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

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

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New post 20 Jul 2017, 21:43
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  95% (hard)

Question Stats:

40% (02:36) correct 60% (02:42) wrong based on 68 sessions

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

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New post 20 Jul 2017, 22:18
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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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New post 21 Mar 2018, 21:02
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   [#permalink] 21 Mar 2018, 21:02
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