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What is the least positive integer which when divided by 2, 3, 4, 5 an
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16 Dec 2021, 03:11
16 Dec 2021, 03:11
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What is the least positive integer which when divided by 2, 3, 4, 5 and 6 leaves 1, 2, 3, 4 and 5 as remainders, respectively, but when divided by 7 leaves no remainder ?
(A) 109
(B) 119
(C) 126
(D) 154
(E) 210
(A) 109
(B) 119
(C) 126
(D) 154
(E) 210
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Re: What is the least positive integer which when divided by 2, 3, 4, 5 an
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16 Dec 2021, 04:39
16 Dec 2021, 04:39
Carcass wrote:
What is the least positive integer which when divided by 2, 3, 4, 5 and 6 leaves 1, 2, 3, 4 and 5 as remainders, respectively, but when divided by 7 leaves no remainder ?
(A) 109
(B) 119
(C) 126
(D) 154
(E) 210
(A) 109
(B) 119
(C) 126
(D) 154
(E) 210
Let's deal with each piece of information individually.
We are told that, when the number is divided by 2, the remainder is 1.
This tells us that the number must be ODD, which means we can eliminate answer choices C, D and E they are all EVEN.
We're also told that, when the number is divided by 7, the reminder is 0.
In other words, the number must be divisible by 7.
Let's check the two remaining answer choices...
109 is NOT divisible by 7, which means we can eliminate answer choice A.
119 IS divisible by 7, so the correct answer must be B.
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Re: What is the least positive integer which when divided by 2, 3, 4, 5 an
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02 Oct 2022, 10:31
02 Oct 2022, 10:31
We need to find What is the least positive integer which when divided by 2, 3, 4, 5 and 6 leaves 1, 2, 3, 4 and 5 as remainders, respectively, but when divided by 7 leaves no remainder
Number when divided by 2 gives 1 remainder
=> Number is odd
Only odd choices are A and B
Number when divided by 3 gives 1 remainder
Remainder of 109 when divided by 3 = Remainder of (1+0+9) when divided by 3 = Remainder of 10 when divided by 3 = 1 => FALSE
So, Answer will be B
Hope it helps!
Watch the following video to learn the Basics of Divisibility Rules
Watch the following video to learn the Basics of Remainders
Number when divided by 2 gives 1 remainder
=> Number is odd
Only odd choices are A and B
Number when divided by 3 gives 1 remainder
Remainder of 109 when divided by 3 = Remainder of (1+0+9) when divided by 3 = Remainder of 10 when divided by 3 = 1 => FALSE
So, Answer will be B
Hope it helps!
Watch the following video to learn the Basics of Divisibility Rules
Watch the following video to learn the Basics of Remainders
