Practice Test

Q1) The least number, which when divided by 16, 18, 21 leaves remainder 3, 5 and 8 is Show Answer

Q2) The LCM of two numbers is 28 times of their HCF. The sum of their LCM and HCF is 1740. If one of the numbers is 240, then the other number is Show Answer

Q3) Three numbers are in the ratio 3 : 4 : 5 and their LCM is 2400. Their HCF is Show Answer

Q4) Find the least number which when divided by 12, 16, 18, 30 leaves remainder 4 in each case but it is completely divisible by 7. Show Answer

Q5) How many numbers less than 10000 are there, which are divisible by 21, 35 and 63? Show Answer

Q6) The HCF of two numbers is 8. Which one of the following can never be their LCM? Show Answer

Q7) What is the least number, which when divided by 12 leaves a remainder of 7, when divided by 15 leaves a remainder of 10 and when divided by 16 leaves a remainder of 11? Show Answer

Q8) What is the least number, which when divided by 8, 9, 12, 15 leaves a remainder 1 in each case? Show Answer

Q9) What is the greatest number of 3 digits, which when divided by 6, 9, 12 leaves a remainder 3 in each case? Show Answer

Q10) Three different containers contain different qualities of mixtures of milk and water, whose measurements are 403 kg, 434 kg and 465 kg. What biggest meausre must be there to measure all the different quantities exactly? Show Answer

Q11) The maximum number of students among whom 1001 pens and 910 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is Show Answer

Q12) An officer was appointed on maximum daily wages on a contract money of Rs. 4956. But on being absent for some days, he was paid Rs. 3894, for how many days was he absent? Show Answer

Q13) Six bells commence tolling together and toll at intervals of 2 s, 4 s, 7 s, 8 s, 10 s and 12 s, respectively. In 30 min how many times do they toll together? Show Answer

Q14) The traffic lights at three different road crossings change after every 48 s, 72 s and 108 s, respectively. If they all change simultaneously at 8 : 20 h, then at what will they again change simultaneously? Show Answer

Q15) Find the largest number that will 1 divide 260, 720 and 145 leaving 7 as remainder in each case. Show Answer

Q16) Seven bells ring at intervals of 2 min, 3 min, 4 min, 6 min, 8 min, 9 min and 12 min, respectively. They started ringing simultaneously at 5 : 00 in the morning. What will be the next time when they all ring simultaneously? Show Answer

Q17) 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 1 h (excluding the toll at the start)? Show Answer

Q18) An electronic device makes a beep after every 30 s. Another device makes a beep after every 31 s. They beeped together at 10 pm. What is the next time when they would together at the earliest? Show Answer

Q19) A General can draw up his soldiers in the rows of 10, 15 or 18 soldiers and he can also draw them up in the form of a solid square. Find the least number of soldiers with the General. Show Answer

Q20) The HCF of two number is 48 and their LCM is 1440. If one of the numbers is 288, then the other number is Show Answer

Q21) On dividing a certain number by 357, the remainder is 39. On dividing the same number by 17. What will be the remainder? Show Answer

Q22) The H.C.F and L.C.M of two numbers are 21 and 4641 respectively. If one of the numbers lies between 200 and 300, then the two numbers are Show Answer

Q23) What is the smallest number which when increased by 5 is completely divisible by 8, 11 and 24? Show Answer

Q24) Which is the least number that must be subtracted from 1856, so that the remainder when divided by 7, 12 and 16 will leave the same remainder 4? Show Answer

Q25) Find the greatest number that will divide 148, 246 and 623 leaving remainders 4, 6 and 11 respectively? Show Answer

Q26) Three balls chime at an interval of 18, 24 and 32 minutes respectively. At a certain time they begin to chime together. What length of time will elapse before they chime together again. Show Answer

Q27) The L.C.M and H.C.F of two numbers are 84 and 21, respectively. If the ratio of two numbers be 1 : 4, then the larger of the two numbers is Show Answer

Q28) If the L.C.M and H.C.F of two numbers are 2400 and 16, one number is 480; find the second number. Show Answer

Q29) The maximum number of students among them 1001 pens and 910 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils is Show Answer

Q30) Find the maximum number of students among whom 429 mangoes and 715 oranges can be equally distributed. Show Answer

Q31) Two numbers both greater than 29, have H.C.F 29 and L.C.M 4147. Five sum of the number is Show Answer

Q32) Find the greatest number which when subtracted from 3000 is exactly divisible by 7, 11, 13. Show Answer

Q33) The L.C.M. of two number is 630 and their H.C.F. is 9. If the sum of numbers is 153, their difference is Show Answer

