Author 
Message 
TAGS:

Hide Tags

Board of Directors
Joined: 17 Jul 2014
Posts: 2729
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

Re: Each digit in the twodigit number G is halved to form a new [#permalink]
Show Tags
23 Dec 2015, 19:08
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.



Manager
Joined: 17 Jun 2015
Posts: 240
GMAT 1: 540 Q39 V26 GMAT 2: 680 Q46 V37

Re: Each digit in the twodigit number G is halved to form a new [#permalink]
Show Tags
28 Dec 2015, 12:56
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
_________________
Fais de ta vie un rêve et d'un rêve une réalité



Intern
Joined: 12 Oct 2015
Posts: 3

Each digit in the twodigit number G is halved to form a new [#permalink]
Show Tags
12 Mar 2016, 16:21
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



Manager
Joined: 09 Aug 2016
Posts: 68

Re: Each digit in the twodigit number G is halved to form a new [#permalink]
Show Tags
12 Jan 2017, 13:48
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.



Intern
Joined: 09 Nov 2015
Posts: 30

Re: Each digit in the twodigit number G is halved to form a new [#permalink]
Show Tags
22 Feb 2017, 23:55
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.



Manager
Joined: 03 Jan 2017
Posts: 180

Re: Each digit in the twodigit number G is halved to form a new [#permalink]
Show Tags
12 Mar 2017, 13:26
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



Intern
Joined: 26 Jan 2017
Posts: 3
Location: United States
GPA: 3.5

Re: Each digit in the twodigit number G is halved to form a new [#permalink]
Show Tags
20 Apr 2017, 00:53
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



Intern
Joined: 23 Nov 2017
Posts: 1

Re: Each digit in the twodigit number G is halved to form a new [#permalink]
Show Tags
28 Dec 2017, 08:47
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.



Intern
Joined: 28 Oct 2015
Posts: 15

Re: Each digit in the twodigit number G is halved to form a new [#permalink]
Show Tags
28 Dec 2017, 14:31
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)
Sent from my iPhone using GMAT Club Forum



Manager
Joined: 23 Oct 2017
Posts: 64

Re: Each digit in the twodigit number G is halved to form a new [#permalink]
Show Tags
28 Dec 2017, 19:04
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



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2570

Re: Each digit in the twodigit number G is halved to form a new [#permalink]
Show Tags
24 Jan 2018, 10:39
u2lover wrote: Each digit in the twodigit number G is halved to form a new twodigit number H. Which of the following could be the sum of G and H?
A. 153 B. 150 C. 137 D. 129 E. 89 We can let a = the tens digit of H and b = units digit of H; thus, H = 10a + b and G = 20a + 2b and the sum of H and G is: H + G = (10a + b) + (20a + 2b) = 30a + 3b = 3(10a + b) = 3H Since the sum G + H is a multiple of 3, we can eliminate choices C and E. Now let’s analyze the remaining three choices: A) 153 3H = 153 H = 51 and G = 102 However, G is a twodigit number, so A couldn’t be the answer. B) 150 3H = 150 H = 50 and G = 100 However, G is a twodigit number, so B couldn’t be the answer. Therefore, the answer must be D. Let’s verify it anyway. D) 129 3H = 129 H = 43 and G = 86 Answer: D
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions




Re: Each digit in the twodigit number G is halved to form a new
[#permalink]
24 Jan 2018, 10:39



Go to page
Previous
1 2 3
[ 51 posts ]



