Q.1
The remainder of $$\frac{{{{39}^{97!}}}}{{40}}$$ is :
Q.2
The remainder of $$\frac{{{2^{59}}}}{{255}}$$ is:
Q.3
Find the least number which will leaves remainder 5 when divided by 8, 12, 16 and 20.
Q.4
The total number of 3 digit numbers which have two or more consecutive digits identical is:
Q.5
A magazine publisher publishes a monthly magazine of 84 pages. One I found that in a magazine 4 pages was missing. One out of them was page number 29 it is known that the page number of the last page of the magazine is 84, (including the cover pages). The numbers printed on the missing pages were :
Q.6
The remainder when 1010 + 10100 + 101000 + . . . . . . + 101000000000 is divided by 7 is
Q.7
There are 154 beads in a rosary and all are coloured, either RED or BLUE or GREEN. The number of blue ones is three less than red and five more than green. The number of Red beads are:
Q.8
76n- 66n, where n is an integer >0, is divisible by
Q.9
After the division of a number successively by 3, 4 and 7, the remainder obtained is 2, 1 and 4 respectively. What will be remainder if 84 divide the same number?
Q.10
Find the remainder when 2256 is divided by 17.
Q.11
The remainder when 6666.. is divided by 10 is :
Q.12
$$\frac{{\left[ {\left( {888 \times 888 \times 888} \right) - \left( {222 \times 222 \times 222} \right)} \right]}}{{\left[ {\left( {888 \times 888} \right) + \left( {888 \times 222} \right) + \left( {222 \times 222} \right)} \right]} }=\, ?$$
Q.13
The remainder , when (22225555 + 55552222) is divided by 7, is
Q.14
Recently, a small village, in Tamilnadu where only male shepherd reside with four sheep each, was devastated by Tsunami waves. Therefore 8 persons and 47 sheep were found to be dead and the person who luckily survived, left the village with one sheep each since 21 sheep were too injured to move so have left on their on luck, in the village. The number of sheep which were earlier in the village was :
Q.15
A boy appeared in CAT for four consecutive year years, but coincidentally each time his net score was 75. He told me that there was $$\frac{1}{3}$$rd negative marking for every wrong answer and 1 mark was allotted for every correct answer. He has attempted all the questions every year, but certainly some answers have been wrong due conceptual problem. Which is not the total number of questions asked for CAT in any year, in that period?
Q.16
Find the remainder when 496 is divided by 6.
Q.17
The remainder of $$\frac{{{{32}^{{{32}^{32}}}}}}{7}:$$
Q.18
The highest power of 17 which can divide exactly the following:
(182 - 1) (184 - 1) (186 - 1) (188 - 1) . . . . (1816 - 1) (1818 - 1) is :
Q.19
The LCM of two numbers is 1890 and their HCF is 30. If one of them is 270, the other will be
Q.20
If 146 Is divisible by 5n, and then find the maximum value of n.
Q.21
The owner of a local jewellery store hired 3 watchmen to guard his diamonds, but a thief still got in and stole some diamonds. On the way out, the thief met each watchman, one at a time. To each he gave $$\frac{1}{2}$$ of the diamonds he had then and 2 more besides. He escaped with one diamond. How many did he steal originally?
Q.22
Find the number of divisors of 1420.
Q.23
Three friends, returning from a movie, stopped to eat at a restaurant. After dinner, they paid their bill and noticed a bowl of mints at the front counter. Sita took $$\frac{1}{3}$$ of the mints, but returned four because she had a monetary pang of guilt. Fatima then took $$\frac{1}{4}$$ of what was left but returned three for similar reasons. Eswari then took half of the remainder but threw two back into the bowl. The bowl had only 17 mints left when the raid was over. How many mints were originally in the bowl?
Q.24
The number of employees in Examveda and Co. is a prime number and less than 300. The ratio of the number of employees who are graduates and above, to that of employees who are not, can possibly be:
Q.25
The square of a number greater than 1000 that is not divisible by three, when divided by three, leaves a remainder of
Q.26
Find the least number of five digits which when divided by 40, 60, and 75, leave remainders 31, 51 and 66 respectively.
Q.27
Find the remainder when 65203 is divided by 7.
Q.28
On a road three consecutive traffic lights change after 36, 42 and 72 seconds respectively. If the lights are first switched on at 9:00 AM sharp, at what time will they change simultaneously?
Q.29
The sum of the digits of two-digit number is 10, while when the digits are reversed, the number decrease by 54. Find the changed number.
Q.30
The HCF of two numbers, each having three digits, is 17 and their LCM is 714. The sum of the numbers will be:
Q.31
What is the sum of all two digit numbers that gives a remainder of 3 when they are divided by 7?
Q.32
Some birds settled on the branches of a tree. First, they sat one to a branch and there was one bird too many. Next they sat two to a branch and there was one branch too many. How many branches were there?
Q.33
When we reverse the digits of the number 13, the increases by 18. How many other two digit numbers increases by 18 when their digits are reversed?
Q.34
A young girl counted in the following way on the fingers of her left hand. She started calling the thumb 1, the index finger 2, middle finger 3, ring finger 4, little finger 5, then reversed direction, calling the ring finger 6, middle finger 7, index finger 8, thumb 9 and then back to the index finger for 10, middle finger for 11 and so on. She counted up 1994. She ended on her
Q.35
There are 576 boys and 448 girls in a school that are to be divided into equal sections of either boys or girls alone. Find the total number of sections thus formed?
Q.36
Find the remainder when 67107 is divided by 7.
Q.37
The HCF of 2472, 1284 and a third number 'N' is 12. If their LCM is 23 × 32 × 5 × 103 × 107, then the number 'N' is:
Q.38
If A381 is divisible by 11, find the value of the smallest natural number A?
Q.39
If 381A is divisible by 9, find the value of the smallest natural number A?
Q.40
The greatest number, which when subtracted from 5834, gives a number exactly divisible by each of 20, 28, 32, 35 is.
Q.41
Ram left $$\frac{1}{3}$$ of his property to his widow and $$\frac{3}{5}$$ of the remainder to his daughter. He gave the rest to his son who received Rs. 6,400. How much was his original property worth?
Q.42
The remainder , when (1523 + 2323) is divided by 19, is
Q.43
What least number must be added to 1056, so that the sum is completely divisible by 23 ?
Q.44
If we divide the unknown two-digit number by the number consisting of the same digits written in the reverse order, we get 4 as quotient and 3 as remainder. If we divide the required number by sum of its digits, we get 8 as a quotient and 7 as a remainder. Find the number?
Q.45
The sum of four consecutive two-digit odd numbers, when divided by 10, become a perfect square. Which of the following can possibly be one of these four numbers?
Q.46
5(x + 3) = 25(3x - 4), then find the value of x
Q.47
The numerator and denominator of a fraction are in the ratio 3 : 4. If 9 is subtracted from the numerator, the resulting fraction in $$\frac{2}{3}$$ of the original fraction. The numerator of the original fraction is
Q.48
How many pairs of natural numbers is there the difference of whose squares are 45.
Q.49
Which of following can never be ending of a perfect square?
Q.50
Find the remainder when 54124 is divided by 17.
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