Competitive Exams: Quantitative Aptitude - HCF/LCM Set 5 Quiz

Question 1

A distributor is packing three types of organic tea leaves weighing 165 kg, 195 kg, and 285 kg into packets of equal weight. What is the maximum possible weight of each packet if no tea is left over, and how many total packets will be formed?

Accepted Answer

A) 15 kg and 43 packets

Answer

B) 5 kg and 129 packets

Answer

C) 15 kg and 45 packets

Answer

D) 25 kg and 27 packets

Question 2

A security light system flashes at intervals of 20, 25, 35, and 40 seconds respectively. If each light is programmed to turn off 6 seconds before its scheduled flash, what is the least number of seconds after which all lights will have completed a cycle simultaneously minus their off-times? (Essentially, find the least positive integer which when divided by 20, 25, 35, and 40 leaves remainders of 14, 19, 29, and 34 respectively.)

Accepted Answer

B) 1394 seconds

Answer

A) 1406 seconds

Answer

C) 1396 seconds

Answer

D) 1400 seconds

Question 3

The HCF and LCM of two positive integers are 13 and 273 respectively. If one of the numbers lies strictly between 60 and 100, what is the value of this number?

Accepted Answer

C) 91

Answer

A) 78

Answer

B) 39

Answer

D) 65

Question 4

Two warehouses store crates of goods. The sum of the number of crates in both warehouses is 528, and the HCF of the crates in both is 33. How many unique pairs of values can represent the number of crates in the two warehouses?

Accepted Answer

D) 4 pairs

Answer

A) 6 pairs

Answer

B) 8 pairs

Answer

C) 3 pairs

Question 5

Three automated watering sensors on a smart farm are scheduled to activate at intervals of 18, 24, and 36 minutes respectively. If they all activate simultaneously at 8:00 AM, at what time will they next activate together, and how many times will they have activated together by 8:00 PM of the same day (excluding the initial 8:00 AM but including the 8:00 PM activation)?

Accepted Answer

A) 9:12 AM, 10 times

Answer

B) 9:24 AM, 9 times

Answer

C) 9:12 AM, 11 times

Answer

D) 9:36 AM, 8 times

Question 6

An event planner has three rolls of fabric of lengths 1356 cm, 1868 cm, and 2764 cm. They want to cut them into equal smaller pieces of maximum possible length such that a remnant of exactly 12 cm is left over from each roll. What is the maximum possible length of each piece?

Accepted Answer

B) 64 cm

Answer

A) 32 cm

Answer

C) 128 cm

Answer

D) 48 cm

Question 7

An interior designer is tiling a rectangular floor measuring 15 meters 17 centimeters in length and 9 meters 2 centimeters in width with identical square tiles of maximum possible size, without cutting any tiles. What is the minimum number of square tiles required to cover the entire floor?

Accepted Answer

C) 814 tiles

Answer

A) 840 tiles

Answer

B) 782 tiles

Answer

D) 912 tiles

Question 8

The capacities of two fuel tanks are in the ratio of 3:4. The Least Common Multiple (LCM) of their capacities is 240 liters. What is the Highest Common Factor (HCF) of their capacities, and what is the combined total capacity of both tanks?

Accepted Answer

D) HCF = 20 liters, Total Capacity = 140 liters

Answer

A) HCF = 15 liters, Total Capacity = 105 liters

Answer

B) HCF = 10 liters, Total Capacity = 70 liters

Answer

C) HCF = 24 liters, Total Capacity = 168 liters

Question 9

A school principal wants to distribute three batches of notebooks containing 640, 960, and 1280 notebooks to a certain number of students. After equal distribution, there are 10, 15, and 20 notebooks left over from each batch respectively. What is the maximum possible number of students?

Accepted Answer

A) 315 students

Answer

B) 105 students

Answer

C) 155 students

Answer

D) 630 students

Question 10

In an algebraic computation, the HCF of two polynomial expressions is (x + 3) and their LCM is (x^3 - 7x + 6). If one of the expressions is (x^2 + 2x - 3), which of the following represents the other polynomial expression?

Accepted Answer

B) x^2 + x - 6

Answer

A) x^2 - x - 6

Answer

C) x^2 + 5x + 6

Answer

D) x^2 - 5x + 6

Question 11

Four automatic chemical dispensers release liquid at intervals of 2/3 minutes, 8/9 minutes, 16/81 minutes, and 10/27 minutes respectively. What is the shortest time after which all four dispensers will release liquid together again?

Accepted Answer

C) 80/3 minutes

Answer

A) 40/9 minutes

Answer

B) 160/3 minutes

Answer

D) 80/27 minutes

Question 12

A laboratory needs to find the Highest Common Factor (HCF) of the fractional weights of four precise compounds: 2/3 gram, 8/9 gram, 16/81 gram, and 10/27 gram. What is the HCF of these weights?

Accepted Answer

D) 2/81 gram

Answer

A) 2/3 gram

Answer

B) 8/81 gram

Answer

C) 10/81 gram

Question 13

A merchant is counting a collection of rare coins. When he groups them by 5, 6, 7, or 8, he always has 3 coins left over. However, when he groups them by 9, no coins are left over. What is the minimum possible number of coins in his collection?

Accepted Answer

A) 1683 coins

Answer

B) 843 coins

Answer

C) 2523 coins

Answer

D) 3363 coins

Question 14

The Highest Common Factor and Least Common Multiple of two industrial machinery cycle times are 11 seconds and 7700 seconds respectively. If the cycle time of the first machine is 275 seconds, what is the cycle time of the second machine?

Accepted Answer

B) 308 seconds

Answer

A) 290 seconds

Answer

C) 318 seconds

Answer

D) 345 seconds

Question 15

A civil engineer is designing a pipeline system where the length must be a multiple of 15, 25, 40, and 75 meters. To fit within a specific urban zone, the length must be the largest possible 4-digit integer value. What is this ideal length?

Accepted Answer

C) 9600 meters

Answer

A) 9800 meters

Answer

B) 9400 meters

Answer

D) 9900 meters