Different breeds of dogs get older at different rates in dog years.

Question

Different breeds of dogs get older at different rates in “dog years.” Livonian wolfhounds age 7 times as fast as humans, whereas Khazarian terriers age 5 times as fast and Akkadian retrievers age 4 times as fast. If Dan bought a newborn Akkadian on January 1, 2010, a newborn Khazarian 1 year later, and a newborn Livonian 1 year after that, in what year will the sum of the dog-year ages of the Akkadian and the Khazarian first be exceeded by twice the age of the Livonian in dog years, rounding all ages down to the nearest integer?

A. 2013
B. 2014
C. 2015
D. 2016
E. 2017

Kudos for a correct solution.

A. 2013
B. 2014
C. 2015
D. 2016
E. 2017

Harley1980 · Accepted Answer

Let's  x  denotes number of years. 
Then  L = 7*(x-2) ;  K = 5*(x-1)  and  A = 4x

And we need to find  x  when  K+A<2L 
 5*(x-1) + 4x < 2*(7*(x-2)) 
 5x - 5 + 4x < 14x-28 
 23 < 5x 
Ans as we know  x  is integer so  x  should be  5

2010+5 = 2015 
Answer is C

Bunuel · Answer

MANHATTAN GMAT OFFICIAL SOLUTION:

Create a variable to represent calendar (human) years since January 1, 2012 (the date of the final purchase). If t = 0 in 2012 and 1 in 2013, then t = calendar year since 2012.

Now you can write functions to give you dog-ages for each breed as a function of t.

Akkadian’s age A(t) = 4t + 8 (since the Akkadian is now 4 × 2 = 8 dog-years old on January 1, 2012)

Khazarian’s age K(t) = 5t + 5 (the second 5 is for the one calendar year, or 5 dog-years for the Khazarian, since 2011)

Livonian’s age L(t) = 7t

The sum of A and K is 9t + 13. Twice L is 14t. We are looking for the t at which the sum (9t + 13) is first exceeded by 14t. So the inequality we’re looking for is this:

14t > 9t + 13
5t > 13
t > 2.6

The smallest integer t for which this is true is 3, so the calendar year = 2012 + 3 = 2015.

The correct answer is C.

nitishgera · Answer

You can solve it by making a table using the values given in the question.

The year when 2L exceeds Sum of A & K is 2015

Hence - C

MarkusKarl · Answer

I'm going with C:

I made a chart starting at 2012:
A+K=13
L=0.

Then I added 9 to a+k for each year and 14 to L for each year.

2013:AK=22 L=14
2014:AK=31 L=28
2015:AK=40 L=42

thus, 2015 is the correct answer. => C

peachfuzz · Answer

Livonian wolfhounds age 7 times as fast as humans: 7h
Khazarian terriers age 5 times as fast: 5h
Akkadian retrievers age 4 times as fast: 4h

Only in year 2015 does
Akkadian + Khazarian be less than twice the age of a Livonian
20+20 < 2*21
40<42

Answer: C

D3N0 · Answer

Ans: C
in one year A will age 4 years, K will age 5 years, L will age 7 years

sol: A+k 2L
------------------------
2013 22 14
2014 31 28
2015 40 42

2015 is the answer

MarkusKarl · Answer

After reconsideration, wouldn't the actual event where 2L=K+A come during 2014? At the beginning of 2015 we know that 2L>K+A, so therefore the event should have happened at 2014.

Harley1980 · Answer

All events occur at 1 January. So technically it's 2015 year.

MarkusKarl · Answer

At January 1st 2015, 2L=42 and K+A=40, as such 2L has been more than K+A prior to January 1st 2015.

What am I missing?

Harley1980 · Answer

31 december 2014, 2L=28 and K+A=31

1st January day of birthday all dogs 
At January 1st 2015, 2L=42 and K+A=40

So only at 1 January 2L became bigger than K+A

MarkusKarl · Answer

This would mean that the dogs age only once a year and that time is discreet, not continuous. How am I to interpret the question to get this definition?

