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# m05 q15

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Re: m05 q15 [#permalink]  30 May 2011, 00:08
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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Re: m05 q15 [#permalink]  30 May 2011, 00:58
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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Re: m05 q15 [#permalink]  30 May 2011, 02:57
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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Re: m05 q15 [#permalink]  30 May 2011, 03:23
1
KUDOS
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 ?

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

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

$$1<2$$
$$1^2<2^2$$

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.

$$(\sqrt{1})^2<(2.5*1-5)^2$$ ------------2
$$1<6.25$$
Yes.

Does this make statement 1 insufficient? No.

It just proves the following:

if $$a<b$$
then, $$a^2<b^2$$ may not be true.
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Re: m05 q15 [#permalink]  30 May 2011, 23:35
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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Re: m05 q15 [#permalink]  31 May 2012, 04:54
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.

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Re: m05 q15 [#permalink]  31 May 2012, 06:04
Expert's post
ConkergMat wrote:
If $$x$$ is a positive integer, is $$\sqrt{x} \lt 2.5x - 5$$ ?

1. $$x \lt 3$$
2. $$x$$ is a prime number

[Reveal] Spoiler: OA
A

Source: GMAT Club Tests - hardest GMAT questions

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.

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Re: m05 q15 [#permalink]  31 May 2012, 07:14
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.

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Re: m05 q15 [#permalink]  31 May 2012, 07:45
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.

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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Re: m05 q15 [#permalink]  31 May 2012, 09:01
Expert's post
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.

Notice that the stem explicitly states that x is a positive integer.
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Re: m05 q15 [#permalink]  31 May 2013, 05:44
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
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Re: m05 q15 [#permalink]  01 Jun 2013, 06:39
Given x > 0 and x is integer.

Restate the question: 2 * SQRT(x) < 5 * (x - 2)

S1: x < 3
x = 1 => 2 * SQRT(1) < 5 * (-1) => NO
x = 2 => 2 * SQRT(2) < 5 * (0) => NO
S1 is Sufficient. Eliminate BCE.

S2: x = prime
x = 1 => NO
x = 7 => 2 * SQRT(7) < 5 * 5 => YES
S2 is not sufficient.

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Re: m05 q15 [#permalink]  03 Jun 2013, 05:17
Simplify the equation a bit you get :

$$\sqrt{X} < 2.5 ( X-2)$$

Now case 1: x<3
so x can only be either 1 or 2

substituting 2, $$\sqrt{2}$$ < 0 ? NO
Substituting 1, $$\sqrt{1}$$ < some negative value ? NO

So since we have a definite answer, A is one of the possibility. Hence, eliminate B,C and E

Now check 2nd case : x is a prime number

$$\sqrt{2}$$ < 0? NO
$$\sqrt{3}$$ < 2.5 YES

Hence, D gets ruled out as well, answer is : A

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Re: m05 q15 [#permalink]  03 Jun 2013, 12:56
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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Re: m05 q15 [#permalink]  19 May 2014, 22:38
If x is a positive integer, is \sqrt{x} \lt 2.5x - 5 ?

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

ANS ---

Equation is , If sqrt(x) < 2.5x - 5 => sqrt(x) < 2.5(x-2)

1. For any x< 3 sqrt(x) is always greater than 2.5(x-2) as x is a positive integer => sufficient

2. x can be any prime, so doesn't reach for any conclusion as,

for x = 2,3 LHS < RHS
BUT for x = 5,7.... LHS > RHS

so, insufficient...

ANS is A.
Re: m05 q15   [#permalink] 19 May 2014, 22:38

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