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# If 42.42 = k(14 + m/50), where k and m are positive integers and m < 5

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Math Expert
Joined: 02 Sep 2009
Posts: 44600
If 42.42 = k(14 + m/50), where k and m are positive integers and m < 5 [#permalink]

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22 May 2016, 14:48
Expert's post
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Difficulty:

45% (medium)

Question Stats:

68% (02:04) correct 32% (02:11) wrong based on 174 sessions

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If 42.42 = k(14 + m/50), where k and m are positive integers and m < 50, then what is the value of k + m ?

(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
[Reveal] Spoiler: OA

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Joined: 26 Mar 2013
Posts: 1612
Re: If 42.42 = k(14 + m/50), where k and m are positive integers and m < 5 [#permalink]

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22 May 2016, 16:57
5
KUDOS
Bunuel wrote:
If 42.42 = k(14 + m/50), where k and m are positive integers and m < 50, then what is the value of k + m ?

(A) 6
(B) 7
(C) 8
(D) 9
(E) 10

42.42 = 14K + Km/50...we can rewrite the number as follows:

42+ 0.42= 14K + Km/50........Since K is integer, then 42=14K..........K=3

0.42=Km/50......42/100=3m/50......m=7

k+m=3+7=10

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Joined: 25 Apr 2016
Posts: 25
Concentration: Entrepreneurship, Marketing
Re: If 42.42 = k(14 + m/50), where k and m are positive integers and m < 5 [#permalink]

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31 May 2017, 19:54
Mo2men wrote:
Bunuel wrote:
If 42.42 = k(14 + m/50), where k and m are positive integers and m < 50, then what is the value of k + m ?

(A) 6
(B) 7
(C) 8
(D) 9
(E) 10

42.42 = 14K + Km/50...we can rewrite the number as follows:

42+ 0.42= 14K + Km/50........Since K is integer, then 42=14K..........K=3

0.42=Km/50......42/100=3m/50......m=7

k+m=3+7=10

As in , how is 42.42 = 42 + 0.42?
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Joined: 22 Aug 2013
Posts: 1021
Location: India
Re: If 42.42 = k(14 + m/50), where k and m are positive integers and m < 5 [#permalink]

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31 May 2017, 23:06
3
KUDOS
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42.42 = 42 + 0.42 = 42 + 42/100 = 42 + 21/50

Now this slightly resembles the right hand side, but still we need to change it to the form: k (14+m/50)
where k and m are positive integers. And we can see that 42 = 14*3

So, 42 + 21/50 = 3 (14 + 7/50) ... (taking out 3 common)
Hence k=3, m=7. Required sum = 3+7 = 10.

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Joined: 26 Mar 2013
Posts: 1612
Re: If 42.42 = k(14 + m/50), where k and m are positive integers and m < 5 [#permalink]

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01 Jun 2017, 03:10
ishitam wrote:
Mo2men wrote:
Bunuel wrote:
If 42.42 = k(14 + m/50), where k and m are positive integers and m < 50, then what is the value of k + m ?

(A) 6
(B) 7
(C) 8
(D) 9
(E) 10

42.42 = 14K + Km/50...we can rewrite the number as follows:

42+ 0.42= 14K + Km/50........Since K is integer, then 42=14K..........K=3

0.42=Km/50......42/100=3m/50......m=7

k+m=3+7=10

As in , how is 42.42 = 42 + 0.42?

It is the same when you say 3.5. It is sum of 3 plus 0.5 . Part of the number is integer number (42) and part is decimal number (0.42)

Hope it helps.
Manager
Joined: 04 Jan 2016
Posts: 167
Location: United States (NY)
GMAT 1: 620 Q44 V32
GMAT 2: 600 Q48 V25
GMAT 3: 660 Q42 V39
GPA: 3.48
Re: If 42.42 = k(14 + m/50), where k and m are positive integers and m < 5 [#permalink]

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04 Jun 2017, 09:06
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We have

$$\frac{4242}{100}= 14k+\frac{km}{50} => 4242 = 1400k + \frac{100km}{50} => 4200+42 = 1400*(3) + 2km => 4200 + 42 = 4200 + 2(3)m => 42=6m => m=\frac{42}{6}=7$$

Therefore,$$m+k=3+7=10$$

Option E

In the beginning, it might seems rough but practice brings all to life.

Please Kudos should you like the detailed solution.
Manager
Joined: 22 May 2015
Posts: 102
Re: If 42.42 = k(14 + m/50), where k and m are positive integers and m < 5 [#permalink]

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28 Jul 2017, 20:24
42.42 = 4242/100 = 2121/50 = 14K + KM/50 = (14K*50+KM)/50

=> 2121 = 14K*50 + KM = K(700+M)
3*7*101 = K(700+M)
Since M < 50

3*707=K(700+M)

K =3 M=7 => K+M = 10
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Re: If 42.42 = k(14 + m/50), where k and m are positive integers and m < 5 [#permalink]

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28 Jul 2017, 22:54
1
KUDOS
Bunuel wrote:
If 42.42 = k(14 + m/50), where k and m are positive integers and m < 50, then what is the value of k + m ?

(A) 6
(B) 7
(C) 8
(D) 9
(E) 10

42.42 = k(14+m/50 )
42 = 14k and 0.42 = km/50
-> k = 3

also
0.42 = 3*m/50
m = 7

k+m = 10

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Re: If 42.42 = k(14 + m/50), where k and m are positive integers and m < 5 [#permalink]

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18 Mar 2018, 18:44
Hi All,

This question has a number of built-in 'limitations' that you can take advantage of that will allow you to really minimize the amount of math that is required.

We're told that K and M are POSITIVE INTEGERS and M < 50.

We're also told that 42.42 = K(14+m/50), which we can rewrite as…

42.42 = 14K + KM/50

Since both variables are positive integers, K MUST be 1, 2, or 3 (otherwise the total would be larger than 42.42…

Since M < 50, then M/50 is < 1, so it's likely that K = 3. This tells us that…

.42 = 3M/50

Now the math will only take a few steps…

21 = 3M

7 = M

The value of K + M = 10

[Reveal] Spoiler:
E

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Re: If 42.42 = k(14 + m/50), where k and m are positive integers and m < 5   [#permalink] 18 Mar 2018, 18:44
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