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# D01-44

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Manager
Joined: 18 Jul 2018
Posts: 52
Location: United Arab Emirates

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28 Mar 2019, 05:04
Bunuel wrote:
Official Solution:

$$x^2 + y^2 = 100$$. All of the following could be true EXCEPT

A. $$|x| + |y| = 10$$
B. $$|x| \gt |y|$$
C. $$|x| \gt |y| + 10$$
D. $$|x| = |y|$$
E. $$|x| - |y| = 5$$

A. $$|x| + |y| = 10$$ is possible if one is 0 and the other is 10.

B. $$|x| \gt |y|$$ is possible if $$|x| \gt |5\sqrt{2}|$$ and $$|y| \lt |5\sqrt{2}|$$

C. $$|x| \gt |y| + 10$$ is never possible because if $$|x| \gt 10$$, $$x^2+y^2$$ becomes greater than 100, which is wrong.

D. $$|x| = |y|$$ is possible if each is equal to $$|5\sqrt{2}|$$.

E. $$|x| - |y| = 5$$ is possible if $$|x| = |9.11|$$ and $$|y| = |4.11|$$.

Therefore all but C are possible. $$|x| \gt |y| + 10$$ means $$x$$ is greater than 10, which is not possible.

Hi Bunuel

Can we solve this in the following manner???

x^2+y^2 = 100.
If we take another look at the given statement, it can be consider an equation of right angle triangle.
We know that sum of any two sides of triangle must be always greater than the third side.

Hence, Option C can never be true.

Manager
Joined: 18 Jul 2018
Posts: 52
Location: United Arab Emirates

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28 Mar 2019, 05:08
Bunuel wrote:
Official Solution:

$$x^2 + y^2 = 100$$. All of the following could be true EXCEPT

A. $$|x| + |y| = 10$$
B. $$|x| \gt |y|$$
C. $$|x| \gt |y| + 10$$
D. $$|x| = |y|$$
E. $$|x| - |y| = 5$$

A. $$|x| + |y| = 10$$ is possible if one is 0 and the other is 10.

B. $$|x| \gt |y|$$ is possible if $$|x| \gt |5\sqrt{2}|$$ and $$|y| \lt |5\sqrt{2}|$$

C. $$|x| \gt |y| + 10$$ is never possible because if $$|x| \gt 10$$, $$x^2+y^2$$ becomes greater than 100, which is wrong.

D. $$|x| = |y|$$ is possible if each is equal to $$|5\sqrt{2}|$$.

E. $$|x| - |y| = 5$$ is possible if $$|x| = |9.11|$$ and $$|y| = |4.11|$$.

Therefore all but C are possible. $$|x| \gt |y| + 10$$ means $$x$$ is greater than 10, which is not possible.

Xylan can you help?? What if i don't want to do number plugging??
Manager
Status: The darker the night, the nearer the dawn!
Joined: 16 Jun 2018
Posts: 69

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28 Mar 2019, 07:56
2
JIAA wrote:
Bunuel wrote:
Official Solution:

$$x^2 + y^2 = 100$$. All of the following could be true EXCEPT

A. $$|x| + |y| = 10$$
B. $$|x| \gt |y|$$
C. $$|x| \gt |y| + 10$$
D. $$|x| = |y|$$
E. $$|x| - |y| = 5$$

A. $$|x| + |y| = 10$$ is possible if one is 0 and the other is 10.

B. $$|x| \gt |y|$$ is possible if $$|x| \gt |5\sqrt{2}|$$ and $$|y| \lt |5\sqrt{2}|$$

C. $$|x| \gt |y| + 10$$ is never possible because if $$|x| \gt 10$$, $$x^2+y^2$$ becomes greater than 100, which is wrong.

D. $$|x| = |y|$$ is possible if each is equal to $$|5\sqrt{2}|$$.

E. $$|x| - |y| = 5$$ is possible if $$|x| = |9.11|$$ and $$|y| = |4.11|$$.

Therefore all but C are possible. $$|x| \gt |y| + 10$$ means $$x$$ is greater than 10, which is not possible.

Xylan can you help?? What if i don't want to do number plugging??

JIAA It's completely okay if you do NOT want to do number plugging.
However, aspire to reach the CORRECT solution in the least possible time so that one can spend judicious time on 700+ Qs.

