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If |x|+|y|>4|x| and x and y are non-zero integers, then which of the f

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chetan2u
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If |x|+|y|>4|x| and x and y are non-zero integers, then which of the f [#permalink] If |x|+|y|>4|x| and x and y are non-zero integers, then which of the f   06 Feb 2019, 20:02
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If |x| + |y| > 4|x| and x and y are non-zero integers, then which of the following cannot be the value of y?

(A) -4
(B) 3
(C) 5
(D) 6
(E) 10

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Chethan92
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Re: If |x|+|y|>4|x| and x and y are non-zero integers, then which of the f [#permalink] If |x|+|y|>4|x| and x and y are non-zero integers, then which of the f   06 Feb 2019, 22:38
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Important relation to note here is |x|+|y| > |x+y|
As x and y are non zero integers, min value of x is 1.
The expression can be written as 1 + |y| > 4
|y| > 3
either y > 3 or y < -3

Y cannot be equal to 3.

B is the answer.
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Re: If |x|+|y|>4|x| and x and y are non-zero integers, then which of the f [#permalink] If |x|+|y|>4|x| and x and y are non-zero integers, then which of the f   08 Feb 2019, 09:09
chetan2u wrote:
If |x|+|y|>4|x| and x and y are non-zero integers, then which of the following cannot be the value of y?
(A) -4
(B) 3
(C) 5
(D) 6
(E) 10

New question!!...

|x|+|y|>4|x|

y>3
IMO b is 3 ; cannot be the value of y ..
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Re: If |x|+|y|>4|x| and x and y are non-zero integers, then which of the f [#permalink] If |x|+|y|>4|x| and x and y are non-zero integers, then which of the f   02 Jan 2021, 07:26
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|y| > 3|x|

|y|/3 > |x|

B) y = 3

3/3 > |x| => 1 > |x| => x cannot take any value. as it in an non zero integer it cannot take 0 too.
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prachisaraf
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Re: If |x|+|y|>4|x| and x and y are non-zero integers, then which of the f [#permalink] If |x|+|y|>4|x| and x and y are non-zero integers, then which of the f   30 Mar 2023, 04:15
Chethan92 wrote:
Important relation to note here is |x|+|y| > |x+y|
As x and y are non zero integers, min value of x is 1.
The expression can be written as 1 + |y| > 4
|y| > 3
either y > 3 or y < -3

Y cannot be equal to 3.

B is the answer.


Can you please explain why min value of x is 1 here ?
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Re: If |x|+|y|>4|x| and x and y are non-zero integers, then which of the f [#permalink] If |x|+|y|>4|x| and x and y are non-zero integers, then which of the f   30 Mar 2023, 23:32
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prachisaraf


Well, technically x can be positive or negative, just not zero. So it's really |x| that has a minimum value of 1. However, since we never have to deal with x itself, but only |x|, we can stick with +1 as our minimum value.
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Re: If |x|+|y|>4|x| and x and y are non-zero integers, then which of the f [#permalink] If |x|+|y|>4|x| and x and y are non-zero integers, then which of the f   31 Mar 2023, 02:53
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chetan2u wrote:
If |x|+|y|>4|x| and x and y are non-zero integers, then which of the following cannot be the value of y?
(A) -4
(B) 3
(C) 5
(D) 6
(E) 10

Chetan's questions



Given: \(|x|+|y|>4|x|\)

\(|y| = 4|x|- |x| = 3|x|\)

Since x is a non zero integer, \(|x|\) can be 1, 2 , 3 etc (since \(x\) can be ... -3, -2, -1, 1, 2, ... etc)

Since \(y > 3|x|\), \(y\) will be greater than 3.

Answer (B)
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Re: If |x|+|y|>4|x| and x and y are non-zero integers, then which of the f [#permalink] If |x|+|y|>4|x| and x and y are non-zero integers, then which of the f   23 May 2024, 13:59
KarishmaB wrote:
chetan2u wrote:
If |x|+|y|>4|x| and x and y are non-zero integers, then which of the following cannot be the value of y?
(A) -4
(B) 3
(C) 5
(D) 6
(E) 10

Chetan's questions


Given: \(|x|+|y|>4|x|\)

\(|y| = 4|x|- |x| = 3|x|\)

Since x is a non zero integer, \(|x|\) can be 1, 2 , 3 etc (since \(x\) can be ... -3, -2, -1, 1, 2, ... etc)

Since \(y > 3|x|\), \(y\) will be greater than 3.

Answer (B)

­Can someone please explain why value of y can be -4?
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If |x|+|y|>4|x| and x and y are non-zero integers, then which of the f [#permalink] If |x|+|y|>4|x| and x and y are non-zero integers, then which of the f   23 May 2024, 14:14
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ishmi wrote:
KarishmaB wrote:
chetan2u wrote:
If |x|+|y|>4|x| and x and y are non-zero integers, then which of the following cannot be the value of y?
(A) -4
(B) 3
(C) 5
(D) 6
(E) 10

Chetan's questions

Given: \(|x|+|y|>4|x|\)

\(|y| = 4|x|- |x| = 3|x|\)

Since x is a non zero integer, \(|x|\) can be 1, 2 , 3 etc (since \(x\) can be ... -3, -2, -1, 1, 2, ... etc)

Since \(y > 3|x|\), \(y\) will be greater than 3.

Answer (B)

­Can someone please explain why value of y can be -4?

|x| + |y| > 4|x|

|y| > 3|x|

Given that x is a nonzero integer, the least value of |x| is 1. Thus, the least value of 3|x| is 3, which means that |y| > 3. Finally, |y| > 3 implies y < -3 or y > 3. Therefore, y can be any integer except from -3 to 3, inclusive.

Answer: B.

To address your question, y can be -4, when x = 1 or x = -1.­
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If |x|+|y|>4|x| and x and y are non-zero integers, then which of the f [#permalink]
23 May 2024, 14:14
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