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If xy ≠ 0, is x = y? (1) |x| = |y| (2) xy > 0

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If xy ≠ 0, is x = y? (1) |x| = |y| (2) xy > 0  [#permalink]

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New post 27 Mar 2018, 01:30
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If xy ≠ 0, is x = y?

(1) |x| = |y|
(2) xy > 0

Statement (1) is not sufficient as x could be either >0 or <0 and same for y

Statement (2) is also insufficient as if x>0 then y must be >0 to have xy>0 and if x<0 then y must be <0 to have xy>0
but x could differ from y

However, I do not understand why taking together statement (1) and statement (2) is sufficient as we have two possibilities:
x>0 y>0 , lxl=lyl , then x=y
x<0 y<0, lxl=lyl, then x=y
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Posts: 52231
Re: If xy ≠ 0, is x = y? (1) |x| = |y| (2) xy > 0  [#permalink]

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New post 27 Mar 2018, 05:06
HIUY wrote:
If xy ≠ 0, is x = y?

(1) |x| = |y|
(2) xy > 0

Statement (1) is not sufficient as x could be either >0 or <0 and same for y

Statement (2) is also insufficient as if x>0 then y must be >0 to have xy>0 and if x<0 then y must be <0 to have xy>0
but x could differ from y

However, I do not understand why taking together statement (1) and statement (2) is sufficient as we have two possibilities:
x>0 y>0 , lxl=lyl , then x=y
x<0 y<0, lxl=lyl, then x=y



If xy ≠ 0, is x = y?

(1) |x| = |y|. This implies that x and y are same distance from 0: either x = y or x = -y. Not sufficient.

(2) xy > 0. This implies that x and y have the same sign. Not sufficient.

(1)+(2) Since from (2) we know that x and y have the same sign and from (1) we know that x and y are same distance from 0, then it must be true that x = y. Sufficient.

Answer: C.

HIUY wrote:
If xy ≠ 0, is x = y?

(1) |x| = |y|
(2) xy > 0

Statement (1) is not sufficient as x could be either >0 or <0 and same for y

Statement (2) is also insufficient as if x>0 then y must be >0 to have xy>0 and if x<0 then y must be <0 to have xy>0
but x could differ from y

However, I do not understand why taking together statement (1) and statement (2) is sufficient as we have two possibilities:
x>0 y>0 , lxl=lyl , then x=y
x<0 y<0, lxl=lyl, then x=y


Are both cases you have there the same? The question asks whether x = y and both cases give an YES answer to the question.
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Re: If xy ≠ 0, is x = y? (1) |x| = |y| (2) xy > 0  [#permalink]

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New post 27 Mar 2018, 12:43
HIUY wrote:
If xy ≠ 0, is x = y?

(1) |x| = |y|
(2) xy > 0

Statement (1) is not sufficient as x could be either >0 or <0 and same for y

Statement (2) is also insufficient as if x>0 then y must be >0 to have xy>0 and if x<0 then y must be <0 to have xy>0
but x could differ from y

However, I do not understand why taking together statement (1) and statement (2) is sufficient as we have two possibilities:
x>0 y>0 , lxl=lyl , then x=y
x<0 y<0, lxl=lyl, then x=y


Straight C.

1- We do not know anything about their sign. X can be +5 and Y can be -5. Not sufficient.
2- X and Y can be any number other than 0. This statement does tell us that both x and y have the same sign.

Statement 1 and 2 together are sufficient. Hence C.
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Posts: 52231
Re: If xy ≠ 0, is x = y? (1) |x| = |y| (2) xy > 0  [#permalink]

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New post 30 Mar 2018, 07:44
HIUY wrote:
If xy ≠ 0, is x = y?

(1) |x| = |y|
(2) xy > 0

Statement (1) is not sufficient as x could be either >0 or <0 and same for y

Statement (2) is also insufficient as if x>0 then y must be >0 to have xy>0 and if x<0 then y must be <0 to have xy>0
but x could differ from y

However, I do not understand why taking together statement (1) and statement (2) is sufficient as we have two possibilities:
x>0 y>0 , lxl=lyl , then x=y
x<0 y<0, lxl=lyl, then x=y



10. Absolute Value



For more check Ultimate GMAT Quantitative Megathread


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New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

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Re: If xy ≠ 0, is x = y? (1) |x| = |y| (2) xy > 0  [#permalink]

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New post 30 Mar 2018, 08:02
HIUY wrote:
If xy ≠ 0, is x = y?

(1) |x| = |y|
(2) xy > 0


Statement 1: It tells you only that distance of x and y from 0 on the number line equal. Insufficient

Statement 2: It tells you only that sign of x and y are same. Insufficient

Combining we know that x = y

(C)
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Re: If xy ≠ 0, is x = y? (1) |x| = |y| (2) xy > 0 &nbs [#permalink] 30 Mar 2018, 08:02
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