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# Two digits in hunter's age are the same as the digit in the titan's ag

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Math Expert
Joined: 02 Sep 2009
Posts: 60468
Two digits in hunter's age are the same as the digit in the titan's ag  [#permalink]

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01 Nov 2019, 04:22
00:00

Difficulty:

75% (hard)

Question Stats:

55% (02:37) correct 45% (03:05) wrong based on 73 sessions

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Two digits in hunter's age are the same as the digit in the titan's age, but in reverse order. In five years hunter will be twice as old as titan will be then. what is the difference in their current age ?

(A) 9
(B) 18
(C) 27
(D) 36
(E) 45

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Joined: 10 Dec 2017
Posts: 174
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Two digits in hunter's age are the same as the digit in the titan's ag  [#permalink]

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01 Nov 2019, 05:07
1
Let the age of hunter is AB=10A+B
Age of Titan BA=10B+A
Difference in current age=9(A-B)
After 5 years Hunter will be twice as old as Titen
(AB+5)=2(BA+5)
10A+B=2(10B+A+5)
9(A-B)=10B+A+5
9(A-B)=BA+5
Check options
1.9(A-B)=9 This gives BA=4( ABSURD)
2.9(A-B)=18 This gives BA=13,AB=31(PERFECT)
3.9(A-B)=27, This gives BA=22, AB=22( ABSURD)
4.9(A-B)=36,This gives BA=31, AB =13 ( ABSURD)
5.9(A-B)=45,This gives BA=40, AB=04( ABSURD)
B

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Re: Two digits in hunter's age are the same as the digit in the titan's ag  [#permalink]

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01 Nov 2019, 06:06
1
Bunuel wrote:
Two digits in hunter's age are the same as the digit in the titan's age, but in reverse order. In five years hunter will be twice as old as titan will be then. what is the difference in their current age ?

(A) 9
(B) 18
(C) 27
(D) 36
(E) 45

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hunters age = 10a+b
titans age = 10b+a
∆ in age = 9(a-b)
5 years later
10a+b+5=2*(10b+a+5)
10a+b+5 = 20b+2a+10
8a=19b+5

∆ in age = 9(a-b)
answer will be one with ∆ of 5
(A) 9 = not possible
(B) 18 ; 18-5 ; 13 and 31 ; correct
(C) 27; 22 ; not possible
(D) 36; 31 and 13 not possible
(E) 45 ; 41 and 14 not possible
IMO B
Math Expert
Joined: 02 Aug 2009
Posts: 8342
Re: Two digits in hunter's age are the same as the digit in the titan's ag  [#permalink]

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01 Nov 2019, 09:10
Bunuel wrote:
Two digits in hunter's age are the same as the digit in the titan's age, but in reverse order. In five years hunter will be twice as old as titan will be then. what is the difference in their current age ?

(A) 9
(B) 18
(C) 27
(D) 36
(E) 45

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hunter's age---10a+b
titan's age-10b+a.

In five years hunter will be twice as old as titan will be then. ---10a+b+5=2(10b+a+5)....10a+b+5=20b+2a+10.....8a=19b+5
8a=19b+5 means b is odd...
$$b=1, 8a=19+5=24......a=3$$..Possible
No need to look forward.. numbers are 31 and 13, and difference = 31-13=18
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Re: Two digits in hunter's age are the same as the digit in the titan's ag  [#permalink]

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02 Nov 2019, 01:05
1
Bunuel wrote:
Two digits in hunter's age are the same as the digit in the titan's age, but in reverse order. In five years hunter will be twice as old as titan will be then. what is the difference in their current age ?

(A) 9
(B) 18
(C) 27
(D) 36
(E) 45

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Let the hunter's age = xy = 10x + y
--> Age of titan = yx = 10y + x

After 5 years, age of hunter = 10x + y + 5
and age of titan = 10y + x + 5

In five years hunter will be twice as old as titan will be then
--> 10x + y + 5 = 2(10y + x + 5)
--> 8x - 19y = 5
--> 8x = 19y + 5
So, y has to be odd,
If y = 1, 8x = 24 --> x = 3 --> Possible
If y = 3, 8x = 62 --> Not Possible
If y = 5, 8x = 100 --> Not Possible (x will have 2 digits)

--> Only Possible value of xy = 31
--> Age of hunter = 31 & age of titan = 13
--> Difference = 31 - 13 = 18

IMO Option B
Re: Two digits in hunter's age are the same as the digit in the titan's ag   [#permalink] 02 Nov 2019, 01:05
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