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Is X \gt Y ? 1. \sqrt{X} \gt \sqrt{Y} 2. X^2 \gt Y^2Source: GMAT Club Tests - hardest GMAT questions I do not agree OA and OE. Please provide explanation OE is From S1, since X and Y are under a radical, they are nonnegative. So we may safely square them and get . So, S1 is sufficient. According to S2 and can be negative, so we may not insist that My Question: Why it is assumed that rt(X) is non-negative? If x=4, rt(x) could be +2 /-2. And based on that answer should be E. Let me know if I am doing any mistake.
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priyankur_saha@ml.com wrote: I do not agree OA and OE. Please provide explanation Attachment: math.JPG OE is From S1, since X and Y are under a radical, they are nonnegative. So we may safely square them and get . So, S1 is sufficient. According to S2 and can be negative, so we may not insist that My Question: Why it is assumed that rt(X) is non-negative? If x=4, rt(x) could be +2 /-2. And based on that answer should be E. Let me know if I am doing any mistake. GMAT considers only +ve value for Sqrt() Sqrt(x) --> lead only one +ve solution. X^2=4 then both +ve and -ve are valid solutions.
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Please elaborate on that. You mean GMAT considers all radical terms positive?
For example, \sqrt{4} can only be 2, whereas x^2=4 x can be +/- 2?
Then why do we have to keep remembering that the sq rt of something can either be positive or negative?
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I marked C first but later I realised that OA should be A. S1: Suffa. If x=1/4 and y=1/9 >>>> x>y b. If x=9 and y=4 >>>> x>y S2: X and Y can be +ve or -ve. Insuff.
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Quote: Source: GMAT Club Tests - hardest GMAT questions I do not agree OA and OE. Please provide explanation OE is From S1, since X and Y are under a radical, they are nonnegative. So we may safely square them and get . So, S1 is sufficient. According to S2 and can be negative, so we may not insist that My Question: Why it is assumed that rt(X) is non-negative? If x=4, rt(x) could be +2 /-2. And based on that answer should be E. Let me know if I am doing any mistake. Reply: If you graph the square root of a number then the graph will always be on the positive side. This is a basic principle of math that we learned from pre-calculus course or even earlier. Even Calculus text-book should have them. This is how i see why square root is always positive. Another way to see this, rt ( -4) doesn't exist because you can not square a number and then get a negative number. I believe that GMAT doesn't want you to break it down from rt(4) to +2/-2. They want you to take it as is. If its rt(4) then you should take it as x=4
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You can see the OA by clicking "Reveal" in the spoiler under the question. RenukaD wrote: What is the OA?
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dzyubam wrote: You can see the OA by clicking "Reveal" in the spoiler under the question. RenukaD wrote: What is the OA? Thanks dzyubam . my answer was also A but ,looking at posts above, which says "GMAT does not consider -ve values of root" so by this are we trying to say in this case "C" is sufficient condition ? If not then in what scenario we should consider only positive values of roots. Thanks in advance
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No, the answer remains A for this question. Here's a quote that should help you understand when only positive roots are considered: Quote: Sqrt(x) --> lead only one +ve solution.
X^2=4 then both +ve and -ve are valid solutions. GMAT deals with only positive numbers under the square root sign.
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dzyubam wrote: No, the answer remains A for this question. Here's a quote that should help you understand when only positive roots are considered: Quote: Sqrt(x) --> lead only one +ve solution.
X^2=4 then both +ve and -ve are valid solutions. GMAT deals with only positive numbers under the square root sign. Thanks again dzyubam Now its clear to me....
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I agree - A is correct in my opinion.
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Is X>Y?
1) X^(1/2) > Y^(1/2)
- Because X and Y are under a square-root they can only be positive, or imaginery numbers. thus we can conclude that statment 1 is sufficient.
2) X^2 > Y^2
- This statement tells us that the absolute value of X is greater than Y, but we cannot determine that X is greater than Y, thus this statement is insufficient. For instance:
X=3, -3
Y=2, -2
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another way to solve this is to solve the inequality -
for the first one: square both sides and you get X> Y .... simple and sufficient.
for the second one: X or Y can be +/- hence not sufficient.
A...
thanks
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Answer is A
sqrt(x) > sqrt(y)
If X=16, Y=4 then sqrt(x) > sqrt (y)
If X=1/4, y=1/16 then sqrt(x) > sqrt(y)
GMAT considers +ve sign for root of numbers. So, this condition is sufficient. Correct answer is A
Condition 2
X2 > Y2
for X<Y, X=-4 and Y=-2, X2>Y2
for X>Y, X=4 and Y=2, X2>Y2
So, Condition 2 is not sufficient
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A is sufficient. You square both sides and you get X > Y. But B otoh is not sufficient. Eg: 25 > 16, but -5 < 4.
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A for me too.. Negative Sq. rt. leads to an imaginary value which we used to refer as 'iota' in school..
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(I) if \sqrt{x}>\sqrt{y} x>y...\sqrt{x} can only be >= 0 x,y are > 0....hence x > y Sufficient (II) if x^2 > y^2 x^2 - y^2 >0 (x+y) or (x-y) > 0 both brackets need to be positive or negative. Both brackets positive: x=4, y= -2; (4-2)(4--2)>0 from here, we have (4-2)(4+2)>0 And x(4) > y.....response is YES sufficient Both brackets Negative: x=-4; y= -2 (-4 -2) and (-4 +2) from here, we have: (-4-2)(-4+2)>0 And x(-4) < y(-2).....response is NO insufficient So, II is INSUFFICIENT OA is A. SImply put, test the pair of numbers with different signs: (i) x(4) and y(2) (ii) x(-4) and y(-2) ... and you will realize the insufficiency in II.
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if sqrtX=sqrtY=0 then not sufficient. Am I wron?
suppose x=0 and y=0.
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Indeed the 1st statement is sufficient Hence A
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thanatoz wrote: Please elaborate on that. You mean GMAT considers all radical terms positive?
For example, \sqrt{4} can only be 2, whereas x^2=4 x can be +/- 2?
Then why do we have to keep remembering that the sq rt of something can either be positive or negative? I know this might come as a source of confusion so let me clarify it well: The square root symbol means, in fact, the +ve square root of. That's a definition and sometimes we just drop the word "positive" to say simply "the square root of". Regarding your equation x^2=4 x can be +/- 2, we have 2 answers because of the x^2 and nothing else so that gives 2 answers: one is the positive square root of 4 (which is 2) and the other is the negative of the square root of 4 (which is -2). Hope this helps...
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A x = -3 and y = 2 9> 4
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