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Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  Let f(x) denotes the sum of the digits of the positive integer x. For

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Math Expert V
Joined: 02 Sep 2009
Posts: 55670
Let f(x) denotes the sum of the digits of the positive integer x. For  [#permalink]

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Difficulty:   95% (hard)

Question Stats: 43% (02:27) correct 57% (02:04) wrong based on 99 sessions

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Let f(x) denotes the sum of the digits of the positive integer x. For example, f(8) =8, f(123) = 1+2+3=6. For how many two-digit values of x is f(f(x))=3?

A. 3
B. 4
C. 6
D. 9
E. 10

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Senior Manager  G
Joined: 13 Feb 2018
Posts: 329
GMAT 1: 640 Q48 V28 Re: Let f(x) denotes the sum of the digits of the positive integer x. For  [#permalink]

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We need two digit integers with the sum of digits equal to 3
here they are
12, 21
30,
49, 94
58, 85
67, 76

IMO
Ans: D
Intern  B
Joined: 26 Feb 2017
Posts: 24
Re: Let f(x) denotes the sum of the digits of the positive integer x. For  [#permalink]

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12,21,30
39,48,57,66,75,84,93

Total 10 possibilities.

So E

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VP  D
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1009
WE: Supply Chain Management (Energy and Utilities)
Re: Let f(x) denotes the sum of the digits of the positive integer x. For  [#permalink]

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Bunuel wrote:
Let f(x) denotes the sum of the digits of the positive integer x. For example, f(8) =8, f(123) = 1+2+3=6. For how many two-digit values of x is f(f(x))=3?

A. 3
B. 4
C. 6
D. 9
E. 10

f(12)=1+2=3; so, f(f(12))=f(3)=3
f(21)=2+1=3; so, f(f(21))=f(3)=3
f(30)=3+0=3; so, f(f(30))=f(3)=3

Now we have to check any pair of integers those sum to 12, 12, and 31 as f(12) yields 3 and f(f(3))=3.

4+8=8+4=12
5+7=7+5=12
6+6=12
3+9=9+3=12
hence, we have 3+7=10 nos. of two-digit values. (12,21,30,48,84,57,75,66,39,93)

Ans. (E)
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Manager  B
Joined: 01 Feb 2018
Posts: 75
Location: India
Concentration: Entrepreneurship, Marketing
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WE: Consulting (Consulting)
Re: Let f(x) denotes the sum of the digits of the positive integer x. For  [#permalink]

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LevanKhukhunashvili wrote:
We need two digit integers with the sum of digits equal to 3
here they are
12, 21
30,
49, 94
58, 85
67, 76

IMO
Ans: D

it will be
12,21,
30,
39, 93
48,84
57, 75
66
Veritas Prep GMAT Instructor D
Joined: 16 Oct 2010
Posts: 9330
Location: Pune, India
Re: Let f(x) denotes the sum of the digits of the positive integer x. For  [#permalink]

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Bunuel wrote:
Let f(x) denotes the sum of the digits of the positive integer x. For example, f(8) =8, f(123) = 1+2+3=6. For how many two-digit values of x is f(f(x))=3?

A. 3
B. 4
C. 6
D. 9
E. 10

Here is how I will think about it:

x needs to be a 2 digit number. It can be anything from 10 to 99 (minimum sum of digits 1 and maximum sum of digits is 18)
So f(x) will vary from 1 to 18.

f(f(x) = 3 when f(x) = 3 or 12 (note that f(x) cannot be 21 or 30 since f(x) cannot take these values)

f(x) = 3 when x = 30/12/21
f(x) = 12 when x = 39/93/48/84/57/75/66

In all, we have 10 values for x.
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Karishma
Veritas Prep GMAT Instructor Re: Let f(x) denotes the sum of the digits of the positive integer x. For   [#permalink] 25 Oct 2018, 00:34
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Let f(x) denotes the sum of the digits of the positive integer x. For  