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Last edited by dvinoth86 on 19 Feb 2012, 18:39, edited 1 time in total.

(1) x^2 > y. Clearly insufficient: if x=2 and y=3 then the answer is NO but if x=2 and y=1 then the answer is YES.

(2) √x < y. Also insufficient: if x=4 and y=5 then the answer is NO but if x=4 and y=3 then the answer is YES. Notice that since x is under the square root sign then it must be true that \(x\geq{0}\).

(1)+(2) \(\sqrt{x}<y<x^2\) --> both \(x\) and \(y\) are between \(\sqrt{x}\) and \(x^2\), but we can not say which one is greater. Not sufficient. For example: if \(x=y=4\) (\(\sqrt{4}<4<4^2\)) then the answer is NO but if \(x=4\) and \(y=3\) (\(\sqrt{4}<3<4^2\)) then the answer is YES. Not sufficient.

(1) x^2 > y. Clearly insufficient: if x=2 and y=3 then the answer is NO but if x=2 and y=1 then the answer is YES. (2) √x < y. Also insufficient: if x=4 and y=5 then the answer is NO but if x=4 and y=3 then the answer is YES. Notice that since x is under the square root sign then it must be true that \(x\geq{0}\).

(1)+(2) \(\sqrt{x}<y<x^2\) --> both \(x\) and \(y\) are between \(\sqrt{x}\) and \(x^2\), but we can not say which one is greater. Not sufficient. For example: if \(x=y=4\) (\(\sqrt{4}<4<4^2\)) then the answer is NO but if \(x=4\) and \(y=3\) (\(\sqrt{4}<3<4^2\)) then the answer is YES. Not sufficient.

Answer: E.

Hope it's clear.

Its not always possible to take examples like you have shown for each statement. I mean sometimes the variable values just doesn't fit. Solving it by use of abstract maths is tough.

Ho do we tackle this situation. Do we have a strategy on how to pick numbers faster for testing.

First of all: on DS questions when plugging numbers, goal is to prove that the statement is not sufficient. So we should try to get a YES answer with one chosen number(s) and a NO with another.

Now, number picking strategy can vary for different problems. Generally it's good to test negative/positive/zero as well as integer/fraction to get a YES and a NO answers. If you deal with two variables it's also helpful to test x<y and x>y in addition to the former.

As for this question: you don't really need to test the numbers for it, I just used them to demonstrate that the statements are not sufficient.

From (1)+(2): we have that \(\sqrt{x}<y<x^2\). Both \(x\) and \(y\) are between \(\sqrt{x}\) and \(x^2\) (\(x\) is between them because \(\sqrt{x}<x^2\), which means that \(x>1\)): \(\sqrt{x}\)------\(x\)------\(x^2\), now \(y\) can be in the green range (answer YES) as well in the red range (answer NO). So, we can not say whether x>y.

(1) x^2 > y. Clearly insufficient: if x=2 and y=3 then the answer is NO but if x=2 and y=1 then the answer is YES. (2) √x < y. Also insufficient: if x=4 and y=5 then the answer is NO but if x=4 and y=3 then the answer is YES. Notice that since x is under the square root sign then it must be true that \(x\geq{0}\).

(1)+(2) \(\sqrt{x}<y<x^2\) --> both \(x\) and \(y\) are between \(\sqrt{x}\) and \(x^2\), but we can not say which one is greater. Not sufficient. For example: if \(x=y=4\) (\(\sqrt{4}<4<4^2\)) then the answer is NO but if \(x=4\) and \(y=3\) (\(\sqrt{4}<3<4^2\)) then the answer is YES. Not sufficient.

Answer: E.

Hope it's clear.

Its not always possible to take examples like you have shown for each statement. I mean sometimes the variable values just doesn't fit. Solving it by use of abstract maths is tough.

Ho do we tackle this situation. Do we have a strategy on how to pick numbers faster for testing.

Can anyone explain a simple method to this could not follovv statement B

\

Bunuel if you can help please

1) Statement 1 only tells us that x is positive and nothing else. So insufficient

2) Statement 2 wants us to go through the process of squaring both sides to make the equation x<y^2, but we do not know anything about the sign so basically it would look like:

Can anyone explain a simple method to this could not follovv statement B

(1) For \(x=-2 > y=-3, \, x^2=4>-3.\) But \(x=2 < y=3\), although \(x^2=4>y=3.\) Not sufficient.

(2) From the given inequality it follows that \(x\) must be non-negative (because of the square root) and since \(y>\sqrt{x}\geq0\), necessarily \(y\) is positive. Therefore, we can square the given inequality and get \(x<y^2.\)

For \(x=4, y=3, \,x=4<y^2=9,\) and \(x>y.\) But if \(y=1,\) we cannot have simultaneously \(x<y^2=1\) and \(x>y=1.\) Not sufficient.

(1) and (2) together: Consider the two cases: \(x=2, y=3\) and \(x=4,y=3.\) Again, not sufficient.

Answer E.
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Last edited by EvaJager on 18 Aug 2012, 23:04, edited 1 time in total.

Can anyone explain a simple method to this could not follovv statement B

\

Bunuel if you can help please

1) Statement 1 only tells us that x is positive and nothing else. So insufficient

2) Statement 2 wants us to go through the process of squaring both sides to make the equation x<y^2, but we do not know anything about the sign so basically it would look like:

x^2 > y

and combined,

x<y^2 or x>y^2

x^2 > y

(2) We know about the signs: \(x\) must be non-negative, otherwise the square root is not defined. Also, because the square root is non-negative, \(y\) must be positive. Therefore, in this case we can square the given inequality and obtain \(x<y^2.\)
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