GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 06 Dec 2019, 11:31

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 59587
Let @x denote the sum of the digits of the positive integer x. For exa  [#permalink]

### Show Tags

20 Mar 2019, 06:15
1
1
00:00

Difficulty:

85% (hard)

Question Stats:

39% (02:18) correct 61% (01:52) wrong based on 41 sessions

### HideShow timer Statistics

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

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 8281
Re: Let @x denote the sum of the digits of the positive integer x. For exa  [#permalink]

### Show Tags

20 Mar 2019, 06:31
1
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

E
_________________
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5428
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: Let @x denote the sum of the digits of the positive integer x. For exa  [#permalink]

### Show Tags

20 Mar 2019, 07:57
1
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
Re: Let @x denote the sum of the digits of the positive integer x. For exa   [#permalink] 20 Mar 2019, 07:57
Display posts from previous: Sort by