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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] New post 05 Sep 2013, 20:24
Bunuel wrote:
u2lover wrote:
Each digit in the two-digit number G is halved to form a new two-digit number H. Which of the following could be the sum of G and H?

A. 153
B. 150
C. 137
D. 129
E. 89


Two-step solution:

G + G/2 = 3G/2 --> the sum is a multiple of 3.

G is a two-digit number --> G < 100 --> 3G/2 < 150.

Among the answer choices the only multiple of 3 which is less than 150 is 129.

Answer: D.


What could be the minimum number ?
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Re: Each digit in the two-digit number G is halved to form a new [#permalink] New post 05 Sep 2013, 22:51
Expert's post
ygdrasil24 wrote:
Bunuel wrote:
u2lover wrote:
Each digit in the two-digit number G is halved to form a new two-digit number H. Which of the following could be the sum of G and H?

A. 153
B. 150
C. 137
D. 129
E. 89


Two-step solution:

G + G/2 = 3G/2 --> the sum is a multiple of 3.

G is a two-digit number --> G < 100 --> 3G/2 < 150.

Among the answer choices the only multiple of 3 which is less than 150 is 129.

Answer: D.


What could be the minimum number ?


Assuming G is a positive number, the least value of G+G/2 will be 20+10=30. G must be even and cannot be less that 20. If it's an even number less than 20, then G/2 will not be a two-digit number.

Hope it's clear.
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Re: Each digit in the two-digit number G is halved to form a new [#permalink] New post 05 Sep 2013, 23:08
What could be the minimum number ?[/quote]

Assuming G is a positive number, the least value of G+G/2 will be 20+10=30. G must be even and cannot be less that 20. If it's an even number less than 20, then G/2 will not be a two-digit number.

Hope it's clear.[/quote] Yes it is thanks :)

So basically G ranges from 20 to 198 for all G >0
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Re: Each digit in the two-digit number G is halved to form a new [#permalink] New post 05 Sep 2013, 23:12
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Re: Each digit in the two-digit number G is halved to form a new [#permalink] New post 05 Sep 2013, 23:21
Bunuel wrote:
ygdrasil24 wrote:
Yes it is thanks :)

So basically G ranges from 20 to 198 for all G >0


No. G must also be a two digit number, so it ranges from 20 to 88.

Hmm... blunder as always :(

By the way why cant G(max) be 98 , H(max) be 49 in that case
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Re: Each digit in the two-digit number G is halved to form a new [#permalink] New post 05 Sep 2013, 23:23
Expert's post
ygdrasil24 wrote:
Bunuel wrote:
ygdrasil24 wrote:
Yes it is thanks :)

So basically G ranges from 20 to 198 for all G >0


No. G must also be a two digit number, so it ranges from 20 to 88.

Hmm... blunder as always :(

By the way why cant G(max) be 98 , H(max) be 49 in that case


We are told that EACH digit in the two-digit number G is halved, thus both digits of G must be even.
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Re: Each digit in the two-digit number G is halved to form a new [#permalink] New post 05 Sep 2013, 23:26
By the way why cant G(max) be 98 , H(max) be 49 in that case[/quote]

We are told that EACH digit in the two-digit number G is halved, thus both digits of G must be even.[/quote]

Hmmm..Okay under even constraint G max =88, Thanks
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Re: Each digit in the two-digit number G is halved to form a new [#permalink] New post 10 Sep 2013, 21:03
I followed the approach as :-

Multiplied each number with 2/3 and saw only 129 gives a 2 digit number i.e 43+86 which is possible,

for all of the rest number it gives a 3 digit number or is not multiple of 3.

Thanks
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Re: Each digit in the two-digit number G is halved to form a new [#permalink] New post 21 Nov 2013, 05:08
Let G be XX. Let H be x/2 x/2. G+H= 3 () Its a multiple of 3. Only two numbers fit the bill 153 and 129. 153/3 = 51 ( not possible because G is a two digit number and 51 is half of 102). Hence (D) 129.
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Re: Each digit in the two-digit number G is halved to form a new [#permalink] New post 04 Mar 2014, 16:14
Let H be the 2-digit number xy (actually 10x+y). Then G must be 2x2y (actually 10(2x) + 2y or 2(10x+y). In other words, the digits of G must be even single-digit numbers. The maximum value of G can be 88 and thereby H can be 44.
Therefore, maximum value of G+H = 132. Therefore, A & B are out.
Now G+H = 3(10x+y) implies, G+H must be a multiple of 3. Only D among the remaining answer choices is a multiple of 3. So D is the answer.
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Re: Each digit in the two-digit number G is halved to form a new [#permalink] New post 04 Mar 2014, 18:45
Maximum largest number = 88 + 44 = 132, so options A,B & C are eliminated

Number should be divisible by 3 (for ex a + a/2 = 3a/2)

129 > Divisible by 3 >>>>>>>>>>>> Answer = D
89 > Not divisible by 3
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Re: Each digit in the two-digit number G is halved to form a new [#permalink] New post 04 Mar 2014, 18:48
prsnt11 wrote:
Let H be the 2-digit number xy (actually 10x+y). Then G must be 2x2y (actually 10(2x) + 2y or 2(10x+y). In other words, the digits of G must be even single-digit numbers. The maximum value of G can be 88 and thereby H can be 44.
Therefore, maximum value of G+H = 132. Therefore, A & B are out.
Now G+H = 3(10x+y) implies, G+H must be a multiple of 3. Only D among the remaining answer choices is a multiple of 3. So D is the answer.



C is also eliminated
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Re: Each digit in the two-digit number G is halved to form a new [#permalink] New post 12 Mar 2015, 06:53
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Each digit in the two-digit number G is halved to form a new [#permalink] New post 13 Mar 2015, 02:11
u2lover wrote:
Each digit in the two-digit number G is halved to form a new two-digit number H. Which of the following could be the sum of G and H?

A. 153
B. 150
C. 137
D. 129
E. 89


let G = 10a+b
=> H = (10a+b)/2
G+H = (3/2)*(10a+b)

out of the options C and E go out as they are not divisible by 3.

substitute other options and try...

1) 153 = 3/2*G
=> G = a three digit number (goes out)

2) G = a three digit number (goes out)

4) no need to check but just to be sure...
G = 86
H = 43
G+H = 129
correct.

takes less than a minute to solve....
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Re: Each digit in the two-digit number G is halved to form a new [#permalink] New post 28 May 2015, 20:24
Each of digits in a 2 digit number when halved gives another number. This means both the digits must be even. Possible combinations are as follows:
Digit Half sum
---------- ---- -----
8 4 12
6 3 9
4 2 6
2 1 3

Looking at choices only 129 is the possible answer : numbers being 86 & 43.
Re: Each digit in the two-digit number G is halved to form a new   [#permalink] 28 May 2015, 20:24

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