number theory

1. Which number should be subtracted from 24, 31, 58 and 79 so that the ratio of the remainders of the first two numbers is proportion to the ratio of the remainders of the other two numbers?

5
7
8
None of the above

Detailed SolutionWhich number should be subtracted from 24, 31, 58 and 79 so that the ratio of the remainders of the first two numbers is proportion to the ratio of the remainders of the other two numbers?

2. How many numbers from 1 to 100 are there each of which is not only exactly divisible by 4 but also has 4 as its digit ?

7
8
18
25

Detailed SolutionHow many numbers from 1 to 100 are there each of which is not only exactly divisible by 4 but also has 4 as its digit ?

3. A prime number between 10 and 40 remains unchanged if its digits are reversed. The square of such a number is

12
484
1089
None of the above

Detailed SolutionA prime number between 10 and 40 remains unchanged if its digits are reversed. The square of such a number is

4. The sum of squares of three natural numbers is 138 and sum of their products taken two at a time is What is the sum of these numbers?

10
20
30
None of the above

Detailed SolutionThe sum of squares of three natural numbers is 138 and sum of their products taken two at a time is What is the sum of these numbers?

5. How many numbers are there from 3 to 100 which are divisible by 4 and either unit digit or tenth digit or both include 4 ?

10
11
19
less than 10

Detailed SolutionHow many numbers are there from 3 to 100 which are divisible by 4 and either unit digit or tenth digit or both include 4 ?

6. The last number, which must be added to 7912 to make it a perfect square, is

8
9
12
16

Detailed SolutionThe last number, which must be added to 7912 to make it a perfect square, is

7. Suppose x, y, z are three positive integers such that x < yz and xyz = Which one of the following values of S yields more than one solution to the equation x+y+z=S?

13
4
15
16

Detailed SolutionSuppose x, y, z are three positive integers such that x < yz and xyz = Which one of the following values of S yields more than one solution to the equation x+y+z=S?

8. If 2028 is the product of two natural number shaving two digits each and 13 is their highest common factor, then the numbers are

26, 78
13, 156
36, 68
39,52

Detailed SolutionIf 2028 is the product of two natural number shaving two digits each and 13 is their highest common factor, then the numbers are

9. The smallest number which when increased by 10, is completely divisible by 12, 15, 18, 20 and 24, is:

230
250
290
350

Detailed SolutionThe smallest number which when increased by 10, is completely divisible by 12, 15, 18, 20 and 24, is:

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Test 1