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Re: m is a three-digit integer such that when it is divided by [#permalink]
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This question is quite tricky.

However, 99% of the time, the more a tricky question is, the more there is always a shortcut or at a closer inspection a solution is suddenly behind the curve.

Reading carefully the stem, it says that you have to consider a 3 digit integer number and you have to find the least possible value.

So, a 3 digit number at least is 100. Now, you do also know that when it is divided by 5 y is the remainder and when it is divided by 7 is yet y the remainder, which means is the same number.

A common number that divides evenly 7 and 5 is 105. 105 divided by 5 AND 7 has no rest or reminder. From this is easy to think that a number divided by both 5 and 7 with the same reminder y, for instance, the reminder is 1, is 106.

106 is the least number with 3 digits you can have when you divide it by 5 and 7.

Hope this helps
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Re: m is a three-digit integer such that when it is divided by [#permalink]
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We have m=5a+y=7b+y where 0<y<5 -> m=35c+y where 0<y<5 (hence min y = 1).

Note that 35*3=105 -> m=35*3+1=106.
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m is a three-digit integer such that when it is divided by [#permalink]
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LCM of 5 and 7 is 35.
The least possible 3 digit number is 105.

Then the only possible smallest possible value of m is 106, which leave the same remainder when divided by 5 and 7.

Hence 106 is the answer
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Re: m is a three-digit integer such that when it is divided by [#permalink]
The way to solve this problem is to realize that if you solve for the least common multiple of 5 and 7 that has 3 digits, it leaves you with 105. If you divide 105 by 5 and 7 your remainder is 0. If you add one to 105 = 106, then your remainder is 1 for both values.
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Re: m is a three-digit integer such that when it is divided by [#permalink]
Simple: Three digit numbers start from 100, and go as 100, 101, 102, 103, 104, 105, 106,....

Remember that the remainder should always be lesser than divisor. Thus y should be lesser than 5 and 7. Note that Smallest possible positive remainder is always 1. Thus look for numbers in the above sequence that when divided by 5 and 7 yield remainder 1. Thus 106 is the answer.
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Re: m is a three-digit integer such that when it is divided by [#permalink]
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Re: m is a three-digit integer such that when it is divided by [#permalink]
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