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The ten’s digit of a two-digit number is twice the unit’s digit. Rever [#permalink] 07 Sep 2021, 03:35
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Question Stats: 92% (01:18) correct 8% (00:58) wrong based on 13 sessionsHide Show timer StatisticsThe 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 _________________
The ten’s digit of a two-digit number is twice the unit’s digit. Rever [#permalink] Updated on: 07 Sep 2021, 10:49
Bunuel 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 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 84Reversing 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 12So, the new number is 9 less than the original number.No good. We need a difference of 27. Reverse 42 to get 24So, the new number is 18 less than the original number.No good. We need a difference of 27. Reverse 63 to get 36So, the new number is 27 less than the original number.Answer: DALTERNATE APPROACH: AlgebraLet 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 21xWhen we REVERSE the digits, we have:Let 2x = the units digit in the original number So x = the tens digit in the original numberSo, the VALUE of the new number = 10(x) + 2x = 10x + 2x = 12xSince the new number is 27 less than the original number we can write: (VALUE of original number) - (VALUE of new number) = 27Substitute to get: (21x) - (12x) = 27Simplify: 9x = 27Solve: x = 3Since x = the units digit in the original number and 2x = the tens digit in the original number, the original number equals 63Answer: D _________________
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Re: The ten’s digit of a two-digit number is twice the unit’s digit. Rever [#permalink] 07 Sep 2021, 10:35
Bunuel 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 Let the tenth's digit of the original number be xunit's digit be ySo, original number = xyGiven: x = 2yAlso, given:10y + x = 10x + y - 27Plug x = 2y:12y = 21y - 27y = 3, x = 2y = 2*3 = 6So, the original number = xy = 63IMO, (D)!Hi BrentGMATPrepNow, I guess you mistyped the correct answer as (C)! _________________
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Re: The ten’s digit of a two-digit number is twice the unit’s digit. Rever [#permalink] 07 Sep 2021, 10:50
Showmeyaa wrote: Hi BrentGMATPrepNow,
Brent Hanneson – Creator of gmatprepnow.comI’ve spent the last 20 years helping students overcome their difficulties with GMAT math, and the biggest thing I’ve learned is… Many students fail to maximize their quant score NOT because they lack the skills to solve certain questions but because they don’t understand what the GMAT is truly testing - Learn more
Re: The ten’s digit of a two-digit number is twice the unit’s digit. Rever [#permalink] 07 Sep 2021, 10:50 Evolet S. the tens digit of a two digit number is twice the ones digit. If the digits are reversed, the new number is 36 less than the original number. Find the number. 1 Expert Answer Raymond B. answered • 11/12/20 Math, microeconomics or criminal justice
original number is 84. switch the digits and 48 is 36 less than 84 48+36 = 84 T=2U, where T = the tens' digit and U = the unit's digit 10U+T = 10T+U-36 9U = 9T -36 divide by 9 U = T -4 U=2U-4 U=4 T = 8 original number is TU = 84 |