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Is (y - 10)^2 > (x + 10)^2

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Is (y - 10)^2 > (x + 10)^2 [#permalink]

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Is \((y - 10)^2 > (x + 10)^2\)

(1) \(-y > x + 5\)
(2) \(x > y\)
[Reveal] Spoiler: OA
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Re: Is (y - 10)^2 > (x + 10)^2 [#permalink]

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Is \((y - 10)^2 > (x + 10)^2\)

Is \((y - 10)^2 > (x + 10)^2\)? --> is \((y - 10)^2 - (x + 10)^2>0\)? --> is \((y-10-x-10)(y-10+x+10)>0\)? --> is \((y-x-20)(y+x)>0\)? This to hold true (y-x-20) and (y+x) must have the same sign.

(1) \(-y > x + 5\) --> \(x+y<-5\). The second multiple, (x+y), is negative but the first multiple, (y-x-20), can be negative as well as positive. Not sufficient.

(2) \(x > y\) --> \(y-x<0\). The first multiple, (y-x-20), is negative but the first multiple, (x+y), can be negative as well as positive. Not sufficient.

(1)+(2) Both (x+y) and (y-x-20) are negative, thus their product is positive. Sufficient.

Answer: C.
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Re: Is (y - 10)^2 > (x + 10)^2 [#permalink]

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New post 19 Nov 2013, 01:15
Bunuel wrote:
Is \((y - 10)^2 > (x + 10)^2\)

Is \((y - 10)^2 > (x + 10)^2\)? --> is \((y - 10)^2 - (x + 10)^2>0\)? --> is \((y-10-x-10)(y-10+x+10)>0\)? --> is \((y-x-20)(y+x)>0\)? This to hold true (y-x-20) and (y+x) must have the same sign.

(1) \(-y > x + 5\) --> \(x+y<-5\). The second multiple, (x+y), is negative but the first multiple, (y-x-20), can be negative as well as positive. Not sufficient.

(2) \(x > y\) --> \(y-x<0\). The first multiple, (y-x-20), is negative but the first multiple, (x+y), can be negative as well as positive. Not sufficient.

(1)+(2) Both (x+y) and (y-x-20) are negative, thus their product is positive. Sufficient.

Answer: C.


Great explanation once again. Thank you
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Re: Is (y - 10)^2 > (x + 10)^2 [#permalink]

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New post 02 Jan 2016, 08:50
registerincog wrote:
Is \((y - 10)^2 > (x + 10)^2\)

(1) \(-y > x + 5\)
(2) \(x > y\)


Question: \(y^2-20y+10 > x^2+20x+100\)--> \((y-x)(y+x) > 20(y+x)\)?
(1) \(x+y < -5\) means we can divide the expression above while changing the sign --> \(y-x < 20\), we cannot go any further here. Not sufficient

(2) We have too many combinations considering this information. Just insert some values in the first expression \((y - 10)^2 > (x + 10)^2\)
\(x=1, y=-90\): \((-100)^2 > (1+10)^2?\) YES
\(x=1, y=2\): \((2-10)^2 > (1+10)^2\)? No, hence not sufficient

(1) + (2)
From (1) \(y-x < 20\) and from (2) \(y-x < 0\)the answer is YES as, if \(y-x\) is negative, then it diffenetelly will be less than 20.
Answer C
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Re: Is (y - 10)^2 > (x + 10)^2 [#permalink]

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New post 02 Jan 2016, 22:19
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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution

Is (y−10)^2>(x+10)^2

(1) −y>x+5
(2) x>y

If we modify the original condition and the question, the question, (y-10)^2>(x+10)^2?, can be changed to (y-10)^2-(x+10)^2>0?. Then, if we further modify, (y-10-x-10)(y-10+x+10)>0? Thus, the question is essentially asking if (y-x-20)(y+x)>0?
There are 2 variables (x and y) in the original condition. In order to match the number of variables and the number of equations, we need 2 equations. Using both the condition 1) and 2), we get y-x<0. Then, y-x-20<0 and x+y<-5<0. So, we get (y-x-20)(y+x)>0 and the answer is always ‘yes’. The condition, thus, is sufficient, and the correct answer is C.

For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
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Re: Is (y - 10)^2 > (x + 10)^2 [#permalink]

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New post 08 Apr 2016, 02:09
Nevernevergiveup wrote:
Is \((y–10)^2 > (x+10)^2\)?

1. \(–y > x + 5\)
2. \(x > y\)


on simplifying we get
x^2 - y^2 - 2(x-y)<0
(x+y-2)(x-y)<0
so, either x<y or/and x+y>2
or x>y or/and x+y<2

1) -y>x+5
x+y<-5
Not sufficient

2) X>y
Not sufficient

Combining 1) and 2) = sufficient
Answer : C
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Re: Is (y - 10)^2 > (x + 10)^2 [#permalink]

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New post 08 Apr 2016, 02:27
registerincog wrote:
Is \((y - 10)^2 > (x + 10)^2\)

(1) \(-y > x + 5\)
(2) \(x > y\)


Hallo Bunuel,could you tell me whether my process is right or not?

Given : Is \((y - 10)^2 > (x + 10)^2\)
or, x^2-y^2>2(x-y)
or,(x-y)(x+y+2)<0

That means either a)x<y or x+y+2>0 OR b) x>y or x+y+2<0

NOW From 1 we get x+y<-5 which satisfy one condition of b that x+y+2<0

From 2 we get x>y which satisfy the other condition of b.

So, the answer is clearly C.
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Re: Is (y - 10)^2 > (x + 10)^2 [#permalink]

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New post 08 Apr 2016, 05:54
techiesam wrote:
registerincog wrote:
Is \((y - 10)^2 > (x + 10)^2\)

(1) \(-y > x + 5\)
(2) \(x > y\)


Hallo Bunuel,could you tell me whether my process is right or not?

Given : Is \((y - 10)^2 > (x + 10)^2\)
or, x^2-y^2>2(x-y)
or,(x-y)(x+y+2)<0


That means either a)x<y or x+y+2>0 OR b) x>y or x+y+2<0

NOW From 1 we get x+y<-5 which satisfy one condition of b that x+y+2<0

From 2 we get x>y which satisfy the other condition of b.

So, the answer is clearly C.


How did you get the highlighted part above?
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Resources:
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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.


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Re: Is (y - 10)^2 > (x + 10)^2 [#permalink]

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Re: Is (y - 10)^2 > (x + 10)^2   [#permalink] 30 Oct 2017, 00:02
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