A courier service assigns a 10-digit barcode to every parcel. One such barcode reads 753924P186, where P is a missing digit that was smudged. For successful dispatch, the barcode must be divisible by 11. What is the correct digit that should replace P?
Consider the following statements:
Statement I: The digit replacing P must be 7.
Statement II: The alternating sum of the digits must be divisible by 11.

Select the correct answer from the options 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

A courier service assigns a 10-digit barcode to every parcel. One such barcode reads 753924P186, where P is a missing digit that was smudged. For successful dispatch, the barcode must be divisible by 11. What is the correct digit that should replace P?
Consider the following statements:
Statement I: The digit replacing P must be 7.
Statement II: The alternating sum of the digits must be divisible by 11.

Select the correct answer from the options 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.

ONLiNE UPSC · Accepted Answer

To test divisibility by 11: compute the alternating sum of digits from left to right.
Barcode: 7 5 3 9 2 4 P 1 8 6
Alternating sum = 7 - 5 + 3 - 9 + 2 - 4 + P - 1 + 8 - 6
= (7 - 5 + 3 - 9 + 2 - 4 - 1 + 8 - 6) + P
= &minus;5 + P
For divisibility by 11:
&minus;5 + P &equiv; 0 mod&thinsp;11
&rArr; P = 5
Statement I is incorrect.
Statement II is correct as it correctly defined the divisibility rule for 11.

Hence, option b is correct.

Min. Time: 121 S Max Time: 121 S
M Question 1	⏱ 0
A courier service assigns a 10-digit barcode to every parcel. One such barcode reads 753924P186, where P is a missing digit that was smudged. For successful dispatch, the barcode must be divisible by 11. What is the correct digit that should replace P? Consider the following statements: Statement I: The digit replacing P must be 7. Statement II: The alternating sum of the digits must be divisible by 11. Select the correct answer from the options 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 Rules

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