If x and y are integers, what is the ratio of 2x to y? 8x3 = 27y3 4x2

Question

Competition Mode Question

If x and y are integers, what is the ratio of 2x to y?

(1)  8x^3 = 27y^3

(2)  4x^2 = 9y^2

Leadership · Answer

We need to find  \frac{2x}{y} ?

(1)  8x^3 = 27y^3  ..... Changing to base 2 and 3
 2^3x^3 = 3^3y^3  ..... Cube roots both sides
 2x = 3y 
 \frac{2x}{y} = 3

Sufficient .. A D /  B C E

(2)  4x^2 = 9y^2  ..... Changing to base 2 and 3
 2^2x^2 = 3^2y^2  ..... Square roots both sides
 2x = 3y 
 \frac{2x}{y} = 3

Sufficient ..  A  D /  B C E

'D' is the Winner

freedom128 · Answer

1. (2x/3y)^3 = 1
--> (2x/3y) = 1
--> 2x/y = 3
SUFFICIENT

2. (2x/3y)^2 = 1
--> (2x/3y) = ±1
--> 2x/y = ±3 = -3 or +3
NOT SUFFICIENT

FINAL ANSWER IS (A)

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madgmat2019 · Answer

(1) 8x3=27y3....after square root we get 2x=3y sufficient

(2) 4x2=9y2............after square root we get-2x/2x and -3y/3y........so insufficient

OA:A

exc4libur · Answer

(1) 8x^3=27y^3   sufic

8x^3=27y^3…2^3x^3=3^3y^3…(x,y)=3,2…2x/y=6/2=3

(2) 4x^2=9y^2   insufic

4x^2=9y^2…2^2x^2=3^2y^2…(x,y)=3,-3,2,-2…2x/y=6/2=3,-3

Ans (A)

siddharthaggarwal · Answer

Eqn 1 is sufficient but eqn 2 is not sufficient so A

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Archit3110 · Answer

target find 2x/y
#1
8x3=27y3
cube root both sides
2x/y =3
sufficient
#2
4x2=9y2
square root both sides
2x/y = 3 +/-
Insufficient
IMO A

If x and y are integers, what is the ratio of 2x to y?

(1) 8x3=27y3

(2) 4x2=9y2

eakabuah · Answer

Given that x and y are integers, we are to find 2x/y
Note that x and y can be either positive or negative.

Statement 1: 8x^3 = 27y^3
x and y must necessarily have the same sign in order to satisfy the given equation in statement 1.
so 2x=3y
2x/y = 3y/y = 3.
Statement 1 is sufficient.

Statement 2: 4x^2=9y^2
x and y do not need to have the same sign in order to satisfy statement 2.
for example, when y=1, 4x^2=9 and 2x=3/ or 2x=-3
When 2x=3, then 2x/y = 3
But when 2x=-3, then 2x/y = -3
Since we have different values for 2x/y, statement 2 is not sufficient.

The answer is A.

ostrick5465 · Answer

(1) 8x^3 = 27y^3 => (8x^3) / (27y^3) = 1 => 2x / 3y = 1 => 2x/y = 3 => Suff
(2) 4x^2 = 9y^2 => (4x^2) / (9y^2) = 1 => (2|x|)/ (3|y|) = 1 => Not Suff
=> Choice A

Bunuel · Answer

OFFICIAL EXPLANATION

Evaluate Statement (1) alone.

Take the cube root of both sides:
8x^3 = 27y^3
2x = 3y

Rearrange in order to find a ratio of 2x to y.
2x/y = 3

Consequently, 2x is 3 times y.

Statement (1) alone is SUFFICIENT.

Evaluate Statement (2) alone.

Take the square root of both sides:
4x^2 = 9y^2
2x = 3y
2x/y = 3

However, we must also consider that in taking the square root, a negative root is possible. To illustrate this, consider the following example:
Let x = 3 and y = 2 --> 4x^2 = 9y^2
Let x = -3 and y = 2 --> 4x^2 = 9y^2
Let x = -3 and y = -2 --> 4x^2 = 9y^2
Let x = 3 and y = -2 --> 4x^2 = 9y^2

In the four examples above, although 4x^2 = 9y^2, there is no consistent ratio of 2x to y since the negative numbers cause ratios to be negative. Consequently, Statement (2) is NOT SUFFICIENT.

Since Statement (1) alone is SUFFICIENT and Statement (2) alone is NOT SUFFICIENT, answer A is correct.

gvij2017 · Answer

Even powers of a variable doesn't tell exact nature of variable. Variable might be positive or negative.

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If x and y are integers, what is the ratio of 2x to y? 8x3 = 27y3 4x2

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If x and y are integers, what is the ratio of 2x to y? 8x3 = 27y3 4x2

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