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# Is x > 0? (1) x + y = 30 (2) y^2 > 10

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Intern
Joined: 05 Dec 2017
Posts: 20
GPA: 3.35
Is x > 0? (1) x + y = 30 (2) y^2 > 10  [#permalink]

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22 Mar 2018, 09:37
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Difficulty:

25% (medium)

Question Stats:

77% (01:04) correct 23% (00:44) wrong based on 45 sessions

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Is $$x > 0?$$

(1) $$x + y = 30$$
(2) $$y^2 > 10$$
Math Expert
Joined: 02 Sep 2009
Posts: 58434
Re: Is x > 0? (1) x + y = 30 (2) y^2 > 10  [#permalink]

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22 Mar 2018, 09:46
Is $$x > 0?$$

(1) $$x + y = 30$$. No info about y. Not sufficient.

(2) $$y^2 > 10$$. Clearly not sufficient.

(1)+(2) If y = 30, then x = 0 and the answer is NO but if y = 29, then x = 1 and the answer is YES. Not sufficient.

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Re: Is x > 0? (1) x + y = 30 (2) y^2 > 10  [#permalink]

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22 Mar 2018, 20:21
Hi Bunuel sir. Thank you for OA.
Would you elaborate the statement y^2>10. basically i need to know,
1. what does it mean by y^2>10?
2. What is the range of y^2>10 on graph line?
3. Is it single line finite? or not?
Math Expert
Joined: 02 Sep 2009
Posts: 58434
Re: Is x > 0? (1) x + y = 30 (2) y^2 > 10  [#permalink]

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22 Mar 2018, 20:51
Jamil1992Mehedi wrote:
Hi Bunuel sir. Thank you for OA.
Would you elaborate the statement y^2>10. basically i need to know,
1. what does it mean by y^2>10?
2. What is the range of y^2>10 on graph line?
3. Is it single line finite? or not?

$$y^2 > 10$$;

Take the square root: $$|y| > \sqrt{10}$$ (recall that $$x^2=|x|$$);

$$y<-\sqrt{10}$$ or $$y > \sqrt{10}$$.

9. Inequalities

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Re: Is x > 0? (1) x + y = 30 (2) y^2 > 10  [#permalink]

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24 Mar 2018, 18:33
Jamil1992Mehedi wrote:
Is $$x > 0?$$

(1) $$x + y = 30$$
(2) $$y^2 > 10$$

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.

Since we have 2 variables (x and y) and 0 equations, C is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)
If x = 15, y = 15, then the answer is 'yes'.
If x = -10, y = 40, then the answer is 'no'.

Thus, both conditions together are not sufficient.

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
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Re: Is x > 0? (1) x + y = 30 (2) y^2 > 10   [#permalink] 24 Mar 2018, 18:33
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