Final

Question 1

The greatest number which divides the numbers x, y and z leaving remainders a, b and c respectively, is given by

Answer 1

HCF of (x − a), (y − b) and (z − c).

Question 2

The greatest number that will divide x, y and z leaving
the same remainder in each case is given by

Answer 2

HCF of |x − y|,|y − z|and|z − x|.

Question 3

The least number which when divided by x, y and z leaves the same remainder k in each case is given by

Answer 3

LCMof(x,y,z)+k.

Question 4

The least number which when divided by x, y and z
leaves the remainders a, b and c respectively, is given by

Answer 4

LCM of (x, y, z) − k, where k = (x − a) = ( y − b) = ( z − c).

Question 5

The greatest n-digit number which when divided by x, y and z leaves
(i) no remainder, then
Required number = ___
(ii) remainder k, then
Required number = ____

Answer 5

(i) no remainder, then
Required number = Greatest n-digit number −R
(ii) remainder k, then
Required number = [Greatest n-digit number −R]+ k
where, R is the remainder obtained when n-digit greatest number is divided by the LCM of x, y and z.

Question 6

The smallest n-digit number which when divided by x, y
and z leaves
(i) no remainder, then
Required number = ___
(ii) remainder k, then
Required number = _____

Answer 6

(i) no remainder, then
Required number = [Smallest n-digit number + (L − R)] (ii) remainder k, then
Required number = [Smallest n-digit number + (L − R)] + k where, R is the remainder obtained when n-digit smallest number isdividedbyLCMofx,y,zandL istheLCMofx,y,z.

Question 7

f the price of a commodity is increased by x%, then reduction in consumption so as not to increase the
expenditure is

Answer 7

{x/(100+x)}100%

Question 8

If the price of a commodity is decreased by x%, then increase in consumption so as not to decrease the
expenditure is

Answer 8

{x/(100-x)}100%

Question 9

Let a quantity (e.g., population) P and it is increased at the rate of r% per annum, then
Quantity after n years = _______
Quantity before n years=______

Answer 9

p{1+(r/100)}^n, p/{1+r/100}^n

Question 10

n an exam x% students pass in subject one and y% students pass in subject two, then pass student in both subjects =

Answer 10

(x + y − 100)%.

Question 11

If a person sells two different articles at the same selling price, one at a gain of a% and another at a loss of a%, then total loss % is calculated as

Answer 11

Loss%=(a/10)^2%

Question 12

If two successive discounts (r1 and r2) are provided,
then
1) Single equivalent discount = __
2)SP=___

Answer 12

1) {r1+r2-(r1r2/100)}%
2) MP{(100-r1)/100}*{(100-r2)/100}

Question 13

Average of squares of first n natural numbers

Answer 13

{(n+1)(2n+1)}/6

Question 14

Average of the cubes of first n natural numbers

Answer 14

{n(n+1)^2}/4

Question 15

Average of first n multiples of any number

Answer 15

Number*(n+1)/2

Question 16

Average of first n odd numbers =

Answer 16

n

Question 17

Average of first n natural numbers

Answer 17

(n+1)/2

Question 18

Average of first n even numbers =

Answer 18

(n + 1)

Question 19

Average of 1 to n even numbers

Answer 19

(LEN+2)/2

Question 20

Average of 1 to n odd numbers

Answer 20

(LON+1)/2

Question 22

Angle between min and hour

Answer 22

11/2 *min -30 *hour

Question 23

How much Hour hand travel in 1 min

Answer 23

0.5 degree

Question 24

In 1 min ___ degree angle is made when hour and minute hand moves relatively

Answer 24

11/2

Question 25

In 12 hours how many time both hands coincides , 180, straight line , 90

Answer 25

11,11,22,22(3 pm and 9 pm)

Question 26

SI and CI difference in 1) 2 years 2) 3 years

Answer 26

PR^2/100^2
PR^2(300+R)/100^3