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605-655 (Medium)|   Algebra|      
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Bunuel
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If x and y are integers, what is the ratio of 3y to x? 01 Jun 2016, 04:32
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59% (01:19) correct 41% (01:20) wrong based on 162 sessions

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If x and y are nonzero integers, what is the ratio of 3y to x?

(1) 8x^3 = 27y^3
(2) 4x^2 = 9y^2
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A
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If x and y are integers, what is the ratio of 3y to x? 01 Jun 2016, 05:15
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1. x^3/y^3 = 27/8 --> y/x = 2/3 --> 3y/x = 2 -- sufficient !!
2. x^2/y^2 = 9/4 --> y/x = + - 2/ + - 3 (4 possible values) --- insufficient !!

A
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If x and y are integers, what is the ratio of 3y to x? 01 Jun 2016, 07:31
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Do we exclude the option that both x & y are 0 because then in the ratio equation we would be dividing by 0?
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If x and y are integers, what is the ratio of 3y to x? 02 Jun 2016, 01:03
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1. x^3/y^3 = 27/8 --> y/x = 2/3 --> 3y/x = 2 -- sufficient !!
2. x^2/y^2 = 9/4 --> y/x = + - 2/ + - 3 (4 possible values) --- insufficient !!

A
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I think it should be D-in statement 2, whether we take values as 3,2 OR -3,-2, the ration remains the same.
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If x and y are integers, what is the ratio of 3y to x? 02 Jun 2016, 12:31
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Bunuel
If x and y are nonzero integers, what is the ratio of 3y to x?

(1) 8x^3 = 27y^3
(2) 4x^2 = 9y^2
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We need to find 3y/x

(1) 8x^3 = 27y^3
x= (27y^3/8)^1/3
x= 3y/2

Since we have odd power, sign of x and y will be same as of x^3 and y^3

By putting value of x in 3y/x, we will get the answer

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

x= (9y^2/4) ^1/2

Sign of x and y may or may not be same as x^2 and y^2. Hence we can not find the ratio. Not sufficient

IMO, A is the answer
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If x and y are integers, what is the ratio of 3y to x? 02 Jun 2016, 12:33
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fantaisie
Do we exclude the option that both x & y are 0 because then in the ratio equation we would be dividing by 0?
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Please note that its given that x and y are non zero integers :)
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If x and y are integers, what is the ratio of 3y to x? 02 Jun 2016, 12:35
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KS15
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1. x^3/y^3 = 27/8 --> y/x = 2/3 --> 3y/x = 2 -- sufficient !!
2. x^2/y^2 = 9/4 --> y/x = + - 2/ + - 3 (4 possible values) --- insufficient !!

A


I think it should be D-in statement 2, whether we take values as 3,2 OR -3,-2, the ration remains the same.
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What if it is -3, 2 or 3 -2 (we can have the +ve ratio or -ve ratio). IMO statement 2 is not sufficient. What do you say?
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If x and y are integers, what is the ratio of 3y to x? 02 Jun 2016, 12:38
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Divyadisha
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1. x^3/y^3 = 27/8 --> y/x = 2/3 --> 3y/x = 2 -- sufficient !!
2. x^2/y^2 = 9/4 --> y/x = + - 2/ + - 3 (4 possible values) --- insufficient !!

A


I think it should be D-in statement 2, whether we take values as 3,2 OR -3,-2, the ration remains the same.

What if it is -3, 2 or 3 -2 (we can have the +ve ratio or -ve ratio). IMO statement 2 is not sufficient. What do you say?
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Agree it should be A-my bad-I must be inattentive to miss such a simple one.Thanks
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If x and y are integers, what is the ratio of 3y to x? 02 Jun 2016, 12:44
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I think it should be D-in statement 2, whether we take values as 3,2 OR -3,-2, the ration remains the same.[/quote]

What if it is -3, 2 or 3 -2 (we can have the +ve ratio or -ve ratio). IMO statement 2 is not sufficient. What do you say?[/quote]


Agree it should be A-my bad-I must be inattentive to miss such a simple one.Thanks[/quote]

Learning together!! :thumbup:
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If x and y are integers, what is the ratio of 3y to x? 02 Jun 2016, 22:34
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If x and y are nonzero integers, what is the ratio of 3y to x?

(1) 8x^3 = 27y^3
(2) 4x^2 = 9y^2

Statement 1-->Sufficient. As given,both x and y are nonzero integers,so both x and y should have same sign( Either both should be positive or both could be negative). In either case 2x = 3y which leads to 3y/x = 2.

Statement 2-->Not Sufficient. (2x-3y)(2x+3y) = 0 ,that makes 3y/x = 2 or -2.
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If x and y are integers, what is the ratio of 3y to x? 21 Sep 2017, 10:58
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