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- Question
How many zeros are there from 1 to 10000 ?
Options- A. 2893
- B. 4528
- C. 6587
- D. 4875
- Correct Answer
- 2893
ExplanationFor solving this problem first we would break the whole range in 5 sections
1) From 1 to 9
Total number of zero in this range = 0
2) From 10 to 99
Total possibilities = 9*1 = 9 ( here 9 is used for the possibilities of a non zero integer)
3) From 100 to 999 - three type of numbers are there in this range
a) x00 b) x0x c) xx0 (here x represents a non zero number)
Total possibilities
for x00 = 9*1*1 = 9, hence total zeros = 9*2 = 18
for x0x = 9*1*9 = 81, hence total zeros = 81
similarly for xx0 = 81
total zeros in three digit numbers = 18 + 81 +81 = 180
4) From 1000 to 9999 - seven type of numbers are there in this range
a)x000 b)xx00 c)x0x0 d)x00x e)xxx0 f)xx0x g)x0xx
Total possibilities
for x000 = 9*1*1*1 = 9, hence total zeros = 9*3 = 27
for xx00 = 9*9*1*1 = 81, hence total zeros = 81*2 = 162
for x0x0 = 9*1*9*1 = 81, hence total zeros = 81*2 = 162
for x00x = 9*1*1*9 = 81, hence total zeros = 81*2 = 162
for xxx0 = 9*9*9*1 = 729, hence total zeros = 729*1 = 729
for xx0x = 9*9*1*9 = 729, hence total zeros = 729*1 = 729
for x0xx = 9*1*9*9 = 729, hence total zeros = 729*1 = 729
total zeros in four digit numbers = 27 + 3*162 + 3*729 = 2700
thus total zeros will be 0+9+180+2700+4 (last 4 is for 4 zeros of 10000)
= 2893 - 1. (3x + 2) (2x - 5) = ax˛ + kx + n. What is the value of a - n + k ?
Options- A. 4
- B. 1
- C. 5
- D. 3 Discuss
- 2. The difference between two numbers is 3355. When the larger number is divided by the smaller one, the quotient is 6 and the remainder is 15. The smaller number and larger number respectively ?
Options- A. 546, 3901
- B. 415, 3770
- C. 668, 4023
- D. 404, 3759 Discuss
- 3. What least number must be substracted from 627349 so that the remaining number is divisible by 15 ?
Options- A. 1
- B. 2
- C. 3
- D. 4 Discuss
- 4. Find the sum to 200 terms of the series 2 + 5 + 7 + 6 + 12 + 7 + ....
Options- A. 30,400
- B. 30,200
- C. 34,600
- D. 38,400 Discuss
- 5. Which of the following can be used to illustrate that not all prime numbers are odd?
Options- A. 1
- B. 2
- C. 3
- D. 4 Discuss
- 6. When a number is divided by 138 the remainder is 26. What will be the remainder if the same number is divided by 23 ?
Options- A. 4
- B. 6
- C. 3
- D. 1 Discuss
- 7. If in the following set of numbers, the first and the third digits are interchanged in each number, which number will be second from the end if arranged in ascending order after interchanging the digits ? 585 546 514 404 206 369
Options- A. 404
- B. 585
- C. 415
- D. 602 Discuss
- 8. There are two numbers such that the sum of twice the first number and thrice the second number is 100 and sum of thrice the first number and twice the second number is 120. Which is the larger number ?
Options- A. 32
- B. 24
- C. 26
- D. 38 Discuss
- 9. Find the remainder when 629 is divided by 5 ?
Options- A. 0
- B. 1
- C. 3
- D. 5 Discuss
- 10. Arun has certain number of books. It is not less than 15 and not more than 30. If he wants to give these books equally to 2 of his friends, then 1 book will remain. If he wants to give these books equally to 3 of his friends, then 2 books will remain. If he wants to give these books equally to 4 of his friends, then 3 books will remain. What is the number of books he had ?
Options- A. 19
- B. 23
- C. 17
- D. 15 Discuss
Numbers problems
Search Results
Correct Answer: 5
Explanation:
(3x + 2) (2x - 5) = ...............(1)
But (3x + 2)(2x - 5) = ........(2)
so by comparing (1) & (2),
we get a= 6, k= -11 , n= -10
(a - n + k) = 6 + 10 - 11 = 5.
Correct Answer: 668, 4023
Explanation:
Let the smaller number be k.
Then, larger number = (3355 + k)
Therefore 3355 + k = (6k + 15)
?=? 5k = 3340
?=? k = 668.
Therefore, the smaller number k = 668 and now the larger number = 3355+668 = 4023.
Correct Answer: 4
Explanation:
On dividing 627349 by 15, we get remainder = 4.
Therefore, the obtained remainder is the least number to be subtracted from the given number so that the the mnumber is divisible by 15.
Here 4 is the least number to be subtracted from 627349 so that it is divisible by 15.
Correct Answer: 30,400
Explanation:
we can treat every two consecutive terms as one.
So, we will have a total of 100 terms of the nature:
(2 + 5) + (7 + 6) + (12 + 7).... => 7, 13, 19,....
We know the sum of n terms
Now, a= 7, d=6 and n=100
Hence the sum of the given series is
S= 100/2 x[2 x 7 + 99 x 6]
=> 50[608]
=> 30,400.
Correct Answer: 2
Explanation:
The only even numbers in the list are 2 and 4, but 4 is not a prime. So 2 can be used to illustrate the statement that all primes are not odd.
Correct Answer: 3
Explanation:
Number = quotient x divisor + remainder;
so, here
number = 138 k + 26
=> (23 x 6k) + (23+3)
=> 23(6k+1)+3
so, remainder is 3.
Correct Answer: 415
Explanation:
Given numbers are 585 546 514 404 206 369
Then interchanging the 1st and 3rd digits of the given numbers, we get
585 645 415 404 602 963
Now, arranging them in ascending order
963 645 602 585 415 404
Then the last second number is 415.
Correct Answer: 32
Explanation:
Let the first number be K and second number be L
Then, 2K + 3L = 100.....(1)
3K + 2L = 120.......(2)
solving (1)&(2), we get
K = 32 and L = 12
Hence the largest number is 32.
Correct Answer: 1
Explanation:
All powers of 6 has 6 in units place so answer will definitely be 1.
Correct Answer: 23
Explanation:
If he wants to give these books equally to 2 of his friends, then 1 book will remain, it means possible number of books = 15,17,19,21,23,25,27,29
If he wants to give these books equally to 3 of his friends, then 2 books will remain, it means possible number of books = 17,20,23,26,29
If he wants to give these books equally to 4 of his friends, then 3 book will remain, it means possible number of books = 15,19,23,27
common number is only 23 so it will be answer
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