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# Is √(x + y) an integer?

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Director
Joined: 10 Mar 2013
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Is √(x + y) an integer?  [#permalink]

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10 Dec 2015, 00:47
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Difficulty:

25% (medium)

Question Stats:

76% (01:44) correct 24% (01:54) wrong based on 140 sessions

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Is $$\sqrt{(x + y)}$$ an integer?

(1) $$x^3 = 64$$
(2) $$x^2 = y – 3$$

Source: Quant 700 to 800 level questions

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Director
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Re: Is √(x + y) an integer?  [#permalink]

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10 Dec 2015, 01:13
BrainLab wrote:
Is $$\sqrt{(x + y)}$$ an integer?

(1) $$x^3 = 64$$
(2) $$x^2 = y – 3$$

Source: Quant 700 to 800 level questions

(1) Is clearly insufficient, as we don't have any Info about y
(2) Here I made a mistake firstly -> I set $$x^2 + 3 = y$$ in the expression and got $$\sqrt{(x^2 + x + 3)}$$. I thought, ok, it's a quadratic, so we can get some values for x and it should be sufficient. It was wrong to stop at that point. Discriminant for this expression < 0, which means there are no X-axis intersects.
For the parabola not to cross the x-axis, it must be that the parabola is always above the axis, so when is it greater than zero (above the axis)? Always! Solution: All X
It means that wwe just need to plugin some values for x, and test wheter we get an integer in any case.
It's an integer when x=2, but it is not an integer when x=1 NOT SUFFICIENT
(1) + (2) Sufficient: x=4, y=19, this expression doesn't yield an integer
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Re: Is √(x + y) an integer?  [#permalink]

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10 Dec 2015, 22:47
statement one gives x =4 and no info on y so insufficient.
statement 2 is x^2=y-3 insufficient as various values can be plugged in
combining both
y=19
we therefore have root(23) which is not an integer so sufficient (C)
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Is √(x + y) an integer?  [#permalink]

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11 Dec 2015, 03:17
BrainLab wrote:
Is $$\sqrt{(x + y)}$$ an integer?

(1) $$x^3 = 64$$
(2) $$x^2 = y – 3$$

Source: Quant 700 to 800 level questions

Required: $$\sqrt{(x + y)}$$ an integer?

Statement 1: $$x^3 = 64$$
This does not tell us anything about y.
INSUFFICIENT

Statement 2: $$x^2 = y – 3$$
We have one equation and two variables, hence this cannot be solved.
Also, we cannot bring down this equation in the required form
INSUFFICIENT

Combining Statement 1 and Statement 2:
From statement 1, we have x = 4
Substituting the value in $$x^2 = y – 3$$, 16 = y -3
y = 19
We have the values of x and y, hence we can find out $$\sqrt{(x + y)}$$

There is no need to solve for it, as we have just one set of values, hence only one possible answer
SUFFICIENT
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Re: Is √(x + y) an integer?  [#permalink]

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20 Aug 2018, 06:13
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Re: Is √(x + y) an integer? &nbs [#permalink] 20 Aug 2018, 06:13
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