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Magoosh Brain Twister: What the #@#@!

brain_twister

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

As always, check back this Thursday for the explanation!
 
Addendum:

This will be the last weekly Brain Twister. Instead, we will have bi-weekly Brain
Twisters. So you’ll have to wait two weeks to get your fill, but I promise I have some
fun ones up my sleeve. 🙂

 

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26 Responses to Magoosh Brain Twister: What the #@#@!

  1. Chinmay September 11, 2014 at 4:19 am #

    The answer will be 5 as @x@ will represent all positive no less than x and we can find primes of negative numbers, so #x# = #(@x@)#

  2. Anteneh Alem September 10, 2014 at 1:14 pm #

    #x#=5 means there are five prime numbers less than @x@.The first five prime numbers are 2,3,5,7 and 11. so @x@=12 and #12#=5 Ans. B

  3. Manuj September 10, 2014 at 7:51 am #

    Answer: E = 1

    x >144 / @x@ = 12 / #x# = 5
    @(@x@)@ = 3
    #(@x@)# = 1

  4. Krithika September 10, 2014 at 7:27 am #

    (E) 1

  5. sukanya September 9, 2014 at 2:41 pm #

    (A) 7
    if #x# = 5; then @x@ has to be greater than or equal to 8 (the five positive primes less than 8 being 1, 2, 3, 5, 7)
    hence # 8 # should be 5 i.e. no. of primes less than 8

    • sukanya September 9, 2014 at 2:42 pm #

      correction (B)

  6. Annina September 9, 2014 at 11:11 am #

    “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@)#?”

    We know #x# = 5, so five prime numbers are less than @x@. The first five prime numbers are 2, 3, 5, 7, and 11, followed by 13; this means that @x@ is either 12 or 13.

    To find #(@x@)# we first have to find @(@x@)@: this is the number of positive perfect squares less than 12 or 13. The square numbers below 12 or 13 are 1, 4, and 9: so there are three of them. This means @(@x@)@ = 3.

    Finally we need the number of primes less than 3; there is only one of these, the number 2.

    Therefore, #(@x@)# = 1, choice E.

  7. Aneesh September 9, 2014 at 9:20 am #

    (E) 1

  8. Gayatri September 9, 2014 at 8:17 am #

    Is the answer (E) 1 ??

  9. Sushant Pritmani September 9, 2014 at 7:14 am #

    Edit : The answer is 1.

  10. Vaibhav Dahiya September 9, 2014 at 3:11 am #

    #x# = 5 (These are 2, 5, 7, 11, 13)

    which implies that x=17

    @x@ = 4 (These are 1, 4, 9, 16)

    So , #(@x@)# = #(4)# = 1 (As 2 is the only prime no. less than 4)

    Hence , the correct option is (E) .

  11. richard baffour awuah September 9, 2014 at 2:06 am #

    5

  12. Vaibhav Dahiya September 9, 2014 at 1:50 am #

    #(x)# = 5
    ( these are 2, 5, 7, 11, 13 )

    which implies that x = 17

    @x@ = 4 (these are 1, 4, 9, 16 )

    # (@x@) # = # (4) # = 1 (that no. is 2)

    So the correct option is (e) .

  13. Hasan Balcı September 9, 2014 at 12:27 am #

    Answer is 1.

    Solution:

    If #x# = 5, then @x@ = 12 or 13, because there are 5 primes less than 12 and 13.

    Question becomes the value of #12# or #13#.

    If x = 12 or 13, then @12@ or @13@ = 3, which are 1, 4 and 9 as the perfect squares.

    If @12@ or @13@ = 3, then #12# or #13# = 1, which is 2 as the prime number.

    Therefore if #x# = 5, then #(@x@)# = 1.

  14. payal September 8, 2014 at 10:23 pm #

    Ans E 1

  15. SriHari September 8, 2014 at 9:29 pm #

    Answer: E-1

    #x# = 5 = number of primes less than @x@
    so @x@ = 12 or @x@ = 13 -> (1)

    #(@x@)# = number of primes less than @(@x@)@
    = number of primes less than (@(12)@ or @(13)@) [from (1)]
    = number of primes less than (number of perfect squares less than 12 or 13)
    = number of primes less than (3)
    = 1

  16. AnkiT September 8, 2014 at 9:00 pm #

    (E)1

  17. bhavana September 8, 2014 at 8:42 pm #

    1

  18. Vikky September 8, 2014 at 6:03 pm #

    Ans: E
    @x@ is 2( perfect squares – 1 and 4)
    so #x# will be 1.

  19. ramya September 8, 2014 at 12:45 pm #

    answer is E= 1..

  20. sunil September 8, 2014 at 12:40 pm #

    Ans – 1

  21. Sriram September 8, 2014 at 11:39 am #

    (E) 1

  22. Utsav September 8, 2014 at 11:12 am #

    The answer is (E).
    Given: #x# = 5
    So, the number of primes less than @x@ = 5
    The primes are 2, 3, 5, 7, 11, 13, …
    Since the 5th prime is 11, @x@ is either 12 or 13.
    Then, @(@x@)@ = the number of positive perfect squares less than @x@ = 3 (1, 4 and 9).
    Therefore, #(@x@)# = The number of primes less than @(@x@)@ = 1 (Since there is only 1 prime less than 3)

  23. Gurjot Makkar September 8, 2014 at 10:48 am #

    If #x# = 5, the five prime numbers will be 2, 3, 5, 7, 11 and x is either 12 or 13.
    Now y = @x@ = 3 (1, 4, 9)
    Now #y# = 1 (2)
    Hence, E

  24. Gandhi Vinay September 8, 2014 at 9:31 am #

    13

    • Gandhi Vinay September 8, 2014 at 9:32 am #

      All the prime no. Less than and 37.


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