In a warehouse inventory system, six different product batches are labelled with the numbers: 55, 61, 85, 92, 95, and 98. The system multiplies all the batch numbers together to generate a tracking key.
Consider the following statements:
Statement I: The product of the six batch numbers is divisible by 25.
Statement II: The remainder when the product is divided by 1000 is zero.

Select the correct answer from below:
(a) Only Statement I is correct.
(b) Only Statement II is correct.
(c) Both Statements I and II are correct.
(d) None of the Statements is correct.

Question

In a warehouse inventory system, six different product batches are labelled with the numbers: 55, 61, 85, 92, 95, and 98. The system multiplies all the batch numbers together to generate a tracking key.
Consider the following statements:
Statement I: The product of the six batch numbers is divisible by 25.
Statement II: The remainder when the product is divided by 1000 is zero.

Select the correct answer from below:
(a) Only Statement I is correct.
(b) Only Statement II is correct.
(c) Both Statements I and II are correct.
(d) None of the Statements is correct.

TutorArc · Accepted Answer

55, 85, and 95 each provide a factor of 5 &rArr; total 3 factors of 5 &rArr; divisible by 125
92 = 2&sup2; &times; 23, 98 = 2 &times; 49 &rArr; total 3 factors of 2 &rArr; divisible by 8
So, product divisible by 8 &times; 125 = 1000
Both Statements I and II are correct.

Hence, option c is correct.

Number Theory

Divisibility and Remainders

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M Question 1	⏱ 0
In a warehouse inventory system, six different product batches are labelled with the numbers: 55, 61, 85, 92, 95, and 98. The system multiplies all the batch numbers together to generate a tracking key. Consider the following statements: Statement I: The product of the six batch numbers is divisible by 25. Statement II: The remainder when the product is divided by 1000 is zero. Select the correct answer from below: (a) Only Statement I is correct. (b) Only Statement II is correct. (c) Both Statements I and II are correct. (d) None of the Statements is correct.

Number Theory

Divisibility and Remainders

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