AMCAT Previous Years Questions on Divisibility

 Topics Sub- Topics Expected Ques Basic Mathematics 6 – 8 Questions Applied Mathematics 8 – 10 Questions Engineering Mathematics 8 – 10 Questions

Question 1
3/7 of the oranges grown are too sour to eat out 3,80,205 oranges that are grown on a farm. The owner has to sell the eatable Orange. How many Oranges can the farm owner sell?
A. 1,62,945
B. 3,25,890
C. 2,17,260
D. 4,34,520

Correct Op: C
(1 – 3/7) * 3,80,205 = 2,17,260

Question 2
When the integer n is divided by 8, the remainder is 3. What is the remainder if 6n is divided by 8?
A. 0
B. 2
C. 1
D. 3

Correct Op: B
When n is divided by 8, the remainder is 3 may be written as n = 8 k + 3 multiply all terms by 6 6 n = 6(8 k + 3) = 8(6k) + 18 Write 18 as 16 + 2 since 16 = 8 * 2. = 8(6k) + 16 + 2 Factor 8 out. = 8(6k + 2) + 2 The above indicates that if 6n is divided by 8, the remainder is 2. The answer is C.

Question 3
The sum of three consecutive natural numbers each divisible by 3 is 72. What is the largest among them?
A. 21
B. 24
C. 27
D. 30

Correct Op: C
Let us take three consecutive numbers which are divisible by 3 are, 3x, 3x+3 and 3x+6. The largest of them= 27.

Question 4
A and B are two number when divided by 7 leaves a remainder 3 and 5. What will be the remainder when A-B is divided by 7 ?
A. 4
B. 5
C. 6
D. 7

Correct Op: B

Question 5
If the number 7×86038 is exactly divisible by 11, then the smallest whole number in place of x?
A. 1
B. 2
C. 3
D. 4

Correct Op: C
The given number =7×86038 Sum of the odd places =8+0+8+7=23 Sum of the even places = 3+6+x (Sum of the odd places)- (Sum of even places) = Number (exactly divisible by 11) 23-(9+x) = divisible by 11 14 – x = divisible by 11. X must be 3, to make given number divisible by 11.

Question 6
The total number of two-digit positive integer < than 100, which are not divisible by 2, 3 and 5 is
A. 23
B. 24
C. 25
D. 26

Correct Op: B

Question 7
X is a 5 digit number when we subtract the sum of the digits form X, it becomes divisible by _____
A. 5
B. 1
C. 9
D. 6

Correct Op: C

Question 8
Dustin is driving his car at speed of 50 kilometres per hour. He going to Texas which is located 345 kilometres from his starting point.How long will it take him to reach Texas?
A. 70
B. 71
C. 72
D. 69

Correct Op: D

Question 9
The average of three numbers is 77.The first number is twice the second and the second number is twice the third. Find the first number?
A. 33
B. 66
C. 77
D. 132
E. None of these

Correct Op: D

Question 10
A and B are two cars travelling to a destination which is 360 kilometres away. A takes 4 hours to reach the destination. How much time will it take B to reach the destination if the speeds of A and B are in the ratio 9: 12?
A. 2.5 hrs
B. 4.5 hrs
C. 3.5 hrs
D. 3 hrs

Correct Op: D