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04 May 2022, 03:15
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E
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Difficulty:
95%
(hard)
Question Stats:
42% (02:23) correct
58%
(02:07)
wrong
based on 123
sessions
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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
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(A) 3
(B) 4
(C) 6
(D) 9
(E) 10
Are You Up For the Challenge: 700 Level Questions
04 May 2022, 04:06
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@(@x) = 3 denotes that the sum of the digits of the sum of the digits of x = 3. This can occur in one of two ways:
1) The sum of the digits of x is 3.
or
2) The sum of the digits of x is 12.
Two digit numbers which sum to 3: \(12, 21\) & \(30\) (3 in total)
Two digit numbers which sum to 12: \(39, 93, 48, 84, 57, 75\) & \(66\) (7 in total)
\(4 + 7 = 10\)
Answer E
1) The sum of the digits of x is 3.
or
2) The sum of the digits of x is 12.
Two digit numbers which sum to 3: \(12, 21\) & \(30\) (3 in total)
Two digit numbers which sum to 12: \(39, 93, 48, 84, 57, 75\) & \(66\) (7 in total)
\(4 + 7 = 10\)
Answer E
12 Nov 2022, 23:30
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Given that @x denote the sum of the digits of the positive integer x and we need to find how many two-digit values of x is @(@x) = 3 ?
@(@x)) = 3
If we open the outer \(@\) then sum of the values = 3
=> number could be 03, 12, 21, 30
@x = 03
=> x = 12, 21, 30
@x = 12
=> x = 39, 48, 57, 66, 75, 84, 93
@x = 21
=> Not possible to get any two digit number whose sum of digits = 21
@x = 30
=> Not possible to get any two digit number whose sum of digits = 30
=> 10 values are possible
So, Answer will be E
Hope it helps!
Watch the following video to learn the Basics of Functions and Custom Characters
@(@x)) = 3
If we open the outer \(@\) then sum of the values = 3
=> number could be 03, 12, 21, 30
@x = 03
=> x = 12, 21, 30
@x = 12
=> x = 39, 48, 57, 66, 75, 84, 93
@x = 21
=> Not possible to get any two digit number whose sum of digits = 21
@x = 30
=> Not possible to get any two digit number whose sum of digits = 30
=> 10 values are possible
So, Answer will be E
Hope it helps!
Watch the following video to learn the Basics of Functions and Custom Characters
