NEOCODE

Divisibility Rules, LCM, and HCF MCQs

1. What least value should be assigned to * so that the number 451*603 is exactly divisible by 9?

Correct Answer: c) 8

Explanation: For a number to be divisible by 9, the sum of its digits must be divisible by 9. The sum of the digits of 451*603 is 4 + 5 + 1 + * + 6 + 0 + 3 = 19 + *. The smallest value of * that makes 19 + * divisible by 9 is 8.

2. What least value should be assigned to * so that the number 63576*2 is divisible by 8?

Correct Answer: d) 3

Explanation: For a number to be divisible by 8, the last three digits must be divisible by 8. The last three digits are *2. The smallest value of * that makes *2 divisible by 8 is 3 (since 32 is divisible by 8).

3. If 256X561 is divisible by 11, then what can be the value of ‘X’?

Correct Answer: a) 3

Explanation: For a number to be divisible by 11, the difference between the sum of the digits in the odd positions and the sum of the digits in the even positions must be a multiple of 11. For 256X561, the difference is (2 + 6 + 5 +1) - (5 + X + 6) = 14 - (11 + X). For this to be divisible by 11, X must be 3.

4. If ABC0 is a 4-digit number divisible by 4, then how many such 4-digit numbers exist?

Correct Answer: c) 450

Explanation: A 4-digit number ending with 0 is divisible by 4 if the last two digits form a number divisible by 4. Since the last two digits are 0, the number is divisible by 4. There are 9000 4-digit numbers, and 1 in every 4 is divisible by 4, so the answer is 9000 / 4 = 2250. However, since the number must end with 0, the correct answer is 450.

5. The LCM of 5, 8, 12, 20 will not be a multiple of?

Correct Answer: b) 9

Explanation: The LCM of 5, 8, 12, and 20 is 120. 120 is not a multiple of 9.

6. Find the L.C.M. of 1.05 and 2.1?

Correct Answer: c) 2.1

Explanation: The LCM of 1.05 and 2.1 is 2.1.

7. How many numbers between 200 and 600 are divisible by 4, 5, and 6?

Correct Answer: b) 6

Explanation: The LCM of 4, 5, and 6 is 60. The numbers between 200 and 600 divisible by 60 are 240, 300, 360, 420, 480, and 540. So, there are 6 such numbers.

8. For how many values of k is the L.C.M of 66, 88, and k equal to 1212? (k is a natural number)

Correct Answer: c) 25

Explanation: The LCM of 66, 88, and k is 1212. The number of possible values of k is 25.

9. Three bells toll at intervals of 9, 12, and 15 minutes respectively. All three begin to toll at 8 a.m. At what time will they first toll together again?

Correct Answer: a) 11 a.m.

Explanation: The LCM of 9, 12, and 15 is 180 minutes (3 hours). So, the bells will toll together again at 11 a.m.

10. A person has to completely put each of the three liquids i.e., 403 liters of petrol, 465 liters of diesel, and 496 liters of Mobil oil in bottles of equal size without mixing any of the three types of liquids such that each bottle is completely filled. What is the least possible number of bottles required?

Correct Answer: c) 31.

Explanation: The HCF of 403, 465, and 496 is 31. The least number of bottles required is (403 + 465 + 496) / 31 = 44.

11. Five bells begin to toll together at intervals of 9 s, 6 s, 4 s, 10 s, and 8 s, respectively. How many times will they toll together in the span of one hour (excluding the toll at the start)?