MarkusKarl · Answer

Wouldn't L be 364/365*7+14 at the next to last day of 2014? (just to clarify how I interpret the continuous flow of age)

Harley1980 · Answer

I'm not sure, but I think it's common rule. For example when some shop make age restrictions on alcohol sale. They do not use continuous flow of age. There is two possible variants: you are 21 and you can bye product or you fewer than 21 and you can't bye this product. 
And it doesn't matter that today you are 20 and tomorrow will be 21.

MarkusKarl · Answer

I get your point, but I don't think that this is really addressing my concern. I will simply hope that the GMAT will not include such a question when I do my test.

D3N0 · Answer

My take on this is "question says rounding all age down to there nearest integer value, so I rounded the age of Humans also, because it is also included in the question and we are comparing all ages in terms of X*human age. 2014,2015,2016 are the rounded age calculation points.

MarkusKarl · Answer

I interpreted that part differently than you as well. That's what actually made me want to pick 2014 after reconsidering.

I decided to round all ages at the end, and then I was at the end of the year 2014, rounding 2014 down instead of up it would yield 2014 as the answer.

But I'm dropping this now, I am afraid I am confusing people even more with this discussion.

Schloop · Answer

Okay so simply put here the answer is ambigupous. imho, it should be 2014, as we are rounding down all years by their own reference points. I have included below an excel table proving it. We are rounding down years by their own metric, which is the logical interpretation of the language. Calculating by 7ths, we get the following.

0.14285714  
  Years  
  Floor A Age  
  Floor B Age  
  C Age  
  C Age *1  
  SUM A+B  
 
   0  
  
  8  
  5  
  0  
  0  
  13  
 
   1  
  0.14285714  
  8  
  5  
  1  
  2  
  13  
 
   2  
  0.28571429  
  9  
  6  
  2  
  4  
  15  
 
   3  
  0.42857143  
  9  
  7  
  3  
  6  
  16  
 
   4  
  0.57142857  
  10  
  7  
  4  
  8  
  17  
 
   5  
  0.71428571  
  10  
  8  
  5  
  10  
  18  
 
   6  
  0.85714286  
  11  
  9  
  6  
  12  
  20  
 
   7  
  1  
  12  
  10  
  7  
  14  
  22  
 
   8  
  1.14285714  
  12  
  10  
  8  
  16  
  22  
 
   9  
  1.28571429  
  13  
  11  
  9  
  18  
  24  
 
   10  
  1.42857143  
  13  
  12  
  10  
  20  
  25  
 
   11  
  1.57142857  
  14  
  12  
  11  
  22  
  26  
 
   12  
  1.71428571  
  14  
  13  
  12  
  24  
  27  
 
   13  
  1.85714286  
  15  
  14  
  13  
  26  
  29  
 
   14  
  2  
  16  
  15  
  14  
  28  
  31  
 
   15  
  2.14285714  
  16  
  15  
  15  
  30  
  31  
 
   16  
  2.28571429  
  17  
  16  
  16  
  32  
  33  
 
   17  
  2.42857143  
  17  
  17  
  17  
  34  
  34  
 
   18  
  2.57142857  
  18  
  17  
  18  
  36  
  35

Different breeds of dogs get older at different rates in dog years.

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0.14285714	Years	Floor A Age	Floor B Age	C Age	C Age *1	SUM A+B
0		8	5	0	0	13
1	0.14285714	8	5	1	2	13
2	0.28571429	9	6	2	4	15
3	0.42857143	9	7	3	6	16
4	0.57142857	10	7	4	8	17
5	0.71428571	10	8	5	10	18
6	0.85714286	11	9	6	12	20
7	1	12	10	7	14	22
8	1.14285714	12	10	8	16	22
9	1.28571429	13	11	9	18	24
10	1.42857143	13	12	10	20	25
11	1.57142857	14	12	11	22	26
12	1.71428571	14	13	12	24	27
13	1.85714286	15	14	13	26	29
14	2	16	15	14	28	31
15	2.14285714	16	15	15	30	31
16	2.28571429	17	16	16	32	33
17	2.42857143	17	17	17	34	34
18	2.57142857	18	17	18	36	35

GMAT Problem Solving (PS) Questions

Different breeds of dogs get older at different rates in dog years.

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615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

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Perfect 805 Score Debrief by Julia

My Rewards