A supermarket assigns 3-digit product codes ranging from 400 to 699. The manager wants to find how many products either have codes that begin with 5 or end with 7.

Consider the following statements:
Statement I: There are 100 product codes that begin with 5.
Statement II: The number of product codes either starting with 5 or ending with 7 is 160.

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 supermarket assigns 3-digit product codes ranging from 400 to 699. The manager wants to find how many products either have codes that begin with 5 or end with 7.

Consider the following statements: 
Statement I: There are 100 product codes that begin with 5.
Statement II: The number of product codes either starting with 5 or ending with 7 is 160.

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

Codes range from 400 to 699 &rArr; total = 699 &minus; 400 + 1 = 300 codes.
Codes beginning with 5: from 500 to 599 &rArr; 100 codes.
Statement I is correct.
Codes ending with 7: from 407, 417, ..., to 697 &rArr; one in every 10 numbers in range &rArr; 30 such codes.
Common to both (starting with 5 and ending with 7): 507, 517, ..., 597 &rArr; 10 codes.
So, required count = 100 + 30 &minus; 10 = 120.
Statement II is incorrect.
Hence, option a is correct.

Number Theory

Divisibility Rules

Website Link

Test Your Knowledge

Student Resources


M Question 1	⏱ 0
A supermarket assigns 3-digit product codes ranging from 400 to 699. The manager wants to find how many products either have codes that begin with 5 or end with 7. Consider the following statements: Statement I: There are 100 product codes that begin with 5. Statement II: The number of product codes either starting with 5 or ending with 7 is 160. 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.