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Is x > y? (1) x > y^3 (2) x/y > 1

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Is x > y? (1) x > y^3 (2) x/y > 1  [#permalink]

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New post Updated on: 08 Aug 2019, 21:29
1
5
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

48% (01:53) correct 52% (01:24) wrong based on 91 sessions

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Is x > y?

(1) x > y^3

(2) x/y > 1

Originally posted by raghavrf on 08 Aug 2019, 20:39.
Last edited by Bunuel on 08 Aug 2019, 21:29, edited 2 times in total.
Renamed the topic and edited the question.
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Re: Is x > y? (1) x > y^3 (2) x/y > 1  [#permalink]

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New post 09 Aug 2019, 10:16
1
When x and y are positive, we can easily get a 'yes' answer to the question (if x = 4 and y = 1, say). But x and y can be negative, and then we can get a 'no' answer to the question. If we have x = -4, and y = -2, then x/y > 1, and x > y^3, but x is not greater than y. So the answer is E.
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Re: Is x > y? (1) x > y^3 (2) x/y > 1  [#permalink]

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New post 09 Aug 2019, 10:25
IanStewart wrote:
When x and y are positive, we can easily get a 'yes' answer to the question (if x = 4 and y = 1, say). But x and y can be negative, and then we can get a 'no' answer to the question. If we have x = -4, and y = -2, then x/y > 1, and x > y^3, but x is not greater than y. So the answer is E.



Hi! Why is B wrong? If X/Y > 1 it should mean that x > y ?If x/y > 0 then we could have said that there can be values between 0 and 1?
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Re: Is x > y? (1) x > y^3 (2) x/y > 1  [#permalink]

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New post 09 Aug 2019, 10:52
kunalbean wrote:
Hi! Why is B wrong? If X/Y > 1 it should mean that x > y ?If x/y > 0 then we could have said that there can be values between 0 and 1?


x/y > 1 does not mean x > y. I gather you're multiplying by y on both sides of the inequality. But you can't do that unless you know whether y is positive or negative. If y is positive, then we can multiply by y and we do not need to flip the inequality. Then it is true that x > y. But if y is negative, then when you multiply by y on both sides, you need to flip the inequality. So if x/y > 1 is true, and y < 0 is true, then x < y is true. You can confirm that by testing any negative numbers at all -- let x = -3 and y = -1, for example. Then x/y > 1 is true, and x < y is true.
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Re: Is x > y? (1) x > y^3 (2) x/y > 1  [#permalink]

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New post 09 Aug 2019, 12:14
IanStewart wrote:
kunalbean wrote:
Hi! Why is B wrong? If X/Y > 1 it should mean that x > y ?If x/y > 0 then we could have said that there can be values between 0 and 1?


x/y > 1 does not mean x > y. I gather you're multiplying by y on both sides of the inequality. But you can't do that unless you know whether y is positive or negative. If y is positive, then we can multiply by y and we do not need to flip the inequality. Then it is true that x > y. But if y is negative, then when you multiply by y on both sides, you need to flip the inequality. So if x/y > 1 is true, and y < 0 is true, then x < y is true. You can confirm that by testing any negative numbers at all -- let x = -3 and y = -1, for example. Then x/y > 1 is true, and x < y is true.



Yes. didnt think of 1 as a possibility .
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Re: Is x > y? (1) x > y^3 (2) x/y > 1  [#permalink]

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New post 09 Aug 2019, 14:06
1
(1) x > y^3

If x=-1, y=-2

x>y and x>y^3

If x=-3, y=-2

x<y and x>y^3

1 is insufficient

(2) x/y > 1

If x=-2 and y=-1

x<y and x/y>1

If x=2 and y=1

x>y and x/y>1

2 is insufficient

(1)+(2)

If x=-3, y=-2

x<y and x>y^3 and x/y>1

If x=2, y=1

x>y and x>y^3 and x/y>1

(1)+(2) is insufficient

Answer is (E)

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Re: Is x > y? (1) x > y^3 (2) x/y > 1  [#permalink]

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New post 06 Mar 2020, 07:06
Is x > y?

(1) x > y^3 --> insuff: if x = 10 & y =2, then x >y^3 & x> y: yes. But if x = 0.1 & y =0.2, then x >y^3 & x< y: no

(2) x/y > 1--> insuff: x/y > 1 => xy/y^2>1 => xy > y^2=> xy-y^2>0=>y(x-y)> 0, so y> 0 & x-y>0 or y<0 & x-y <0 => 0<y<x i.e if y> 0: yes, but x<y<0 i.e if y< 0: no

combining (1) & (2) also, we can say if y> 0 also, we can say from case-1, that it's insuff.

Answer: E
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Re: Is x > y? (1) x > y^3 (2) x/y > 1   [#permalink] 06 Mar 2020, 07:06

Is x > y? (1) x > y^3 (2) x/y > 1

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