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# What is the value of positive integer m? (1) The remainder when any

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Math Expert
Joined: 02 Sep 2009
Posts: 51263
What is the value of positive integer m? (1) The remainder when any  [#permalink]

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03 Jul 2018, 10:00
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2
00:00

Difficulty:

85% (hard)

Question Stats:

35% (01:58) correct 65% (01:59) wrong based on 48 sessions

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What is the value of positive integer m?

(1) The remainder when any integer is divided by m is less than 5.
(2) The remainder when any integer is divided by m is an even number.

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Joined: 02 Aug 2009
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Re: What is the value of positive integer m? (1) The remainder when any  [#permalink]

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03 Jul 2018, 10:52
What is the value of positive integer m?

(1) The remainder when any integer is divided by m is less than 5.
so m could be any number 1,2,3,4 or 5
for example 5 will always leave a remainder from 0 to 4
insuff

(2) The remainder when any integer is divided by m is an even number.
HOW can this be possible ??? ----ANY integer
it can only be when the even number left is 0 and all integers are div by ONLY1
so m=1
suff

B
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: What is the value of positive integer m? (1) The remainder when any  [#permalink]

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05 Jul 2018, 03:26
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Solution

Given:
• ‘m’ is a positive integer

To find:
• The value of ‘m’

Approach and Working:
• ‘m’ is a positive integer => m ≥ 1
• When a number is divided by m, the range of the remainder is from 0 to (m-1)
• For example,
o When any number is divided by 5, the possible values of remainder are: 0, 1, 2, 3 and 4
o When divided by 6, the possible values of remainder are: 0, 1, 2, 3, 4 and 5

Analysing Statement 1
“The remainder when any integer is divided by m is less than 5”
• From this statement, we can infer that m is a positive integer less than 6
o For the remainder to always be less than 5, ‘m’ can at most be equal to 5
o Thus, m could be 1, 2, 3, 4 or 5
• However, we cannot find a unique value of ‘m’
• Therefore, Statement (1) ALONE is not sufficient to answer this question

Analysing Statement 2
“The remainder when any integer is divided by m is an even number”
• For the remainder to always be even, when any number is divided by m,
o All the integers from 0 to m-1 should be even, where m is a positive integer
o This is possible only when m =1
• Therefore, Statement (2) ALONE is sufficient to answer this question

Hence, the correct answer is option B.

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Re: What is the value of positive integer m? (1) The remainder when any &nbs [#permalink] 05 Jul 2018, 03:26
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