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# Let x be defined as the number of positive perfect squares less than

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Joined: 02 Sep 2009
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Let x be defined as the number of positive perfect squares less than  [#permalink]

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20 Jul 2017, 20:43
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Difficulty:

95% (hard)

Question Stats:

37% (02:32) correct 63% (02:50) wrong based on 61 sessions

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Let @x@ be defined as the number of positive perfect squares less than x
Let #x# be defined as the number of primes less than @x@
If #x# = 5, what is the value of #(@x@)#?

(A) 7
(B) 5
(C) 4
(D) 2
(E) 1

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Let x be defined as the number of positive perfect squares less than  [#permalink]

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20 Jul 2017, 21:18
1
1
Given: #x# = 5
#x# is defined as the number of primes less than @x@
where @x@ is the number of positive perfect squares less than x

If #x# = 5, then @x@ = 12 which has 5 primes(2,3,5,7,11) less than @x@
and @x@ is number of positive perfect squares less than 12, which is 3(1,4,9)

Now, we have been asked to find the value of #(@x@)# - which is the number of primes less than 3

Therefore, #(@x@)# or #3# = 1(Option E) as only 2 is a prime lesser than 3.
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Re: Let x be defined as the number of positive perfect squares less than  [#permalink]

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21 Mar 2018, 20:02
pushpitkc wrote:
Given :
#x# is defined as the number of primes less than @x@
where @x@ is the number of positive perfect squares less than x
#x# = 5

If #x# = 5, then @x@ = 12 which has 5 primes(2,3,5,7,11) less than @x@
and @x@ is number of positive perfect squares less than 12, which is 3(1,4,9)

Now, we have been asked to find the value of #(@x@)# or #3#
which is the number of primes less than 3 = 1(Option E) as only 2 is a prime lesser than 3.

Hi pushpitkc

As per the question statement $$Xmin = 145, @x@ = 12 & #x# = 5.$$

Now, As per your explanation -

If #x# = 5, then @x@ = 12 which has 5 primes(2,3,5,7,11) less than @x@
and @x@ is number of positive perfect squares less than 12, which is 3(1,4,9)

@x@ is number of positive perfect squares less than x but in your above highlighted solution you are considering x itself as 12 for finding the number of @x@. But that is wrong because x will be fixed to minimum of 145.

Please correct me if my understanding is wrong.
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Re: Let x be defined as the number of positive perfect squares less than &nbs [#permalink] 21 Mar 2018, 20:02
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