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Each digit in the two-digit number G is halved to form a new

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Re: Each digit in the two-digit number G is halved to form a new [#permalink]

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New post 23 Dec 2015, 18:08
so, the digits of G must be even.
suppose G = 10A+B where A- tens digit, and B units digit.
now we are told that 5A+0.5B=H.

we are asked for the sum of G and H, or 15A+1.5B

knowing that A and B must be even, there aren't that many ways it can be arranged in that way. 4*4 = 16 possibilities.
nevertheless, since the results are over 100, we can definitely rule out 2, 4, and 6 as A. Thus, A must be 8.

Now, we have 15*8 = 120.
We're getting closer to the answer choice.
B can be 2 = so the min digit of H can be 1.
B can be 8 = so the max digit of H can be 4.

suppose B = 8 => 1.5B = 12, and the sum of G+H=132.
suppose B = 2 => 1.5B = 3, and the sum of G+H=123.

now we know for sure that G+H must be a number between 123 and 132. only one answer choice satisfies this condition.

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Re: Each digit in the two-digit number G is halved to form a new [#permalink]

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New post 28 Dec 2015, 11:56
G = 10x + y
H = 10 (x/2) + (y/2)

Adding the two, the number is in the form 1.5 (10x + y)

Look for options that can be represented in this format and is also a two digit number. Only D satisfies the condition. Hence, D
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Each digit in the two-digit number G is halved to form a new [#permalink]

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New post 12 Mar 2016, 15:21
G=10a+b
H=10c+d, here c=a/2 & d=b/2 or a=2c and b=2d substitute these values
G=20c+2d;
G+H =30c+3d = 3(10c+d)
now in options check for which options are divisible by 3;
options A, B and D are divisible by 3;
A. 153 => 153/3=51 => c cannot be 5 as d will be a single digit integer.
B. 150 => 150/3=50 => c cannot be 5 as d will be a single digit integer.
D. 129 => 129/3=43 ---- CORRECT ANS. option D

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Re: Each digit in the two-digit number G is halved to form a new [#permalink]

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New post 12 Jan 2017, 12:48
Let G = 10a + b hence [halved G] = H = 10a/2 + b/2 = 5a + 3/2

Then G + H = 15a + 3/2b . Multiplying both sides by 2 we get 2(G+H) = 30a + 3b = 3(10a+b)

This means that (G+H) HAS TO BE A MULTIPLE OF 3 and this is fulfilled by answer D.

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Re: Each digit in the two-digit number G is halved to form a new [#permalink]

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New post 22 Feb 2017, 22:55
There is a way of saving 60% time by eliminating the first three answers (A, B & C):
Since both digits of G must be even (so as to yield an integer when halved), the highest possible value of G is 88. So the highest possible value of G+H is 88+44=132 which eliminates the first three answers. So, we now have to test only the last two answers to find out which satisfies the equation 3G/2 for an integer value of G.

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Re: Each digit in the two-digit number G is halved to form a new [#permalink]

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New post 12 Mar 2017, 12:26
let's find firstly the max number: 88+44=132
A, B, C are out
D and E
when it is easy to get 9 (6+3)
is it possible to get 8? x+x/2=8 then x is no integer
is it possible to get 12? x+x/2=12 x=8
Answer is D

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Re: Each digit in the two-digit number G is halved to form a new [#permalink]

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New post 19 Apr 2017, 23:53
Another angle, not sure if some one has already covered this.
1) G can end with 0,2,4,6,8
2) Half of each is 5,1,2,3,4
3) Sum of units could be 5 or 3 or 6 or 9 or 2
So A or D or E
4) Sum of Tens 5,3,6,9,12
Only D remains

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Re: Each digit in the two-digit number G is halved to form a new [#permalink]

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New post 28 Dec 2017, 07:47
Hi Guys,
This is the first time I am giving a solution :-)

given G=xy and H=(x/2).(y/2)

so plugging in x=4 and y=6 as these have to be even numbers( as we can divide them by 2).

we get 46 and its half is 23 and total is 69 .We see that the total is 3 times H.
applying same rule to all the numbers :

153 ---> 51 and 102 ( rejected as we are looking for 2 digit numbers)
129 ---> 43 and 86 ( accepted)
137 --> not divisible by 3
150 -->50 and 100 (same as 1)
89 --> not divisible by 3

hence only 129 or option D in the question.

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Re: Each digit in the two-digit number G is halved to form a new [#permalink]

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New post 28 Dec 2017, 13:31
The easiest way to do is thinking of the biggest 2 digit number that can be halved .. obviously it has to be even as u can’t divide odd to get whole number .. so it can be 88 or 86 .. 132 is not an option so we are left with 129 (86 + 43)


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Re: Each digit in the two-digit number G is halved to form a new [#permalink]

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New post 28 Dec 2017, 18:04
Let G be the 2 digit number represented by xy, thus H would be x/2 y/2
Now possible pairs of (y,y/2) = (0,0) (2,1) (4,2) (6,3) (8,4)
thus possible sum of units place (0,3,6,9,2 with one carried)

For (x,x/2) = (2,1) (4,2) (6,3) (8,4)
Now possible values (3,4 - for one carried, 6,7 ; 9,10 ; 12,13)

Now browse through the options for this combination

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Re: Each digit in the two-digit number G is halved to form a new   [#permalink] 28 Dec 2017, 18:04

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