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# If x and y are positive integers, is x > y? (1) (x)(x) < y (2) The squ

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Joined: 02 Sep 2009
Posts: 64242
If x and y are positive integers, is x > y? (1) (x)(x) < y (2) The squ  [#permalink]

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07 Aug 2019, 02:27
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Difficulty:

65% (hard)

Question Stats:

47% (01:10) correct 53% (01:40) wrong based on 34 sessions

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

(1) x^2 < y
(2) The square root of x is less than y

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Joined: 07 Mar 2019
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Re: If x and y are positive integers, is x > y? (1) (x)(x) < y (2) The squ  [#permalink]

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07 Aug 2019, 03:20
If x and y are positive integers, is x > y?

(1) $$x^2$$ < y
(2) The square root of x is less than y

Since x > 0 and y > 0.
Statement 1) $$x^2 < y$$
x*x < y so x would definitely be less than y always.

ALTERNATIVELY:
Verifying using numbers and fractions.
Case 1: x = $$\frac{1}{2}$$ and y > 1(2 OR 3 OR any value).
Case 2: x = $$\frac{1}{2}$$ and 0 < y < 1 such that $$x^2$$ < y always (y = $$\frac{2}{3}$$ OR $$\frac{4}{9}$$)

Case 3: x > 1 and y > 1 such that $$x^2$$ < y always. Take x = 2 so that $$x^2$$ = 4 and y ≥ 5

Only Case 3 is required here as per question
Sufficient.

Statement 2) $$\sqrt{x}$$ < y
As both x and y are positive we can square the inequality
x < $$y^2$$

Take x = 1 and y = 2, So x > y ? NO
OR
x = 2 and y = 2, So x > y ? NO
OR
x = 3 and y = 2, So x > y ? YES

Insufficient.

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Re: If x and y are positive integers, is x > y? (1) (x)(x) < y (2) The squ  [#permalink]

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13 Aug 2019, 22:09
Bunuel wrote:
If x and y are positive integers, is x > y?

(1) x^2 < y
(2) The square root of x is less than y

x and y are positive integers
Possible values of x = {1, 2, 3, 4, . . . .. }
Possible values of y = {1, 2, 3, 4, . . . .. }

(1) x^2 < y
If x = 1, y > 1 --> x < y (Answer - Definite NO)
If x = 2, y > 4 --> x < y (Answer - Definite NO)
If x = 3, y > 9 --> x < y (Answer - Definite NO)

--> Sufficient

(2) The square root of x is less than y
√x < y
If x = 1, y > 1 --> x < y (Answer - Definite NO)
If x = 4, y > 2 --> Possible values (x, y) = (4, 3), (4, 5) --> Can't say

--> Insufficient

IMO Option A

Pls Hit Kudos if you like the solution
Re: If x and y are positive integers, is x > y? (1) (x)(x) < y (2) The squ   [#permalink] 13 Aug 2019, 22:09