Q34) Suppose you have 108 green marbles and 144 red marbles. You decide to separate them into packages of equal number of marbles. Find the maximum possible number of marbles in each package. Show Answer

Q35) Find the lowest number which when subtracted from 3000, is exactly divisible by 7, 11 and 13. Show Answer

Q36) Find the greatest number that will divide 55, 127 and 175, so as to leave the same remainder in each case. Show Answer

Q37) One pendulum ticks 57 times in 58 seconds and another 608 times in 609 seconds. If they started simultaneously, find the time after which they will tick together. Show Answer

Q38) Find the greatest possible rate at which a man should walk to cover a distance of 70 km and 245 km in exact number of days? Show Answer

Q39) The least number, which when divided by 2, 3, 4, 5 and 6, leaves in each case, a remainder 1, but when divided by 7 leaves no remainder. The number is Show Answer

Q40) I have a certain number of beads which lie between 600 and 900. If 2 beads are taken away the remainder can be equally divided among 3, 4, 5, 6, 7 or 12 boys. The number of beads I have Show Answer

Q41) The greatest number which will divide 410, 751 and 1030 leaving a remainder 7 in each case is Show Answer

Q42) From 3 drums of milk, 279, 341 and 465 respectively are to be drawn out. To do it in a minimum time, the capacity of the measuring can be Show Answer

Q43) A man was engaged for a certain number of days for Rs. 404.30 p but being absent for some days he was paid only Rs. 279.90 p. His daily wages cannot exceed by Show Answer

Q44) Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits is N is Show Answer

Q45) The L.C.M. of two numbers is 45 times their H.C.F. If one of the numbers is 125 and the sum of H.C.F. and L.C.M. is 1150, the other number is Show Answer

Q46) The H.C.F. of two numbers is 23 and the other factors of their L.C.M. are 13 and 14. The larger of the two numbers is Show Answer

Q47) An electric wire is sold only in multiples of 1 meter, and a customer required several lengths of wire, each 85 cm long. To avoid any wastage and to minimize labour, he should purchase minimum lengths of Show Answer

Q48) There are 4 numbers. The H.C.F. of each pair is 3 and the L.C.M. of all the 4 numbers is 116. What is the product of 4 numbers? Show Answer

Q49) Three wheels can complete respectively 60, 36, 24 revolutions per minute. There is a red spot on each wheel that touches the ground at time zero. After how much time, all these sports will simultaneously touch the ground again? Show Answer

Q50) Number of students who have opted the subjects A, B, C are 60, 84, 108 respectively. The examination is to be conducted for these students such that only the students of the same subject are allowed in one room. Also the number of students in each room must be same. What is the minimum number of rooms that should be arranged to meet all these conditions? Show Answer

Q51) What will be the least number which when doubled will be exactly divisible by 12, 18, 21 and 30? Show Answer

Q52) A hall is 13 meters 53 cm long and 8 meters 61 cm broad is to be paved with minimum number of square tiles. The number of tiles required is Show Answer

Q53) In a school there are 391 boys and 323 girls. These are to be divided into the largest possible equal classes, so that there are equal number of boys and girls in each class. How many classes are possible? Show Answer

Q54) A shopkeeper has three kinds of sugar 184 kg; 230 kg and 276 kg. He wants to store it into minimum number of bags to equal size without mixing. Find the size of the bag and the number of bags required to do the needful? Show Answer

Q55) There are four prime numbers written in the ascending order of magnitude. The product of first three numbers and that of the last three number is 385 and 1001 respectively. The fourth prime number is Show Answer

Q56) If the sum of two numbers is 55 and the H.C.F. and L.C.M. of these numbers are 5 and 120 respectively, then the sum of the reciprocals of the numbers is equal to Show Answer

Q57) Product of two co-prime numbers is 117. Their L.C.M. should be Show Answer

Q58) The least number of five digits which is exactly divisible by 12, 15 and 18 is Show Answer

Q59) The sum of two numbers is 462 and their highest common factor is 22. What is the maximum number of pairs that satisfy these conditions? Show Answer

Q60) Three numbers are in the ratio of 3 : 4 : 5 and their L.C.M. is 2400. Their H.C.F. is Show Answer

Q61) A number when divided by 49 leaves 32 as remainder. This number when divided by 7 will have the remainder as Show Answer

Q62) The traffic light at three different road crossing changes after 24 second, 36 second, 54 second respectively. If they all changes simultaneously at 10 : 15 : 00 AM then at what time will they again changes, simultaneously Show Answer

Q63) The least number which when divided by 48, 64, 90, 120 will leave the remainders 38, 54, 80, 110 respectively, is Show Answer