If x= 3y , is x^2 > y^2 ?
1 ) y+x > y-x
2) x^2 = 9y^2
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
i think its D..
considering that its x^2 and y^2 so any value of x or y we take either negative or positive, its square is going to be positive….
hence x^2=9y^2
hence x^2 will always be greater than y^2…
D
D
D
Aren’t the statements unnecessary?
If x = 3y, the question is asking if (3y)^2 > y^2. Negative/positive isn’t going to matter because it’s being squared, and 3/fraction squared is always going to be bigger than 1/same fraction squared. So – why are the two statements necessary at all?
I agree with Laura
None of the statements are necessary .it can be answered on its oqwn.
Yes laura’s ans goes with the right approach.
B
x^2 > y^2
=>x^2 – y^2 > 0
=>9y^2-y^2 >0
this implies either y> 0 or y<
for y = 0 x^2> y^2 does not hold true.
this is the Mistake Laura made.
Statement 1 : y+x > y-x
substituting x=3y
=>y + 3y > y – 3y
=> 4y > -2y
=> 6y> 0
y > o sufficient.
Statement 2 : x^2 > 9y^2 does not tell us whether y is greater or less than 0. so insufficient.
Hope this helps.
Answer (A)
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
1) y+x>y-x
take y = 3, x=2
then 5>1
take y=2, x=3
again 5>-1
hence insufficient
2) x^2 = 9y^2
sufficient
B is the correct answer! i.e Statement 2 alone is sufficient to answer the question.
The question is – Is x^2 > y^2?
From statement (2) we find that x^2 > 9y^2. i.e X squared is greater than 9 times Y squared! Here, we are checking only for squared quantitites. Therefore it can be safely established that X squared is greater than Y squared.
In case of statement (1) the value of y cancels out y-y on moving y to any side. and we are left with 2x>0. This can only mean that x>0 and says nothing of y. Hence we are unable to answer the question is x^2>y^2 from this statement.
The answer is A.
x^2 > y^2 will ALWAYS hold true EXCEPT the case where x = y = 0. 1) y+x > y-x implies that x and y cannot be equal to zero both at the same time (0 > 0 -> FALSE), so it is sufficient to answer the question.
Take GMAT team…. Please give the correct answer.
Ans is A
for all choices where y is negative, positive or fraction, x^2 > y^2
But if y=0 then 3y = 0 therefore x =0
is x^2 = y^2 in this case. So B is not sufficient.
Ans A tells us that these values are not 0s because in that case x+y and y-x will be 0 and cant be written as y+x > y-x