If x and y are positive integers, is x y ?

Question

If x and y are positive integers, is x > y ?

(1)  x^2 < y

(2)  \sqrt{x} < y

Hatakekakashi · Answer

Given x and y are Z+ i.e 1,2,3,.. etc ST 1 - x^2 < Y X^2=1 , Y = 2 X>Y no x^2=4 y = 5 x>y no x^2=9 y=10 x>y no Sufficient ST 2- sqrt x Y yes x=1 Y^2=9 x < y^2 x>y no insufficient (A) imo

Mo2men · Answer

(1)  x^2 < y

We are dealing with +ve INTEGERS....then

x < x^2 < y........the x < y............Answer is always NO

Sufficient

(2)  \sqrt{x} < y

We are dealing with +ve INTEGERS....then

x <  \sqrt{x} ........but y >  \sqrt{x} ...........Here we can't establish a relationship like above. check numbers

Let x = 9, y = 4........... \sqrt{9}  < 4 ......3 < 4.............Answer is Yes

Let x = 9, y = 10........... \sqrt{9}  < 10 ......3 < 10.............Answer is NO

Insufficient

Answer: A

GMATinsight · Answer

Question : is x > y ? Statement 1 : x^2 < y If we try to check the information with a few numbers then we realise that for every value of x for which x^2 is less than y, x must be less than y Hence SUFFICIENT Statement 1 : \sqrt{x} < y Case 1: x = 4, y = 3, x > y Case 1: x = 4, y = 5, x < y NOT SUFFICIENT Answer: option A

MathRevolution · Answer

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the question.

We can modify the question as follows.
Since  x  and  y  are positive integers, we have  x ≥ 1  and  y ≥ 1 .
Since  x ≥ 1 , we have  1 ≤\sqrt{x} ≤ x ≤ x^2 .

Condition 1)
From  x ≤ x^2  and  x^2 < y , we have  x ≤ x^2 < y  or  x < y .
Condition 1) is sufficient.

Condition 2):
 x = 4, y = 3 : Yes
 x = 2, y = 3 : No
Since we don't have a unique answer from the condition 2), it is not sufficient.

Therefore, A is the answer.

Wongderful · Answer

Question: is x > y ? Additional Info: X & Y are positive integers (1) x^2 x is greater than y if x is 1, y is 2 -> x is smaller than y Hence not sufficient. IMO (A) as well. Took 3 mins to solve though

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If x and y are positive integers, is x > y ?

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