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# If x1, x2, x3… xn is a sequence such that xn=n/2 for all values x≥1, i

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Math Expert
Joined: 02 Sep 2009
Posts: 50730
If x1, x2, x3… xn is a sequence such that xn=n/2 for all values x≥1, i  [#permalink]

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28 Sep 2017, 03:56
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Difficulty:

65% (hard)

Question Stats:

52% (01:40) correct 48% (01:47) wrong based on 84 sessions

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If $$x_1$$, $$x_2$$, $$x_3$$, … $$x_n$$ is a sequence such that $$x_n=\frac{n}{2}$$ for all values $$x \geq 1$$, is $$x_b$$ less than $$x_h$$ ?

(1) $$\sqrt{b} \geq \sqrt{h}$$

(2) b and h are distinct prime numbers.

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Joined: 12 Feb 2015
Posts: 58
Location: India
GPA: 3.84
Re: If x1, x2, x3… xn is a sequence such that xn=n/2 for all values x≥1, i  [#permalink]

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28 Sep 2017, 04:21
Bunuel wrote:
If $$x_1$$, $$x_2$$, $$x_3$$, … $$x_n$$ is a sequence such that $$x_n=\frac{n}{2}$$ for all values $$x \geq 1$$, is $$x_b$$ less than $$x_h$$ ?

(1) $$\sqrt{b} \geq \sqrt{h}$$

(2) b and h are distinct prime numbers.

eventually the question is whether b>h
a)considering b=1 h=1 1<1 No
b=2 h=1 2>1 yes...Insuff

b)b and can be any prime no,making either of the two possibilities of b>h or h>b..insuff

c)makes sense
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If x1, x2, x3… xn is a sequence such that xn=n/2 for all values x≥1, i  [#permalink]

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28 Sep 2017, 06:25
1
Bunuel wrote:
If $$x_1$$, $$x_2$$, $$x_3$$, … $$x_n$$ is a sequence such that $$x_n=\frac{n}{2}$$ for all values $$x \geq 1$$, is $$x_b$$ less than $$x_h$$ ?

(1) $$\sqrt{b} \geq \sqrt{h}$$

(2) b and h are distinct prime numbers.

To find $$x_b$$$$<$$$$x_h$$

or $$\frac{b}{2}<\frac{h}{2}=> b<h$$

Statement 1: as $$b$$ & $$h$$ are positive, we can directly square the inequality to get $$b≥h$$

Now if $$b>h$$, then the answer to our question stem is NO

and if $$b=h$$, then also answer to our question stem is NO. Hence Sufficient

Statement 2: $$b$$ and $$h$$ can be any prime nos and hence $$b>h$$ or $$b<h$$. Hence Insufficient

Option A
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Joined: 15 Jan 2017
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Re: If x1, x2, x3… xn is a sequence such that xn=n/2 for all values x≥1, i  [#permalink]

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11 Sep 2018, 00:31
1
St 1: root b >= root h

--> root b - root h >= 0
squaring:

b + h -2root b root h> = 0
b + h >= 2 root b root h
so b not equal to h
as root b> root h
and terms are divisble 2, its suff

2) b , h prime
no idea about the distance from 0 --> -2,0,2,4 --< b is 2 or -2 (or h) we don't know. Not Suff
Re: If x1, x2, x3… xn is a sequence such that xn=n/2 for all values x≥1, i &nbs [#permalink] 11 Sep 2018, 00:31
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# If x1, x2, x3… xn is a sequence such that xn=n/2 for all values x≥1, i

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