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Is y an integer? (1) y^3 is an integer (2) 3y is an integer

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Is y an integer?

(1) y^3 is an integer
(2) 3y is an integer
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Is y an integer? (1) y^3 is an integer (2) 3y is an integer [#permalink]

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Is y an integer?

(1) y^3 is an integer --> y is either an integer (..., -1, 0, 1, 2, ...) or \(\sqrt[3]{integer}\), for example \(\sqrt[3]{2}\). Not sufficient. Notice here that y cannot be some reduced fraction like 1/3 or 13/5, because in this case y^3 won't be an integer.


(2) 3y is an integer --> y is either an integer or integers/3, for example: 1/3, 2/3, ... Not sufficient. Notice here that y cannot be some irrational number like \(\sqrt{2}\) or \(\sqrt[3]{integer}\), because in this case 3y won't be an integer.

(1)+(2) Since both y^3 and 3y are integers then, as discussed above, y must be an integer. Sufficient.

Answer: C.
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Re: Is y an integer [#permalink]

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New post 10 Feb 2012, 06:30
Bunuel wrote:
Is y an integer?

(1) y^3 is an integer --> y is either an integer (..., -1, 0, 1, 2, ...) or \(\sqrt[3]{integer}\), for example \(\sqrt[3]{2}\). Not sufficient. Notice here that y can not be some reduced fraction like 1/3 or 13/5, because in this case y^3 won't be an integer.


B) 3y is an integer --> y is either an integer or integers/3, for example: 1/3, 2/3, ... Not sufficient. Notice here that y can not be some irrational number like \(\sqrt{2}\) or \(\sqrt[3]{integer}\), because in this case 3y won't be an integer.

(1)+(2) Since both y^3 and 3y are integers then, as discussed above, y must be an integer. Sufficient.

Answer: C.


Bunnel can you explain here by putting in some values for y. I am still unable to trace how by using both I can find that y is an integer.
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subhajeet wrote:
Bunuel wrote:
Is y an integer?

(1) y^3 is an integer --> y is either an integer (..., -1, 0, 1, 2, ...) or \(\sqrt[3]{integer}\), for example \(\sqrt[3]{2}\). Not sufficient. Notice here that y can not be some reduced fraction like 1/3 or 13/5, because in this case y^3 won't be an integer.


B) 3y is an integer --> y is either an integer or integers/3, for example: 1/3, 2/3, ... Not sufficient. Notice here that y can not be some irrational number like \(\sqrt{2}\) or \(\sqrt[3]{integer}\), because in this case 3y won't be an integer.

(1)+(2) Since both y^3 and 3y are integers then, as discussed above, y must be an integer. Sufficient.

Answer: C.


Bunnel can you explain here by putting in some values for y. I am still unable to trace how by using both I can find that y is an integer.


Sure. Generally \(\sqrt[3]{integer}\) is either an integer itself or an irrational number, it can not be some reduced fraction like 1/2 or 2/3. (The same way as \(\sqrt{integer}\) is either an integer itself or an irrational number).

From (1) \(y=integer\) or \(y=\sqrt[3]{integer}\);

From (2) \(y=integer\) or \(y=\frac{integer}{3}\);

So, from (1)+(2) \(y=integer\).

Because if from (1) \(y=\sqrt[3]{integer}\), for example if \(y=\sqrt[3]{2}\), then \(3y=integer\) won't hold true for (2): \(3y={3*\sqrt[3]{2}}\neq{integer}\). The same way: if from (2) \(y=\frac{integer}{3}\), for example if \(y=\frac{1}{3}\), then \(y^3=integer\) won't hold true for (1): \(y^3=(\frac{1}{3})^3\neq{integer}\).

Hope it's clear.
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Re: Is y an integer? (1) y^3 is an integer (2) 3y is an integer [#permalink]

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New post 25 May 2013, 03:42
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Re: Is y an integer [#permalink]

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New post 02 Jan 2014, 09:43
Bunuel wrote:
subhajeet wrote:
Bunuel wrote:
Is y an integer?

(1) y^3 is an integer --> y is either an integer (..., -1, 0, 1, 2, ...) or \(\sqrt[3]{integer}\), for example \(\sqrt[3]{2}\). Not sufficient. Notice here that y can not be some reduced fraction like 1/3 or 13/5, because in this case y^3 won't be an integer.


