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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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321kumarsushant wrote: 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.
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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
So, my pick was E. Any comments ?
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seku wrote: 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<1^21<21^2<2^2Thus, 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. (\sqrt{1})^2<(2.5*1-5)^2 ------------2 1<6.25Yes. Does this make statement 1 insufficient? No. It just proves the following: if a<bthen, a^2<b^2 may not be true.
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I would go for A. Question: x + int | sqrt(x) < 2.5x-5 ? 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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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.
The answer is A.
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ConkergMat wrote: If x is a positive integer, is \sqrt{x} \lt 2.5x - 5 ? 1. x \lt 32. x is a prime number Source: GMAT Club Tests - hardest GMAT questions 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. Answer: A.
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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!
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Cosmas wrote: 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"
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