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The ten’s digit of a two-digit number is twice the unit’s digit. Rever
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30 Nov 2021, 07:11
30 Nov 2021, 07:11
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The ten’s digit of a two-digit number is twice the unit’s digit. Reversing the digits yields a new number that is 27 less than the original number. Which one of the following is the original number?
(A) 12
(B) 21
(C) 43
(D) 63
(E) 83
(A) 12
(B) 21
(C) 43
(D) 63
(E) 83
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Re: The ten’s digit of a two-digit number is twice the unit’s digit. Rever
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30 Nov 2021, 07:19
30 Nov 2021, 07:19
1
Carcass wrote:
The ten’s digit of a two-digit number is twice the unit’s digit. Reversing the digits yields a new number that is 27 less than the original number. Which one of the following is the original number?
(A) 12
(B) 21
(C) 43
(D) 63
(E) 83
(A) 12
(B) 21
(C) 43
(D) 63
(E) 83
I believe the fastest approach here is to test the small handful of 2-digit numbers that satisfy the given information...
The ten’s digit of a two-digit number is twice the unit’s digit.
So the original number must be one of the four following numbers: 21, 42, 63 or 84
Reversing the digits yields a new number that is 27 less than the original number. Which one of the following is the original number?
Reverse 21 to get 12
So, the new number is 9 less than the original number.
No good. We need a difference of 27.
Reverse 42 to get 24
So, the new number is 18 less than the original number.
No good. We need a difference of 27.
Reverse 63 to get 36
So, the new number is 27 less than the original number.
Answer: D
ALTERNATE APPROACH: Algebra
Let x = the units digit in the original number
So 2x = the tens digit in the original number (since the tens digit is twice the units digit)
So, the VALUE of the original number = 10(2x) + x (in much the same way that (7)(10) + 3 is the VALUE of the number 73)
We can simplify 10(2x) + x to get 21x
When we REVERSE the digits, we have:
Let 2x = the units digit in the original number
So x = the tens digit in the original number
So, the VALUE of the new number = 10(x) + 2x = 10x + 2x = 12x
Since the new number is 27 less than the original number we can write: (VALUE of original number) - (VALUE of new number) = 27
Substitute to get: (21x) - (12x) = 27
Simplify: 9x = 27
Solve: x = 3
Since x = the units digit in the original number and 2x = the tens digit in the original number, the original number equals 63
Answer: D
gmatclubot
Re: The ten’s digit of a two-digit number is twice the unit’s digit. Rever [#permalink]
30 Nov 2021, 07:19
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