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Each digit of a two digit number X is half the corresponding digit of
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27 Jan 2022, 04:00
27 Jan 2022, 04:00
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Each digit of a two digit number X is half the corresponding digit of another two digit number Y. If both digits of X are positive integers, how many possible values does X have?
A. 16
B. 20
C. 24
D. 28
E. 32
A. 16
B. 20
C. 24
D. 28
E. 32
Dream Score Representative
Joined: 07 Oct 2021
Posts: 388
Given Kudos: 2
Re: Each digit of a two digit number X is half the corresponding digit of
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31 Jan 2022, 17:49
31 Jan 2022, 17:49
1
Kudos
Bunuel wrote:
Each digit of a two-digit number X is half the corresponding digit of another two-digit number Y. If both digits of X are positive integers, how many possible values does X have?
A. 16
B. 20
C. 24
D. 28
E. 32
A. 16
B. 20
C. 24
D. 28
E. 32
Number Properties:
The unit digit of X can be any digit from 0 to 4. That is 5 options.
The tens digit of X can be any digit from 1 to 4. That is 4 options.
Thus in total, we have 5*4 = 20 numbers.
Answer: B
Re: Each digit of a two digit number X is half the corresponding digit of
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18 Feb 2022, 23:20
18 Feb 2022, 23:20
1
Kudos
Each digit of a two digit number X is half the corresponding digit of another two digit number Y. If both digits of X are positive integers, how many possible values does X have?
Y = 10A+B
x = \(10(\frac{A}{2})+(\frac{B}{2})\)
Therefore, A and B in Y must be EVEN DIGITS
EVEN DIGITS are = 0,2,4,6,8
This means Ten's Digit of Y i.e A has four options (except zero as Y is a two-digit number) = 2, 4, 6, 8
And Unit's Digit of Y i.e B has five options = 0,2,4,6,8
Total options for Y and X = 4*5 = 20
But it is given in the question that "both digits of X are positive integers", thus we will have to subtract those options which have ZERO as their Unit Digit and such options are = 20, 40, 60 and 80 (Total 4 options)
Therefore, our final answer = 20-4 = 16 (A)
Y = 10A+B
x = \(10(\frac{A}{2})+(\frac{B}{2})\)
Therefore, A and B in Y must be EVEN DIGITS
EVEN DIGITS are = 0,2,4,6,8
This means Ten's Digit of Y i.e A has four options (except zero as Y is a two-digit number) = 2, 4, 6, 8
And Unit's Digit of Y i.e B has five options = 0,2,4,6,8
Total options for Y and X = 4*5 = 20
But it is given in the question that "both digits of X are positive integers", thus we will have to subtract those options which have ZERO as their Unit Digit and such options are = 20, 40, 60 and 80 (Total 4 options)
Therefore, our final answer = 20-4 = 16 (A)
