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

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

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New post 26 Jun 2017, 23:16
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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

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Re: The three-digit integer kss is the sum of the two-digit integers ks an  [#permalink]

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New post 26 Jun 2017, 23:38
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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
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Re: The three-digit integer kss is the sum of the two-digit integers ks an  [#permalink]

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New post 26 Jun 2017, 23:47
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.
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Re: The three-digit integer kss is the sum of the two-digit integers ks an  [#permalink]

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New post 27 Jun 2017, 00:23
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

Hence Answer B
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The three-digit integer kss is the sum of the two-digit integers ks an  [#permalink]

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New post 02 Nov 2018, 02:57
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.

Answer = B

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Re: The three-digit integer kss is the sum of the two-digit integers ks an  [#permalink]

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New post 06 Nov 2018, 04:37
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
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Re: The three-digit integer kss is the sum of the two-digit integers ks an &nbs [#permalink] 06 Nov 2018, 04:37
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