GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Feb 2019, 19:35

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

## Events & Promotions

###### Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Free GMAT practice

February 15, 2019

February 15, 2019

10:00 PM EST

11:00 PM PST

Instead of wasting 3 months solving 5,000+ random GMAT questions, focus on just the 1,500 you need.

# If 72.42 = k(24+n/100), where k and n are positive integers and n <100

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52905
If 72.42 = k(24+n/100), where k and n are positive integers and n <100  [#permalink]

### Show Tags

06 Feb 2019, 01:35
00:00

Difficulty:

35% (medium)

Question Stats:

44% (00:59) correct 56% (02:29) wrong based on 9 sessions

### HideShow timer Statistics

If $$72.42 = k(24+\frac{n}{100})$$, where k and n are positive integers and n < 100, then k + n =

A 17
B 16
C 15
D 14
E 13

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 7334
Re: If 72.42 = k(24+n/100), where k and n are positive integers and n <100  [#permalink]

### Show Tags

06 Feb 2019, 03:54
1
Bunuel wrote:
If $$72.42 = k(24+\frac{n}{100})$$, where k and n are positive integers and n < 100, then k + n =

A 17
B 16
C 15
D 14
E 13

Let us get both sides in similar terms..

$$72.42 = k(24+\frac{n}{100})$$.....$$72+0.42 =72+\frac{42}{100}=3(24+\frac{14}{100})= k(24+\frac{n}{100})$$
Therefore equating both sides, we get k as 3 and n as 14, so k+n=3+14=17..

A
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

GMAT Expert

VP
Joined: 31 Oct 2013
Posts: 1116
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: If 72.42 = k(24+n/100), where k and n are positive integers and n <100  [#permalink]

### Show Tags

06 Feb 2019, 03:59
Bunuel wrote:
If $$72.42 = k(24+\frac{n}{100})$$, where k and n are positive integers and n < 100, then k + n =

A 17
B 16
C 15
D 14
E 13

**** we know the range of n. we don't have any idea about k. This question is a perfect one for trail and error method.

So, 0<n<100.

when k=1,

$$72.42 = k(24+\frac{n}{100})$$

$$72.42 = 1*(24+\frac{n}{100})$$

n/100 = 48.42

n = 48.42 *100.

n = 4842, which is far beyond our scope.

So, k can't be 1.

when k = 2,

$$72.42 = 2(24+\frac{n}{100})$$

72.42 = 48 + $$\frac{2n}{100}$$

24.42 =$$\frac{2n}{100}$$

2442/2 = n

still n is out side of the range.

k can't be 2.

when k=3,

72.42 = 72 + 3n/100

0.42 = 3n/100

3n = 42

n= 14

14 could be the value of n .

k can'be 4. if we take k=4, we get negative value for n.

So, k = 3. and n=14.

k + n = 3 + 14 = 17.

SVP
Joined: 18 Aug 2017
Posts: 1770
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If 72.42 = k(24+n/100), where k and n are positive integers and n <100  [#permalink]

### Show Tags

06 Feb 2019, 04:11
Bunuel wrote:
If $$72.42 = k(24+\frac{n}{100})$$, where k and n are positive integers and n < 100, then k + n =

A 17
B 16
C 15
D 14
E 13

$$72.42 = k(24+\frac{n}{100})$$

equate both sides
72.42 = 3 *( 24+ 14/100)
k=3 , n= 14
K+N= 17
IMO A
_________________

If you liked my solution then please give Kudos. Kudos encourage active discussions.

Manager
Joined: 09 Jun 2014
Posts: 239
Location: India
Concentration: General Management, Operations
Schools: Tuck '19
Re: If 72.42 = k(24+n/100), where k and n are positive integers and n <100  [#permalink]

### Show Tags

06 Feb 2019, 04:20
chetan2u wrote:
Bunuel wrote:
If $$72.42 = k(24+\frac{n}{100})$$, where k and n are positive integers and n < 100, then k + n =

A 17
B 16
C 15
D 14
E 13

Let us get both sides in similar terms..

$$72.42 = k(24+\frac{n}{100})$$.....$$72+0.42 =72+\frac{42}{100}=3(24+\frac{14}{100})= k(24+\frac{n}{100})$$
Therefore equating both sides, we get k as 3 and n as 14, so k+n=3+14=17..

