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# For integer n, f(n) denotes the remainder when n is divided by integer

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Math Expert
Joined: 02 Sep 2009
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For integer n, f(n) denotes the remainder when n is divided by integer  [#permalink]

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21 Mar 2019, 02:51
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Difficulty:

95% (hard)

Question Stats:

21% (04:00) correct 79% (02:30) wrong based on 28 sessions

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For integer n, f(n) denotes the remainder when n is divided by integer k. Is k greater than 10?

(1) f(k + 32) = 8

(2) f(k + 42) = 6

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For integer n, f(n) denotes the remainder when n is divided by integer  [#permalink]

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21 Mar 2019, 02:58
Bunuel wrote:
For integer n, f(n) denotes the remainder when n is divided by integer k. Is k greater than 10?

(1) f(k + 32) = 8

(2) f(k + 42) = 6

Questions dealing with remainders are usually solved Logically, via fundamental properties of integers.

(1) The remainder of k when divided by k is 0, so f(k+32) = f(k)+f(32) = f(32) = 8. Since the remainder is always smaller than the number you're dividing by, then k > 8. So we only have to check 9 and 10: the remainder of 32 divided by 9 is 5 and that of 32 divided by 10 is 2. So k > 10.
Sufficient.

(2) Similarly to the above, f(42) = 6. So k > 6. If k = 7, then f(42) = 0, if k = 8, then f(42) = 5, if k = 9, f(42) = 6. So k < 10 is possible. Additionally, if k = 36 then f(42) = 6. So k > 10 is possilbe.
Insufficient.

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Re: For integer n, f(n) denotes the remainder when n is divided by integer  [#permalink]

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21 Mar 2019, 03:09
Bunuel wrote:
For integer n, f(n) denotes the remainder when n is divided by integer k. Is k greater than 10?

(1) f(k + 32) = 8

(2) f(k + 42) = 6

#1
f(k + 32) = 8
will true at k = 12,24..
sufficient so k>10
#2
f(k + 42) = 6
will be true at k=9,12
so k is not>10
IMO A
Re: For integer n, f(n) denotes the remainder when n is divided by integer   [#permalink] 21 Mar 2019, 03:09
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