Statement 1: The smallest number of 6-digits using only the first three digits is 100022.
Statement 2: To get the largest number using a given set of digits, the largest digit is written at the right most and then the remaining digits are written in descending order of their values to the right.
Which of the following options is correct?
Both the statements are true.
Both the statements are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.
Answer
Statement 1 : The first three digits are 0, 1 and 2. To form the smallest 6-digit number using these digits, the smallest non-zero digit (1) is placed at the left most place, followed by 0s, and 2 is placed at the ones place. So, the smallest 6-digit number formed is 100002, and not 100022. Hence, Statement 1 is false.
Statement 2 : To get the largest number using a given set of digits, the largest digit is written at the left most place (and not the right most place), and then the remaining digits are written in descending order of their values to the right. Hence, Statement 2 is false.
Hence, option 2 is the correct option.
25 - 42 + 63 = ?
Statement 1: 25 - 42 + 63 before rounding off the given numbers = 88 - 42 = 46 = 50
Statement 2: After rounding off the given numbers to the nearest 10;
25 - 42 + 63 = 30 - 40 + 60 = 50
Both the statements are true.
Both the statements are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.
Answer
Statement 1 : Without rounding off, 25 - 42 + 63 = 88 - 42 = 46. The statement then writes 46 = 50, which is incorrect since 46 ≠ 50. Hence, Statement 1 is false.
Statement 2 : Rounding off each number to the nearest 10, we get 25 → 30, 42 → 40 and 63 → 60. So, 30 - 40 + 60 = 90 - 40 = 50. Hence, Statement 2 is true.
So, Statement 1 is false and Statement 2 is true.
Hence, option 4 is the correct option.