Question 1

Find the sum to 200 terms of the series 2 + 5 + 7 + 6 + 12 + 7 + ....

Accepted Answer

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 n n + 1 2 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.

Question 2

What least number must be substracted from 627349 so that the remaining number is divisible by 15 ?

Accepted Answer

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.

Question 3

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 ?

Accepted Answer

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.

Question 4

(3x + 2) (2x - 5) = ax² + kx + n. What is the value of a - n + k ?

Accepted Answer

(3x + 2) (2x - 5) = a x 2 + k x + n ...............(1) But (3x + 2)(2x - 5) = 6 x 2 - 11 x - 10 ........(2) so by comparing (1) & (2), we get a= 6, k= -11 , n= -10 (a - n + k) = 6 + 10 - 11 = 5.

Question 5

How many zeros are there from 1 to 10000 ?

Accepted Answer

For 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

Question 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 ?

Accepted Answer

Number = quotient x divisor + remainder; so, here number = 138 k + 26 => (23 x 6k) + (23+3) => 23(6k+1)+3 so, remainder is 3.

Question 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

Accepted Answer

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.

Question 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 ?

Accepted Answer

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.

Question 9

Find the remainder when 629 is divided by 5 ?

Accepted Answer

All powers of 6 has 6 in units place so answer will definitely be 1.

Question 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 remai…

Accepted Answer

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

Question 11

A thief steals half the total number of loaves of bread plus 1/2 loaf from a bakery. A second thief steals half the remaining number of loaves plus 1/2 loaf and so on. After the 5th thief has stolen there are no more loaves left in the bakery. What …

Accepted Answer

Let y be the total number of loaves a be the remaining loaves after 1st thief b be the remaining loaves after 2nd thief and c, d..so on after 3 and 4 th e = 0 be the remaining loaves after 5th thief a = y - (y/2 + 1/2) = y/2 - 1/2 b = a - (a/2 + 1/2) = a/2 - 1/2 c = b - (b/2 + 1/2) = b/2 - 1/2 d = c - (c/2 + 1/2) = c/2 - 1/2 e = d - (d/2 + 1/2) = d/2 - 1/2 we know that, e = 0, thus by substitution, we get d = 1 c = 3 b = 7 a = 15 y = 31 Therefore total number of bread loaves in bakery was 31.

Question 12

Maheshwari wants to buy 7 floors in an 68 storied building whose numbering stars from 1 upto 68. But she has to follow certain rules which are as follows : 1) None of the floor should be a prime number 2) None of the digit of the floor should be a p…

Accepted Answer

Since floor starts form the 1 therefore 2 will be the 1st floor. Form 1 to 10 only 4,6,8,9,10 are not prime. Form 11 to 20 only 14 ,16,18 are not prime also non of their digits are prime. From 21 to 30 each number has a prime number so it must no be consider. In between 40 to 49 we have to consider only 40,44,46,48,49. 50 to 59 follow either of the condition so we have too neglect it. In between 60 to 68 60,64,66,68. total option = 17.

Question 13

25 divided by 7

Accepted Answer

Here we have 25 divided by 7. 25 will not go directly in 7 Hence, we get the result in decimals. 25/7 = 3.571.

Question 14

The sum of three prime numbers is 100. If one of them exceeds another by 36, then one of the numbers is

Accepted Answer

none

Question 15

A straight fence is to be constructed from posts 6 inches wide and separated by lengths of chain 5 feet long. If a certain fence begins and ends with a post, which of the following could be the length of the fence in feet? (12 inches = 1 foot).

Accepted Answer

The fence will consist of one more post than there are chains. (e.g. P-c-P-c-P). Therefore, a total length has to be a multiple of the length of the chain plus one post (5.5) plus one post extra.We have length = (5.5n + 0.5), where n can be any positive whole number. If n= 3, length =17

Question 16

What is the simplified result of following the steps below in order? 1.Add 5y to 2x 2.Multiply the sum by 3 3.Substract x+y from the product

Accepted Answer

Step 1 :2x + 5y Step 2 :3(2x + 5y) = 6x + 15y Step 3 :(6x + 15y) - (x +y) = 6x + 15y - x - y (watch that last minus sign!) This gives 5x + 14y

Question 17

K men agree to donate a gift of Rs. L to trust. If three men drop out how much more will each have to contribute towards the purchase of the gift ?

Accepted Answer

Intial contribution = L/K After 3 men drop, then contribution =L/K-3 The amount more to pay in contribution = L K - 3 - L K = 3 L K ( K - 3 )

Question 18

From the given series of numbers, if half of the second highest number is subtracted from the third highest number, what will be the value ? 519 328 746 495 837

Accepted Answer

From the given series of numbers, if half of the second highest number is subtracted from the third highest number, what will be the value ? Now arranging the given numbers in descending order. 837 746 519 495 328 519 - 746/2 = 519 - 373 = 146.

Question 19

There is a 3 digited number. 3rd digit is the square root of the 1st digit. 2nd digit is the sum of 1st and 3rd. And that number is divisible by 2,3,6,7. What is that number?

Accepted Answer

Assume that the number is taken as XYZ. Condition 1 => Z = sq.root(x) => Possible digits of X is 1,4,9 Condition 2 => Y = X + Z X Y Z 1 2 1 4 6 2 9 12 3 => (wrong because it is 4 digit.) and 121 is not divisible by 2 The answer is 462.

Question 20

Find the regular polygon whose interior angel is 150 more than exterior angle. note the total sum of interior and exterior angle should be 180 at one point ?

Accepted Answer

Sum of Interior angle is 180 . and it is given that interior angle is 150 more than exterior, so let exterior angle is x then interior will be x+150 now , interior + exterior =180 x+150+x=180 x=15 now , number of sides of polygon = 360 / exterior angle n = 360 / 15 n = 24

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