Quote:
Remember, Our arsenal should be equipped with all sorts of ammunition to tame the beast such as Reverse-solving, plugging different numbers, edge-case scenarios, etc.

The equation $$x^2 + y^2 = 100$$ is actually the locus of a circle with the origin as the center and radius of 10 units.
If possible Pre-Think the problem such as the allowable value of X and Y -
According to the question, the maximum value of either $$x^2$$ or $$y^2$$ can be 100, which implies that the greatest absolute value of either X or Y can be 10.
Thus, $$|x|$$ must be $$<= 10$$. Refer the attached picture.

Hence, $$|x|$$ CANNOT be $$> 10$$. Let alone $$|x|$$ being greater than $$|y| + 10$$.

If we take another look at the given statement $$x^2 + y^2 = 100$$, it can be considered an equation of right angle triangle with hypotenuse = 10 and perpendicular-sides as X and Y.
$$x^2 + y^2 = 100$$
And we know that the sum of two sides is always greater than the third side.
Thus: |y| + 10 > |x| : The third-side is smaller than the sum of other two-sides.
Therefore, OptionC is incorrect as it says $$|x| > |y| + 10$$, which can NEVER be true.

>> !!!

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Manager
Joined: 18 Jul 2018
Posts: 52
Location: United Arab Emirates

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28 Mar 2019, 09:29
Xylan wrote:
JIAA wrote:
Bunuel wrote:
Official Solution:

$$x^2 + y^2 = 100$$. All of the following could be true EXCEPT

A. $$|x| + |y| = 10$$
B. $$|x| \gt |y|$$
C. $$|x| \gt |y| + 10$$
D. $$|x| = |y|$$
E. $$|x| - |y| = 5$$

A. $$|x| + |y| = 10$$ is possible if one is 0 and the other is 10.

B. $$|x| \gt |y|$$ is possible if $$|x| \gt |5\sqrt{2}|$$ and $$|y| \lt |5\sqrt{2}|$$

C. $$|x| \gt |y| + 10$$ is never possible because if $$|x| \gt 10$$, $$x^2+y^2$$ becomes greater than 100, which is wrong.

D. $$|x| = |y|$$ is possible if each is equal to $$|5\sqrt{2}|$$.

E. $$|x| - |y| = 5$$ is possible if $$|x| = |9.11|$$ and $$|y| = |4.11|$$.

Therefore all but C are possible. $$|x| \gt |y| + 10$$ means $$x$$ is greater than 10, which is not possible.

Xylan can you help?? What if i don't want to do number plugging??

JIAA It's completely okay if you do NOT want to do number plugging.
However, aspire to reach the CORRECT solution in the least possible time so that one can spend judicious time on 700+ Qs.

Quote:
Remember, Our arsenal should be equipped with all sorts of ammunition to tame the beast such as Reverse-solving, plugging different numbers, edge-case scenarios, etc.

The equation $$x^2 + y^2 = 100$$ is actually the locus of a circle with the origin as the center and radius of 10 units.
If possible Pre-Think the problem such as the allowable value of X and Y -
According to the question, the maximum value of either $$x^2$$ or $$y^2$$ can be 100, which implies that the greatest absolute value of either X or Y can be 10.
Thus, $$|x|$$ must be $$<= 10$$. Refer the attached picture.

Hence, $$|x|$$ CANNOT be $$> 10$$. Let alone $$|x|$$ being greater than $$|y| + 10$$.

If we take another look at the given statement $$x^2 + y^2 = 100$$, it can be considered an equation of right angle triangle with hypotenuse = 10 and perpendicular-sides as X and Y.
$$x^2 + y^2 = 100$$
And we know that the sum of two sides is always greater than the third side.
Thus: |y| + 10 > |x| : The third-side is smaller than the sum of other two-sides.
Therefore, OptionC is incorrect as it says $$|x| > |y| + 10$$, which can NEVER be true.

Xylan this makes perfect sense! THANKS for the detailed explanation.
Much appreciated!
Intern
Joined: 19 Feb 2019
Posts: 6

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04 Apr 2019, 00:49
I solved it using the equation for a circle; x^2 + y^2 = r^2. In this case r = 10, and the centre of the circle is the origin (0,0).

With this in mind we can conclude that point |x|>|y|+10 will lie outside the circle. Hence not possible
D01-44   [#permalink] 04 Apr 2019, 00:49

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# D01-44

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