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Let @x denote the sum of the digits of the positive integer x. For exa

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Let @x denote the sum of the digits of the positive integer x. For exa  [#permalink]

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New post 20 Mar 2019, 06:15
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  55% (hard)

Question Stats:

42% (01:58) correct 58% (01:38) wrong based on 19 sessions

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Re: Let @x denote the sum of the digits of the positive integer x. For exa  [#permalink]

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New post 20 Mar 2019, 06:31
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Bunuel wrote:
Let @x denote the sum of the digits of the positive integer x. For example, @8 = 8 and 123 = 1 + 2 + 3 = 6. For how many two-digit values of x is @(@x) = 3 ?

(A) 3
(B) 4
(C) 6
(D) 9
(E) 10


Restriction - x is a 2-digit number
So, 2 digits number having digits totaling 3 will have its digits \(\leq{3}\), so 1,2,3,0..
Numbers 12, 21, 30..
Now 21 and 30 cannot be sum of two digits because max sum can be 99 and total is 9+9 18..
so three ways..
(I) @(@x) = 3 and @x=30, only possibility of x is 30.. Reason sum cannot be greater than 18.
(II) @(@x) = 3 and @x=21, only possibility of x is 21.. Reason sum cannot be greater than 18.
(I) @(@x) = 3 and @x=12, possibilities of x are 12, 39, 93, 48, 84, 57, 75 and 66.. so 8

Total 1+1+8=10

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Re: Let @x denote the sum of the digits of the positive integer x. For exa  [#permalink]

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New post 20 Mar 2019, 07:57
Bunuel wrote:
Let @x denote the sum of the digits of the positive integer x. For example, @8 = 8 and 123 = 1 + 2 + 3 = 6. For how many two-digit values of x is @(@x) = 3 ?

(A) 3
(B) 4
(C) 6
(D) 9
(E) 10


for @(@x) = 3
this can be obtained
when @(@30) = 3
@(@21)= 3
and
@(12) = 3 ; 12 can be obtained ; @(12,39,48,57,66,75,84,93) ; 8 such no
so
total 8+1+1= 10
IMO E
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Re: Let @x denote the sum of the digits of the positive integer x. For exa   [#permalink] 20 Mar 2019, 07:57
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