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

 It is currently 14 Oct 2019, 15:59

### 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

# The three-digit integer kss is the sum of the two-digit integers ks an

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58320
The three-digit integer kss is the sum of the two-digit integers ks an  [#permalink]

### Show Tags

27 Jun 2017, 00:16
3
11
00:00

Difficulty:

45% (medium)

Question Stats:

69% (02:21) correct 31% (02:09) wrong based on 200 sessions

### HideShow timer Statistics

The three-digit integer kss is the sum of the two-digit integers ks and rs, where k, r, and s are the digits of the integers. Which of the following must be true?

I. k = 2
II. r = 9
III. s = 5

A. I only
B. II only
C. III only
D. I and II
E. II and III

_________________
Current Student
Joined: 18 Aug 2016
Posts: 612
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
Re: The three-digit integer kss is the sum of the two-digit integers ks an  [#permalink]

### Show Tags

27 Jun 2017, 00:38
2
4
Bunuel wrote:
The three-digit integer kss is the sum of the two-digit integers ks and rs, where k, r, and s are the digits of the integers. Which of the following must be true?

I. k = 2
II. r = 9
III. s = 5

A. I only
B. II only
C. III only
D. I and II
E. II and III

From the question we can identify the value of s

since ks + rs = kss

s cannot be 1,2,3,4,5,6,7,8,9 (1+1=2, 2+2=4,3+3=6,4+4=8,5+5=0,6+6=2,7+7=4,8+8=6,9+9=8)
s can only be 0

now since a three digit number has to be broken down to two two digit numbers, we cannot exceed 200
hence k can take only 1 or 2
k=1
100 = 10 + 90 (k=1,s=0,r=9)
k=2
200 = 20 + 180..not possible

Hence
only II r=9 must be true

B
_________________
We must try to achieve the best within us

Thanks
Luckisnoexcuse
##### General Discussion
Director
Joined: 13 Mar 2017
Posts: 728
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: The three-digit integer kss is the sum of the two-digit integers ks an  [#permalink]

### Show Tags

27 Jun 2017, 00:47
1
Bunuel wrote:
The three-digit integer kss is the sum of the two-digit integers ks and rs, where k, r, and s are the digits of the integers. Which of the following must be true?

I. k = 2
II. r = 9
III. s = 5

A. I only
B. II only
C. III only
D. I and II
E. II and III

Number kss =100k+10s +s
Number ks = 10k+s
Number rs = 10r+s

So, 100k + 10s + s = 10k + s +10r + s
-> 90 k + 9s = 10 r

-> r = 9 (10k + s)/10

To make r an integer s must be a multiple of 10, So s = 0 (to cancel 10 in denominator).
we can't take s as 5 since if s = 5 , r = 9*5(2k+1)/10 . So it won't result an integer r.

Now, if s = 0 , r = 9(10k+0)/10 = 9k
So r i a multiple of 9, r= 0 or 9 . But r can't be 0 as it is tens digit, also if r = 0, then k =0 (not possible)

So r = 9
-->9k = 9
--> k =1

So the values are k = 1 , r = 9 , s = 0

hence only II is correct .. Answer B.

We can't solve it by plugging values in first go as, we have 3 unknowns. So we need to simplify it by common logic and then we can put the values and check..

Anyway it was a tricky but nice question.
Hope you like the solution, appreciate it my clicking kudos below.
_________________
CAT 2017 (98.95) & 2018 (98.91) : 99th percentiler
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu

Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)

What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".
Senior Manager
Joined: 28 May 2017
Posts: 281
Concentration: Finance, General Management
Re: The three-digit integer kss is the sum of the two-digit integers ks an  [#permalink]

### Show Tags

27 Jun 2017, 01:23
1
Bunuel wrote:
The three-digit integer kss is the sum of the two-digit integers ks and rs, where k, r, and s are the digits of the integers. Which of the following must be true?

I. k = 2
II. r = 9
III. s = 5

A. I only
B. II only
C. III only
D. I and II
E. II and III

k s
+ r s
--------
k s s
-------
Only one value of s would suffice before mentioned condition, "s" has to be 0

Since s = 0, there would not be any carry over, we can safely assume
k
+ r
--------
k s
-------

Only one value of k & r would suffice before mentioned condition, "k" & "r" have to be 1 & 9 respectively

_________________
If you like the post, show appreciation by pressing Kudos button
Manager
Joined: 21 Jun 2018
Posts: 71
The three-digit integer kss is the sum of the two-digit integers ks an  [#permalink]

### Show Tags

02 Nov 2018, 03:57
The max value of kss would be 198. since sum of biggest 2 digit nos. is 99 +99 = 198.

Hence the hundreth's place is 1. k = 1

s = 0 since the sum of 2 digits such that the output is the same has to be 0.

______________________________________________________________________________________

Kudosity killed the Kat, But I would appreciate it if you showed me some
_________________
_______________________________________________________________________________________________________
Please give Kudos. Kudos encourage active discussions and help the community grow.
Manager
Joined: 29 May 2017
Posts: 125
Location: Pakistan
Concentration: Social Entrepreneurship, Sustainability
Re: The three-digit integer kss is the sum of the two-digit integers ks an  [#permalink]

### Show Tags

06 Nov 2018, 05:37
shashankism wrote:
Bunuel wrote:
The three-digit integer kss is the sum of the two-digit integers ks and rs, where k, r, and s are the digits of the integers. Which of the following must be true?
So, 100k + 10s + s = 10k + s +10r + s
-> 90 k + 9s = 10 r

-> r = 9 (10k + s)/10

To make r an integer s must be a multiple of 10, So s = 0 (to cancel 10 in denominator).
we can't take s as 5 since if s = 5 , r = 9*5(2k+1)/10 . So it won't result an integer r.

really good solution......but i do have a question.....

why cant s be 20 or 30 and so on..since all these will result in an integer too.

regards
Re: The three-digit integer kss is the sum of the two-digit integers ks an   [#permalink] 06 Nov 2018, 05:37
Display posts from previous: Sort by