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x is an integer such that it leaves a remainder of 2 when divided by 3, leaves a remainder of 3 when divided by 5, and leaves a remainder of 5 when divided by 7. What could be a possible value of x from among the following options?
- a)53
- b)68
- c)74
- d)83
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
x is an integer such that it leaves a remainder of 2 when divided by 3...
According to the given questions, the number is
x = 3P1 + 2
Also, x = 5P2 + 3
and x = 7P3 + 5
From above
x = 3P1 + 2 = 5P2 + 3 = 7P3 + 5
⇒ On solving we get P1 = 22, P2 = 13, P3 = ?
so the solution is x = 68.
x = 3P1 + 2
Also, x = 5P2 + 3
and x = 7P3 + 5
From above
x = 3P1 + 2 = 5P2 + 3 = 7P3 + 5
⇒ On solving we get P1 = 22, P2 = 13, P3 = ?
so the solution is x = 68.
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Community Answer
x is an integer such that it leaves a remainder of 2 when divided by 3...
Explanation:
1. Finding the LCM of 3, 5, and 7:
- The least common multiple (LCM) of 3, 5, and 7 is 105.
2. Checking for x:
- Since x leaves a remainder of 2 when divided by 3, we can express x as 3a + 2.
- Similarly, x can be expressed as 5b + 3 and 7c + 5 based on the given remainders.
3. Setting up equations:
- From the above expressions, we have:
- 3a + 2 = 5b + 3 = 7c + 5
- Solving these equations simultaneously, we get a = 23, b = 17, c = 12.
4. Calculating the value of x:
- Substituting the values of a, b, and c in any of the expressions:
- x = 3(23) + 2 = 69 + 2 = 71
- x = 5(17) + 3 = 85 + 3 = 88
- x = 7(12) + 5 = 84 + 5 = 89
5. Identifying the possible value of x:
- Among the options provided, x = 88 satisfies all the given conditions.
Therefore, the possible value of x from the given options is 68 (option B).
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