B) 3y is an integer --> y is either an integer or integers/3, for example: 1/3, 2/3, ... Not sufficient. Notice here that y can not be some irrational number like \(\sqrt{2}\) or \(\sqrt[3]{integer}\), because in this case 3y won't be an integer.

(1)+(2) Since both y^3 and 3y are integers then, as discussed above, y must be an integer. Sufficient.

Answer: C.


Bunnel can you explain here by putting in some values for y. I am still unable to trace how by using both I can find that y is an integer.


Sure. Generally \(\sqrt[3]{integer}\) is either an integer itself or an irrational number, it can not be some reduced fraction like 1/2 or 2/3. (The same way as \(\sqrt{integer}\) is either an integer itself or an irrational number).

From (1) \(y=integer\) or \(y=\sqrt[3]{integer}\);

From (2) \(y=integer\) or \(y=\frac{integer}{3}\);

So, from (1)+(2) \(y=integer\).

Because if from (1) \(y=\sqrt[3]{integer}\), for example if \(y=\sqrt[3]{2}\), then \(3y=integer\) won't hold true for (2): \(3y={3*\sqrt[3]{2}}\neq{integer}\). The same way: if from (2) \(y=\frac{integer}{3}\), for example if \(y=\frac{1}{3}\), then \(y^3=integer\) won't hold true for (1): \(y^3=(\frac{1}{3})^3\neq{integer}\).

Hope it's clear.


Unable to understand from the explanation provided...... how from (1) + (2) --> y=Integer ???
Can you pls provide some alternate solution/explanation.
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Re: Is y an integer? (1) y^3 is an integer (2) 3y is an integer [#permalink]

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subhajeet wrote:
Is y an integer?

(1) y^3 is an integer
(2) 3y is an integer


Statement I is insufficient

y ^ 3 = 1 y = 1 (YES y is an integer)
y ^ 3 = 2 y = 2^1/3 (y is not an integer)

Statement II is insufficient
3y = 3 y = 1 (YES y is an integer)
3y = 1 y = 1/3 (y is not an integer)

Combining is sufficient (Usually your approach should be algebraic here)
y^3 = p
3y = q

If 3y = q then the only problem which makes y not an integer is that y is a fraction which is ruled out by the first statement as Fraction ^ 3 can never be an integer. Similarly the number being a cube root (problem in the first statement) is ruled out by the second statement as 3(Surd) cannot be an integer.

Hence the answer is C
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Re: Is y an integer? (1) y^3 is an integer (2) 3y is an integer [#permalink]

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New post 29 Nov 2014, 07:00
Hi there,

I have doubt here. As per option 1 it is given as "y^3 is an integer" which means y power, but why are we discussing cube root of y.

Switching from y^3 to cube root of y would change our answer completely. Either the question is wrong or the analysis is wrong.

Please do comment.

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Re: Is y an integer? (1) y^3 is an integer (2) 3y is an integer [#permalink]

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New post 29 Nov 2014, 08:06
Adigo wrote:
Hi there,

I have doubt here. As per option 1 it is given as "y^3 is an integer" which means y power, but why are we discussing cube root of y.

Switching from y^3 to cube root of y would change our answer completely. Either the question is wrong or the analysis is wrong.

Please do comment.

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Everything is correct.

\(y^3=integer\) is the same as \(y=\sqrt[3]{integer}\).
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Re: Is y an integer? (1) y^3 is an integer (2) 3y is an integer [#permalink]

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Re: Is y an integer? (1) y^3 is an integer (2) 3y is an integer [#permalink]

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New post 27 Oct 2016, 06:23
subhajeet wrote:
Is y an integer?

(1) y^3 is an integer
(2) 3y is an integer


i got to C.
1 -> what if sqrt3(y) is a non-integer? not sufficient
2 -> y can be an integer, or can be a fraction, for ex. 1/3. not sufficient.

1+2
if y^3 is an integer
and 3y is an integer
i don't think there is such a number that would be a non-integer..
thus, sufficient.
Re: Is y an integer? (1) y^3 is an integer (2) 3y is an integer   [#permalink] 27 Oct 2016, 06:23
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