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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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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 < 6.25True substitute 2 in the simplified equation, 2 < (2.5 (2) - 5)^2 => 2 < (0)^2 => 2 < 0False 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 < 0False substitute 3 in the simplified equation, 3 < (2.5 (3) - 5)^2 => 3 < (2.5)^2 => 3 < 6.25True 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 < 6.25True substitute 2 in the simplified equation, 2 < (2.5 (2) - 5)^2 => 2 < (0)^2 => 2 < 0False 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 < 0False substitute 3 in the simplified equation, 3 < (2.5 (3) - 5)^2 => 3 < (2.5)^2 => 3 < 6.25True 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

=> 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