AMCAT Previous Years Questions on Divisibility


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Expected Ques

Basic Mathematics


       6 - 8 Questions


Applied Mathematics



      8 - 10 Questions


Engineering Mathematics


       8 - 10 Questions



Ques. The number of prime factors of (3 x 5)12 (2 x 7)10 (10)25 is:



Op 1: 47
Op 2: 60
Op 3: 72
Op 4: None of these
Op 5:

Correct Op : 4

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

Op 1: 1
Op 2: 2
Op 3: 3
Op 4: 4
Op 5:

Correct Op : 3

Ques. Which of the following numbers is exactly divisible by 24 ?

Op 1: 35718
Op 2: 63810
Op 3: 537804
Op 4: 3125736
Op 5:

Correct Op : 4

Ques. The number nearest to 15207, which is divisible by 467, is:

Op 1: 14342
Op 2: 15211
Op 3: 14944
Op 4: 15411
Op 5: None of these

Correct Op : 4

Ques. The smallest number, which is a perfect square and contains 7936 as a factor is:

Op 1: 251664
Op 2: 231564
Op 3: 246016
Op 4: 346016
Op 5: None of these

Correct Op : 3

Ques. In a division problem, the divisor is twenty times the quotient and five times the remainder. If
remainder is 16, the number will be:

Op 1: 3360
Op 2: 336
Op 3: 1616
Op 4: 20516
Op 5: None of these

Correct Op : 2

Ques. If a number is exactly divisible by 85, then what will be the remainder when the same number is
divided by 17?
Op 1: 3
Op 2: 1
Op 3: 4
Op 4: 0
Op 5:

Correct Op : 4

Ques. The least perfect square number which is exactly divisible by 3, 4, 7, 10 and 12 is:
Op 1: 8100
Op 2: 17600
Op 3: 44100
Op 4: None of these

Op 5:

Correct Op : 3

Ques. (xn+yn) is divisible by (x-y):
Op 1: for all values of n
Op 2: only for even values of n
Op 3: only for odd values of n
Op 4: for no values of n
Op 5:

Correct Op : 4

Ques. The greatest number that will divide 63, 138 and 228 so as to leave the same remainder in each
case:
Op 1: 15
Op 2: 20
Op 3: 35
Op 4: 40
Op 5:

Correct Op : 1

Ques. Find the largest number, smaller than the smallest four-digit number, which when divided by 4,5,6
and 7 leaves a remainder 2 in each case.
Op 1: 422
Op 2: 842
Op 3: 12723
Op 4: None of these
Op 5:

Correct Op : 2

Ques. What is the highest power of 5 that divides 90 x 80 x 70 x 60 x 50 x 40 x 30 x 20 x 10?
Op 1: 10
Op 2: 12
Op 3: 14
Op 4: None of these
Op 5:

Correct Op : 1

Ques. If a and b are natural numbers and a-b is divisible by 3, then a3-b3 is divisible by:
Op 1: 3 but not by 9
Op 2: 9
Op 3: 6
Op 4: 27
Op 5:

Correct Op : 2

Ques. What is the greatest positive power of 5 that divides 30! exactly?
Op 1: 5
Op 2: 6
Op 3: 7
Op 4: 8
Op 5:

Correct Op : 3

Ques. In how many ways can a number 6084 be written as a product of two different factors ?
Op 1: 27
Op 2: 26
Op 3: 13
Op 4: 14
Op 5:

Correct Op : 3

Ques. What is the smallest four-digit number which when divided by 6, leaves a remainder of 5 and
when divided by 5 leaves a remainder of 3?
Op 1: 1043
Op 2: 1073
Op 3: 1103
Op 4: None of these
Op 5:

Correct Op : 4

Ques. P is an integer. P>883. If P-7 is a multiple of 11, then the largest number that will always divide
(P+4) (P+15) is:
Op 1: 11
Op 2: 121
Op 3: 242
Op 4: None of these
Op 5:

Correct Op : 3

Ques. Let C be a positive integer such that C + 7 is divisible by 5. The smallest positive integer n (>2) such
that C + n2 is divisible by 5 is:
Op 1: 4
Op 2: 5
Op 3: 3
Op 4: Does not exist
Op 5:
Correct Op : 4

Ques. Four bells begin to toll together and then each one at intervals of 6 s, 7 s, 8 s and 9 s respectively.
The number of times they will toll together in the next 2 hr is:
Op 1: 14 times
Op 2: 15 times
Op 3: 13 times
Op 4: 11 times
Op 5:

Correct Op : 1

Ques. On dividing a number by 999,the quotient is 366 and the remainder is 103.The number is:
Op 1: 364724
Op 2: 365387
Op 3: 365737
Op 4: 366757
Op 5:

Correct Op : 3

Ques. The difference between two numbers is 1365.When the larger number is divided by the smaller
one ,the quotient is 6 and the remainder is 15.The smaller number is:
Op 1: 240
Op 2: 270
Op 3: 295
Op 4: 360
Op 5:

Correct Op : 2

Ques. The least perfect square which is divisible by 3, 4, 5, 6, 8 is:
Op 1: 900
Op 2: 1200
Op 3: 2500
Op 4: 3600
Op 5:

Correct Op : 4

Ques. What is the remainder when 1723 is divided by 16?
Op 1: 0
Op 2: 1
Op 3: 2
Op 4: 3
Op 5:

Correct Op : 2

Ques. What will be the remainder when 1336 is divided by 2196?
Op 1: 0
Op 2: 1
Op 3: 12
Op 4: 2195
Op 5:

Correct Op : 2

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