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GUYS..after reading all the posts and explanation ...i am not able to find correct explanation for the answer. statement 1: sufficient (0=No,1=No,2=No) statement 2: Sufficient ( 2=No, 5=Yes)

the question is asking whether sqrt(x) is less than or not. the Answer can be Yes or No both (as evident from statement 1 & 2 both)

whats wrong with my way of thinking??

ConkergMat,, can you please post OA & Explanation.

can somebody help me out!!!!
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kudos me if you like my post.

Attitude determine everything. all the best and God bless you.

GUYS..after reading all the posts and explanation ...i am not able to find correct explanation for the answer. statement 1: sufficient (0=No,1=No,2=No) statement 2: Sufficient ( 2=No, 5=Yes)

the question is asking whether sqrt(x) is less than or not. the Answer can be Yes or No both (as evident from statement 1 & 2 both)

whats wrong with my way of thinking??

ConkergMat,, can you please post OA & Explanation.

can somebody help me out!!!!

Why do you think Statement 2 is sufficient while you took two numbers and 2: no and 5 is yes. You fell the same trap as me. This is data sufficient, not problem solving, the 1st statement gives us sufficient data to answer the question (Answer: No) while the 2nd is not (You don't know whether Yes or No). Please read fluke's post answering me, you will see the point.

Question: \(\sqrt{x} < (2.5x - 5)\) and x is a positive integer By squaring on both sides, it can be simplified as \(x < (2.5x-5)^2\)

statement 1. x < 3, which means the possible values are 1 or 2 only substitute 1 in the simplified equation, \(1 < (2.5 (1) - 5)^2 => 1 < (-2.5)^2 => 1 < 6.25\) True substitute 2 in the simplified equation, \(2 < (2.5 (2) - 5)^2 => 2 < (0)^2 => 2 < 0\) False NOT SUFFICIENT

statement 2. x is prime #, which means the possible values are 2,3,5,7 etc substitute 2 in the simplified equation, \(2 < (2.5 (2) - 5)^2 => 2 < (0)^2 => 2 < 0\) False substitute 3 in the simplified equation, \(3 < (2.5 (3) - 5)^2 => 3 < (2.5)^2 => 3 < 6.25\) True NOT SUFFICIENT

Question: \(\sqrt{x} < (2.5x - 5)\) and x is a positive integer By squaring on both sides, it can be simplified as \(x < (2.5x-5)^2\). This is not always correct.

statement 1. x < 3, which means the possible values are 1 or 2 only substitute 1 in the simplified equation, \(1 < (2.5 (1) - 5)^2 => 1 < (-2.5)^2 => 1 < 6.25\) True substitute 2 in the simplified equation, \(2 < (2.5 (2) - 5)^2 => 2 < (0)^2 => 2 < 0\) False NOT SUFFICIENT

statement 2. x is prime #, which means the possible values are 2,3,5,7 etc substitute 2 in the simplified equation, \(2 < (2.5 (2) - 5)^2 => 2 < (0)^2 => 2 < 0\) False substitute 3 in the simplified equation, \(3 < (2.5 (3) - 5)^2 => 3 < (2.5)^2 => 3 < 6.25\) True NOT SUFFICIENT

So, my pick was E. Any comments ?

\(-100<1\) \((-100)^2>1^2\)

\(-0.1<1\) \((-0.1)^2<1^2\)

\(1<2\) \(1^2<2^2\)

Thus, squaring both sides in inequality may give undesired result, esp when we don't know the signs of the expression on both sides.

Something similar happened here:

\(\sqrt{x}<{2.5*x-5}\) ------------1 For x=1 \(\sqrt{1}<{2.5*1-5}\) No.

Statement#1 - Sufficient x < 3 and from the given info in the question that x + int, so x = 1 or 2 X=1 --> sqrt (1) = 1 < 2.5 (1) -5 = -2.5 ? --> No X=2 --> sqrt (2) ~ 1.4 < 2.5 (2) -5 = 0 ? --> No Ans always no --> Sufficient as this given info can help answer the question

Statement#2 - Insufficient X is prime # - Let's pick # x= 2 and 3 X=2 --> sqrt (2) ~ 1.4 < 2.5 (2) -5 = 0 ? --> No X=5 --> sqrt (3) ~ 1.7 < 2.5 (3) -5 = 2.5 ?--> Yes Ans --> Insufficient as the given info can yield the answer to this question either Yes or No.
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"You can do it if you believe you can!" - Napoleon Hill "Insanity: doing the same thing over and over again and expecting different results." - Albert Einstein

Statement 1- if x is any number below 3, the value of X will always be greater than the square root of X. this is sufficient to answer the question.

Statement 2- If we plug in two, the result is a NO to the stem question but if we plug in a 3 or any other prime number, the result is a YES. So the answer is MAYBE-Insufficient.

If \(x\) is a positive integer, is \(\sqrt{x}<2.5x - 5\) ?

First of all notice that since \(x\) is a positive number then \(\sqrt{x}>0\).

(1) \(x<3\) --> since \(x\) is is a positive integer then \(x=1\) or \(x=2\). For both those values, the right hand side (\(2.5x - 5\)) is less than or equal to zero, so it cannot be more than the left hand side (\(\sqrt{x}\)) which is positive. Hence the answer to the question is NO. Sufficient.

(2) \(x\) is a prime number. If \(x=2\) then the answer is NO but if \(x=11\) then the answer is YES. Not sufficient.

1) x<3 --> since x is is a positive integer then x=1 or x=2

@GMAT Club Legend, is it correct to say the above? We are not told that X is a positive integer in Statement 1. so any number even 2.9or 2.5 or 2 or 1.9 or 1 satisfies statement 1.

Otherwise your answer is correct. Is that right?am juss thinking aloud,lol!

1) x<3 --> since x is is a positive integer then x=1 or x=2

@GMAT Club Legend, is it correct to say the above? We are not told that X is a positive integer in Statement 1. so any number even 2.9or 2.5 or 2 or 1.9 or 1 satisfies statement 1.

Otherwise your answer is correct. Is that right?am juss thinking aloud,lol!

I think the question says to consider only cases where x is a positive integer. It says "If x is a positive integer"

1) x<3 --> since x is is a positive integer then x=1 or x=2

@GMAT Club Legend, is it correct to say the above? We are not told that X is a positive integer in Statement 1. so any number even 2.9or 2.5 or 2 or 1.9 or 1 satisfies statement 1.

Otherwise your answer is correct. Is that right?am juss thinking aloud,lol!

Notice that the stem explicitly states that x is a positive integer.
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The answer is A because if X is a positive integer, Statement 1 tells us that X must be either 1 or 2.

Solving for both of these: X=1 1<-2.5 NO X=2 root 2 <0 NO ... SUFFICIENT remember when X is already given under the square root sign, only consider positive answers. When solving for X^2, consider both positive and negative roots.

Statement 2: X is a prime number We already know from 1. that if X is 1 or 2 the answer is NO. Let's test 5 root 5 < 2.5x - 5 root 5 < 12.5 - 5 YES ... INSUFFICIENT

If x is a positive integer, is \(\sqrt{x}<2.5x - 5\)?

1. x<3 2. x is a prime number

=> \(2\sqrt{x} - 5x <-10\) =>\(5x - 2\sqrt{x} > 10\) For above to be true x>3 -- we already know x>=1 (Since its is a positive integer) 1. x<3 - this means x = 1 or 2 - either case -- exp is less than 10 2. Consider x = 2 => No x = 4 ; (20) - 4 = 16 => yes IMO A
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