What is the smallest integer greater than 1 that leaves a remainder of 1 when divided by any of the integers 6, 8, and 10?
A) 21
B) 41
C) 121
D) 241
E) 481
The OA is C.
How can I get the correct answer? I don't know how to can I do it.
What is the smallest integer greater than 1
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The remainder is 1 when the integer is divided by 6Vincen wrote:What is the smallest integer greater than 1 that leaves a remainder of 1 when divided by any of the integers 6, 8, and 10?
A) 21
B) 41
C) 121
D) 241
E) 481
Check the answer choices...
A) 21 divided by 6 equals 3 with remainder 3. ELIMINATE A
B) 41 divided by 6 equals 6 with remainder 5. ELIMINATE B
C) 121 divided by 6 equals 20 with remainder 1. KEEP C
D) 241 divided by 6 equals 40 with remainder 1. KEEP D
C) 481 divided by 6 equals 80 with remainder 1. KEEP E
The remainder is 1 when the integer is divided by 8
C) 121 divided by 8 equals 15 with remainder 1. KEEP C
D) 241 divided by 8 equals 30 with remainder 1. KEEP D
C) 481 divided by 8 equals 60 with remainder 1. KEEP E
The remainder is 1 when the integer is divided by 10
C) 121 divided by 10 equals 1 with remainder 1. KEEP C
Since the question asks for the SMALLEST integer, and since we've already eliminated A and B (numbers that are both smaller than 121), we can be certain that the correct answer is C
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You could also find the LCM of 6, 8, and 10, then add 1 to it.
This trick generalizes well to other such remainder problems too!
This trick generalizes well to other such remainder problems too!
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The key to solving this problem is to find the least common multiple (LCM) of 6, 8, and 10, since the LCM of these three numbers will leave a remainder of 0 when divided by each of them. Since the LCM of 6, 8, and 10 is 120, the smallest number that leaves a remainder of 1 when divided by any of these numbers is 121.Vincen wrote:What is the smallest integer greater than 1 that leaves a remainder of 1 when divided by any of the integers 6, 8, and 10?
A) 21
B) 41
C) 121
D) 241
E) 481
Alternate Solution:
We can try each answer choice starting from the smallest one. We see that answer choice A does not meet the given criteria, since 21 divided by 6 leaves a remainder of 3. We see that answer choice B does not meet the given criteria either, since 41 divided by 6 leaves a remainder of 5. Since 121 leaves a remainder of 1 when divided by 6, 8, and 10, and since we are looking for the smallest such number, that is the number we are looking for.
Answer: C
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