know both x and y are positive.

x/y>1

x>y.

Statement 1: y = x + 3. Sufficient. As per this statement , y>x.

Statement 2: \(\frac{x + 5}{y} > 1\)

x> y - 5.

As we don't know the value of x or y, It's not possible to determine whether x>y or not.

NOT sufficient.

A is the correct answer.
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Solution



Given:
    • x and y are positive integers

To find:
    • Whether \(\frac{x}{y} > 1\) or not
    • Or, whether x > y or not

Analysing Statement 1
As per the information given in statement 1, x + 3 = y
    • Because both x and y are positive integers, we can definitely say that x > y

Hence, statement 1 is sufficient to answer the question.

Analysing Statement 2
As per the information given in statement 2, \(\frac{x + 5}{y} > 1\)
    • From this statement, we can write that x + 5 > y
    • But, we cannot conclude whether x > y or not

Hence, statement 2 is not sufficient to answer the question.

Hence, the correct answer is option A.

Answer: A

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Bunuel
If x and y are positive integers, is \(\frac{x}{y} > 1\)?

(1) \(x + 3 = y\)

(2) \(\frac{x + 5}{y} > 1\)

Asked: If x and y are positive integers, is \(\frac{x}{y} > 1\)?

(1) \(x + 3 = y\)
x/y = x+3/x = 1 + 3/x > 1; since x>0
SUFFICIENT

(2) \(\frac{x + 5}{y} > 1\)
x/y + 5/y > 1
x/y > 1 -5/y < 1
NOT SUFFICIENT

IMO A
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