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Manager  Joined: 21 May 2011
Posts: 179
If xy is not equal to 0, is xy = 70?  [#permalink]

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4
3 00:00

Difficulty:   65% (hard)

Question Stats: 51% (01:37) correct 49% (01:32) wrong based on 118 sessions

### HideShow timer Statistics If xy is not equal to 0, is xy = 70?

(1) x > y

(2) x^2 = y^2

Originally posted by bschool83 on 07 Aug 2011, 10:36.
Last edited by Bunuel on 11 Jul 2013, 02:03, edited 1 time in total.
Manager  Joined: 14 Mar 2011
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1
bschool83 wrote:
If xy is not equal to 0, is xy = 70?

(1) x > y

(2) x^2 = y^2

Statement 1 is insufficient as values of x and y are not given

Statement 2 is insufficient too. if x^2 = Y^2 then |x| = |y| if x and y are equal to root 70 then xy will be 70. But if anything else then not.

Combining statement 1 and 2 we get sufficient answer that xy is not equal to 70. statement one tells that x is greater than y and statement 2 tells that x has same absolute value as y. so x = -Y. In that case xy must be negative.

If my answer is wrong then please correct it and please provide the OA and correct explanation.
Senior Manager  Joined: 24 Mar 2011
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great question. Agree with C.

B is not sufficient alone, since X, Y are not specified as integers.

also as per A and B, X can be 8.4 and Y can be -8.4. But then XY = -70
Manager  Joined: 16 May 2011
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S1 x=70 y=1 yes. x=3 y=1 no
S2 X=ROOT 70 Y=ROOT 70 YES (x^2=y^2=70). X=9 Y=9 NO (x^2=y^2=81)

combined:
[x]=[y] and x>y means that x must be positive and y negative. Pos*Neg=Neg hence xy will never be 70. so C
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If xy is not equal to 0, is xy = 70?  [#permalink]

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1
If $$xy\neq{0}$$, is $$xy = 70$$?

(1) $$x > y$$

(2) $$x^2 = y^2$$

OE

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If xy is not equal to 0, is xy = 70?  [#permalink]

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Nevernevergiveup wrote:
If $$xy\neq{0}$$, is $$xy = 70$$?

(1) $$x > y$$

(2) $$x^2 = y^2$$

Given xy \neq 0, is xy=70?

Per statement 1, x>y ---> not sufficient.

Per statement 2, x^2=y^2 ----> yes to the question if $$x=y=\sqrt{70}$$ but no if x=y=any other number!

Combining, if $$y=-\sqrt{70}$$, $$x =\sqrt{70}$$, and clearly you can see that $$x= \pm y$$ ---> you will never get $$xy = 70$$ (a positive value!). Hence C is the correct answer.

Hope this helps.

Originally posted by ENGRTOMBA2018 on 04 Mar 2016, 05:14.
Last edited by ENGRTOMBA2018 on 04 Mar 2016, 05:32, edited 2 times in total.
Edited the solution.
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Re: If xy is not equal to 0, is xy = 70?  [#permalink]

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Because x>y is not sufficient.
X^2=Y^2=> X=±Y Not sufficient
But by combining both A and B, we can conclude X=-Y. So, xy≠positive number 70, xy will always be negative.
So C

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Re: If xy is not equal to 0, is xy = 70?  [#permalink]

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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.

If xy is not equal to 0, is xy = 70?

(1) x > y

(2) x^2 = y^2

In the original condition, there are 2 variables(x,y), which should match with the number of equations. So you need 2 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make C the answer. When 1) & 2), x=y or x=-y -> x>y, which makes x=-y. In this case, xy<0 is derived and xy is not 70, which is no and sufficient.

 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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If xy is not equal to 0, is xy = 70?  [#permalink]

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bschool83 wrote:
If xy is not equal to 0, is xy = 70?

(1) x > y

(2) x^2 = y^2

what a tricky one...makes you feel that E is the answer...

1 alone is clearly not sufficient
2 alone says |x| = |y|. don't know anything. x can be+, y can be -, or vice versa, or x=y
different outcomes - not sufficient.

1+2
x>y
so x and y have different signs.
xy must be negative.

sufficient.

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Re: If xy is not equal to 0, is xy = 70?  [#permalink]

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_________________ Re: If xy is not equal to 0, is xy = 70?   [#permalink] 06 Jul 2018, 06:34
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