A

Thanks for the nice solution..

However I wanted to know whats wrong with my approach..

If I adjust the main equation ..I get K= 7242 % (2400+N)

Now I was looking for value of N that will make K as a positive integer..so the value of N was
N=42 (since 2400+ 42 can divide 7242 giving K=3 as positive integer)
However this means N+K= 3+42=45 (Out of range of the options)

With my approach I will and up taking 3 mins in the test and no solution.

Is there any alternative approach to try those problems.

Most important question:How do you identify what approach needs to be taken in these problems.

Math Expert
Joined: 02 Aug 2009
Posts: 7334
Re: If 72.42 = k(24+n/100), where k and n are positive integers and n <100  [#permalink]

### Show Tags

06 Feb 2019, 06:51
prabsahi wrote:
chetan2u wrote:
Bunuel wrote:
If $$72.42 = k(24+\frac{n}{100})$$, where k and n are positive integers and n < 100, then k + n =

A 17
B 16
C 15
D 14
E 13

Let us get both sides in similar terms..

$$72.42 = k(24+\frac{n}{100})$$.....$$72+0.42 =72+\frac{42}{100}=3(24+\frac{14}{100})= k(24+\frac{n}{100})$$
Therefore equating both sides, we get k as 3 and n as 14, so k+n=3+14=17..

A

Thanks for the nice solution..

However I wanted to know whats wrong with my approach..

If I adjust the main equation ..I get K= 7242 % (2400+N)

Now I was looking for value of N that will make K as a positive integer..so the value of N was
N=42 (since 2400+ 42 can divide 7242 giving K=3 as positive integer)
However this means N+K= 3+42=45 (Out of range of the options)

With my approach I will and up taking 3 mins in the test and no solution.

Is there any alternative approach to try those problems.

Most important question:How do you identify what approach needs to be taken in these problems.

You are perfectly fine with the solution, but you have gone wrong in the highlighted part..
$$k=\frac{7242}{2400+n}$$.. Looking at 7242 and 2400 doen below, you should realize 2400*3=7200..
7242 divided by 3 is 2414=2400+14 so our fraction becomes $$3=\frac{7242}{2400+14}$$
k+n=3+14=17
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

GMAT Expert

Manager
Joined: 09 Jun 2014
Posts: 239
Location: India
Concentration: General Management, Operations
Schools: Tuck '19
If 72.42 = k(24+n/100), where k and n are positive integers and n <100  [#permalink]

### Show Tags

06 Feb 2019, 07:00
Let us get both sides in similar terms..

$$72.42 = k(24+\frac{n}{100})$$.....$$72+0.42 =72+\frac{42}{100}=3(24+\frac{14}{100})= k(24+\frac{n}{100})$$
Therefore equating both sides, we get k as 3 and n as 14, so k+n=3+14=17..

A[/quote]

Thanks for the nice solution..

However I wanted to know whats wrong with my approach..

If I adjust the main equation ..I get K= 7242 % (2400+N)

Now I was looking for value of N that will make K as a positive integer..so the value of N was
N=42 (since 2400+ 42 can divide 7242 giving K=3 as positive integer)
However this means N+K= 3+42=45 (Out of range of the options)

With my approach I will and up taking 3 mins in the test and no solution.

Is there any alternative approach to try those problems.

Most important question:How do you identify what approach needs to be taken in these problems.

You are perfectly fine with the solution, but you have gone wrong in the highlighted part..
$$k=\frac{7242}{2400+n}$$.. Looking at 7242 and 2400 doen below, you should realize 2400*3=7200..
7242 divided by 3 is 2414=2400+14 so our fraction becomes $$3=\frac{7242}{2400+14}$$
k+n=3+14=17[/quote]

Just got my mistake.Thank you so much for seeing it through and pointing it out

I guess the mistake was my calculation 2442*3 will give 7326 and not 7242.
If 72.42 = k(24+n/100), where k and n are positive integers and n <100   [#permalink] 06 Feb 2019, 07:00
Display posts from previous: Sort by