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What is the remainder when integer n is divided by 10?

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Bunuel
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What is the remainder when integer n is divided by 10? [#permalink] New post  01 May 2019, 02:14
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What is the remainder when integer n is divided by 10?

(1) When n is divided by 110 the remainder is 75.
(2) When n is divided by 100 the remainder is 25.
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What is the remainder when integer n is divided by 10? [#permalink] New post  Updated on: 01 May 2019, 02:41
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Bunuel wrote:
What is the remainder when integer n is divided by 10?

(1) When n is divided by 110 the remainder is 75.
(2) When n is divided by 100 the remainder is 25.


#1
n=110a+75
unit digits always ; 5 remainder is 5 sufficient
#2
n=100b+25
unit digits always ; 5 remainder is 5 sufficient
IMO D

Originally posted by Archit3110 on 01 May 2019, 02:29.
Last edited by Archit3110 on 01 May 2019, 02:41, edited 1 time in total.
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Re: What is the remainder when integer n is divided by 10? [#permalink] New post  01 May 2019, 02:39
From (1)

n can be 75, 185, 295, 405 and so on

From (2)

n can be 25, 125, 225, 325, 425 and so on

In both cases, n/10 will leave a remainder of 5

Answer is (D)

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Re: What is the remainder when integer n is divided by 10? [#permalink] New post  01 May 2019, 02:47
Archit3110

What is the remainder when integer n is divided by 10? ==>What is the Unit digit of the number. In both the cases we can find out the unit digit.

I think D is the answer
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Re: What is the remainder when integer n is divided by 10? [#permalink] New post  31 Jan 2020, 08:05
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Bunuel wrote:
What is the remainder when integer n is divided by 10?

(1) When n is divided by 110 the remainder is 75.
(2) When n is divided by 100 the remainder is 25.


Target question: What is the remainder when integer n is divided by 10?

REPHRASED target question: What is the UNITS DIGIT of n?

Statement 1: When n is divided by 110 the remainder is 75.
In other words: n = 110k + 75 (for some integer k)
Since 110k will have units digit 0 for ANY integer k, we know that 110k + 75 MUST have a units digit of 5
In other words, n MUST have a units digit of 5
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: When n is divided by 100 the remainder is 25
In other words: n = 100k + 25 (for some integer k)
Since 100k will have units digit 0 for ANY integer k, we know that 100k + 25 MUST have a units digit of 5
In other words, n MUST have a units digit of 5
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

Answer: D

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Re: What is the remainder when integer n is divided by 10? [#permalink] New post  07 Dec 2020, 14:32
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Bunuel wrote:
What is the remainder when integer n is divided by 10?

(1) When n is divided by 110 the remainder is 75.
(2) When n is divided by 100 the remainder is 25.



(1)\( n=110x+75; 75, 185;\) if these 75 or 185 are divided by 10 the remainder will be 5. Sufficient.

(2) \(n=100x+25; 25, 125;\) if these 25 or 125 are divided by 10 the remainder will be 5. Sufficient.

The answer is \(D\)
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Re: What is the remainder when integer n is divided by 10? [#permalink]
07 Dec 2020, 14:32
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