Is |x| + |y| = 0
1)x + 2|y| = 0
2)y + 2|x| = 0
absolute value
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- indiantiger
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Is |x| + |y| = 0
1)x + 2|y| = 0
2)y + 2|x| = 0
Lets take Statement 1 :
for this x + 2|y| = 0 to be valid
either x = 0 and y = 0 (one of the solutions) (this proves the question)
or
x= +/-2y or x=-6 and y = +/-3(one of the solutions) (this does not prove the question)
not sufficient
Lets take Statement 2 :
for this y + 2|x| = 0 to be valid
either x = 0 and y = 0 (one of the solutions) (this proves the question)
or
y=+/-2x or y = -6 and x = +/-3 (one of the solutions) (this does not prove the question)
not sufficient
rules out A,B,D
left with C or E
if we combine st1 and st2 we get one common solution that is x = 0 and y =0
hence (C)
1)x + 2|y| = 0
2)y + 2|x| = 0
Lets take Statement 1 :
for this x + 2|y| = 0 to be valid
either x = 0 and y = 0 (one of the solutions) (this proves the question)
or
x= +/-2y or x=-6 and y = +/-3(one of the solutions) (this does not prove the question)
not sufficient
Lets take Statement 2 :
for this y + 2|x| = 0 to be valid
either x = 0 and y = 0 (one of the solutions) (this proves the question)
or
y=+/-2x or y = -6 and x = +/-3 (one of the solutions) (this does not prove the question)
not sufficient
rules out A,B,D
left with C or E
if we combine st1 and st2 we get one common solution that is x = 0 and y =0
hence (C)
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|x| + |y| = 0 only possible when both x = y = 0colakumarfanta wrote: Is |x| + |y| = 0
1)x + 2|y| = 0
2)y + 2|x| = 0
Statement 1:
x + 2|y| = 0
x = - 2|y|
x is -ve and y can be either -ve or +ve
Not Sufficient
Statement 2:
Same as statement 1
Not Sufficient
Statement 1 and 2:
x = - 2|y| ----- a
y = -2 |x| or |y| = 2|x| -----b
from a and b
x = - 2|y| = -4|x|
x + 4|x| = 0 only possible when x = 0
x = 0 then y=0
Sufficient
Answer: C
What is OA?
One should post Q along with OA. It is a better practice.
- tpr-becky
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recieve a PM for this one
becuase absolute values can only be positive - the question is really asking whether x and y are both equal to zero.
1) here it is possible for both x and y to be zero but not required (x could be -1/2 and y could be 1/4) so this is insufficient BCD
2) same applies to this one so it is also insufficient CE
if you try them together you find that you can replace y in the equation with, and as explained below you end up wiht
X +4/x/=0 which means that x must be zero, which also means that y must be zero
Answer is C.
becuase absolute values can only be positive - the question is really asking whether x and y are both equal to zero.
1) here it is possible for both x and y to be zero but not required (x could be -1/2 and y could be 1/4) so this is insufficient BCD
2) same applies to this one so it is also insufficient CE
if you try them together you find that you can replace y in the equation with, and as explained below you end up wiht
X +4/x/=0 which means that x must be zero, which also means that y must be zero
Answer is C.
Becky
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- Stuart@KaplanGMAT
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A slightly different approach (although similar in many respects to those already posted):colakumarfanta wrote:Is |x| + |y| = 0
1)x + 2|y| = 0
2)y + 2|x| = 0
|x| and |y| are both non-negative; according, the only way to get a "Yes" answer is if both are 0. So, we can rephrase the question as:
Is x=y=0?
(1) we could pick x=y=0 to satisfy the statement, so we can get a "yes" answer.
However, we could also pick a negative value for x, in which case y could be negative or positive, so we can get a "no" answer.
Can get both a yes and a no: insufficient, eliminate A and D.
(2) exactly same logic as (1), swapping x and y. Insufficient: eliminate B.
Combined:
we can rewrite the statements as:
(1) |y| = -x/2
(2) |x| = -y/2
Ignoring the signs, we can see that y= .5x AND x = .5y. The only way this relationship can hold true is if x and y are both 0; that's a definite "yes" - together sufficient, choose (C).
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Hi all
Thank you for excellent ans above.
Can anyone help me with how to handle combining statements with Yes/No D.S questions. I always (everytime!) fail to select the correct ans on yes/no D.S, or takes me forever to figure out.
I normally try using testing values systematically e.g. -2, -1/2, 0 ,1/2, 2 to make sure it answers both statements and the question so as to decide C or E is the ans. It's too time consuming for actual GMAT sitting and error prone. Is this the right approach or is there a better way.
For instance, on the above example:
I tested 0 & -2, -1/2 and 0 on Statement 1 and 2 individally and narrowed down to C or E.
Then now i have to test -2, -1/2, 0 ,1/2, 2 on both statements and question to make sure i cover all possibilities. Is this the right approach. Is there any clever tips and quicker way of handling the assessment of combine statements for Y/N D.S questions.
Thank you for excellent ans above.
Can anyone help me with how to handle combining statements with Yes/No D.S questions. I always (everytime!) fail to select the correct ans on yes/no D.S, or takes me forever to figure out.
I normally try using testing values systematically e.g. -2, -1/2, 0 ,1/2, 2 to make sure it answers both statements and the question so as to decide C or E is the ans. It's too time consuming for actual GMAT sitting and error prone. Is this the right approach or is there a better way.
For instance, on the above example:
I tested 0 & -2, -1/2 and 0 on Statement 1 and 2 individally and narrowed down to C or E.
Then now i have to test -2, -1/2, 0 ,1/2, 2 on both statements and question to make sure i cover all possibilities. Is this the right approach. Is there any clever tips and quicker way of handling the assessment of combine statements for Y/N D.S questions.
- aslan
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@vanquish:For DS just try to come up with a 'yes' first and then a 'no' first if both are coming then the statement is insufficient.Do not plugin values randomly from -1/2,0/12/1....Just think f those values first which will give you a 'yes' and 'no' statements.If you get a constant statement with pluggin then that stem holds true and is sufficient
P.S:this is for 'yes' no' DS only.
P.S:this is for 'yes' no' DS only.
- bacchewar_prashant
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I was totally confused by the question. It totally sliped out of my that question is asking both x and y are zero or not.
Thanks for post nice question.
Thanks for post nice question.
- Taran
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Hello all,
I was able to clearly see that ST1 and ST2 were not sufficient independently. However i made puppy face when i had to combine both to check the sufficiency. I was randomly about to pick E but suddenly realised something and went for C. Please help me as to how to combine the two statements and come up with an answer. Thanks....
I was able to clearly see that ST1 and ST2 were not sufficient independently. However i made puppy face when i had to combine both to check the sufficiency. I was randomly about to pick E but suddenly realised something and went for C. Please help me as to how to combine the two statements and come up with an answer. Thanks....
Absolute values are positive. The only way two positive numbers can equal 0 is if they are both 0. Neither statement alone is sufficient to establish this, so both are needed.
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- amit2k9
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possible only if x=y=0
a x=y=0 and x=-2 y=1|-1. not sufficient.
b x=y=0 and x=1|-1 y=2. not sufficient.
a+b only x=y=0 satisfies.
C it is.
a x=y=0 and x=-2 y=1|-1. not sufficient.
b x=y=0 and x=1|-1 y=2. not sufficient.
a+b only x=y=0 satisfies.
C it is.
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i am still not able to understand why the answer is C.how have been the two options combined.can anyone explain
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