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# Let m, n and k be digits, where m + n = k. What is k?

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Math Expert
Joined: 02 Sep 2009
Posts: 58445
Let m, n and k be digits, where m + n = k. What is k?  [#permalink]

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15 Dec 2016, 04:44
2
4
00:00

Difficulty:

45% (medium)

Question Stats:

53% (00:59) correct 47% (00:59) wrong based on 138 sessions

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Let m, n and k be digits, where m + n = k. What is k?

(1) m = 4
(2) n > m

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Joined: 13 Oct 2016
Posts: 359
GPA: 3.98
Re: Let m, n and k be digits, where m + n = k. What is k?  [#permalink]

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15 Dec 2016, 05:19
3
Bunuel wrote:
Let m, n and k be digits, where m + n = k. What is k?

(1) m = 4
(2) n > m

We have set of digits to choose from {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

$$m + n = k$$

(1) $$m=4$$ It can be $$(4 + 0), (4 + 1), (4 + 2)$$ ... till $$(4 + 5)$$ Insufficient

(2) $$n > m$$ Again it can be $$(0 + 1), (1 + 5)$$ etc. Clearly insufficient.

(1) & (2) together: If $$m = 4$$ and $$n > m$$ than only option awailable for n can me 5. And our k = 4 + 5 = 9 Sufficient.

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Re: Let m, n and k be digits, where m + n = k. What is k?  [#permalink]

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15 Dec 2016, 06:05
1
Option C)

Given: m, n & k are all digits "or" Simplifying - m, n & k can have any possible value from set [0,9].
Also, m + n = k; k = ?

I: m = 4
: 4 + n = k; as 0 <= n <= 9
:for n = 0, k = 4
:n= 1, k =5
: ...
multiple values possible
Insufficient

II: n > m
: m + n = k
:for m = 0; n = 1 or 2 or 3 or 4 or 5 or 6 . . .
:m = 1; n = 2 or 3 or 4 or 5 or 6 . . .
multiple values possible
Insufficient

I + II:
:m = 4 and n > m
: 4 < n <= 9
: k = m + n = 4 + n
: for n = 5, k = 4 + 5 = 9 and being a digit, max. possible value k can take is 9.
Sufficient.
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Re: Let m, n and k be digits, where m + n = k. What is k?  [#permalink]

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02 May 2017, 15:35
Bunuel wrote:
Let m, n and k be digits, where m + n = k. What is k?

(1) m = 4
(2) n > m

since we speak about digits, the only value that m, n, and k can take are: 0 1 2 3 4 5 6 7 8 9

1. m=4. we don't know anything about n. if n=1 then k=5. if n=2, then k=6. not sufficient.
2. n>m. if m=1, then n can be anything from 2 to 8. if m=2, then n can be anything from 3 to 7. not sufficient.

1+2.
m=4, and n>m. since k must be a digit, and since the maximum value n can take is 5, so as for k to be a digit itself and satisfy the condition, we know for sure that m=5, and k=9.
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Re: Let m, n and k be digits, where m + n = k. What is k?  [#permalink]

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19 Feb 2019, 04:59
Bunuel wrote:
Let m, n and k be digits, where m + n = k. What is k?

(1) m = 4
(2) n > m

All m, n and k are digits

Now m + n =k

from 1, m= 4, n can be 1,2,3,4,5 for k to be 5,6,7,8,9

from 2, n>m, nothing is required

Combination
Only one value

4 + 5 = 9

C
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Re: Let m, n and k be digits, where m + n = k. What is k?   [#permalink] 19 Feb 2019, 04:59
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