NUMBERS

What could be the maximum value of y in the following equation? 5X9 3Y7 2Z8 = 1114

clearly,2 X Y Z= 11

(11-2) =9 when X=0,Z=0)

7589 – ? =3434

Let 7589 -x=3434

then x=(7589 – 3434)

= 4155

In this sum ,? stands for which digit ? 1? 2? 3? ?1=21?

let x (10 x) (20 x) (10x 3) (10x 1)=200 10 x

total x = 23

23x 34=210 x

23x-x=210-34

22x=176

x=176/22

x=8

Find the sum of prime numbers lying between 60 and 75

61, 67, 71, 73

sum =(61 67 71 73)=272

12345679* 72 is equal to:

simple multiplication 888888888

The least prime number is 2

How many numbers between 200 and 600 are divisible by 4,5 and 6?

L.C.M. of 4,5 and 6 = 60

240,300,360,420,480,540

there are 6 such numbers

The greatest number by which the product of three consecutive multiples of 3 is always divisible is :

Required Number = Product of first three multiples of 3 =(3*6*9) = 162

The unit’s digit in the product ( 7⁷¹ * 6⁵⁹ * 3⁶⁵ ) IS :

Unit digit in 7⁶⁸ is 1

Unit digit in 7⁷¹ is 3

Again , every power of 6 will give unit digit  6

: Unit digit is 6⁵⁹ is 6

Unit digit in 3⁴ is 1

: Unit digit in 3⁶⁵ is 1 .  Unit digit in 3⁶⁵ is 3

:  Unit digit in ( 7⁷¹ * 6⁵⁹ * 3⁶⁵ ) =Unit digit in (3*6*3) = 4

If x is a whole number, then xx²-1) is always divisible by :

put x=2

2²(2²-1)

4(4-1)

4(3)

12

4⁶¹ 4⁶² 4⁶³ 4⁶⁴ is divisible by :

4⁶¹ 4⁶² 4⁶³ 4⁶⁴=4⁶¹(1 4 4² 4³)=4⁶¹* 85=4⁶⁰ * 340

divisible by 10

The smallest number that must be added to 803642 in order to obtain a multiple of 11 is :

required number to be  added = (11-4)=7

If 1*548 is divisible by 3 which of the digit can replace * ?

1 x 5 4 8=(18 x)

digit can replace by  = 3

Find the sum of even number between 1 to 100

odd number 1 to 100 are 2,4,6,8,………100

n=50 , first term =2, last term =100

sum = n/2(first term last term )

50/2(2 100)

25(102)

2550

The digit in unit’s place of the product 81*82*…..*89 is

unit digit in (1*2*3*4*5*6*7*8*9)=0

Which one of the numbers is exactly divisible by 11?

235641; 245642; 315624; 415624

sum of digits at odd places- sum of digits at even places

235641

(1 6 3)-(4 5 2)=1(NO)

2). 245642

(2 6 4)-(4 5 2)=1(NO)

3.) 315624

(4 6 1)-(2 5 3)=1(NO)

4). 415624

(4 6 1)-(2 5 4)=0(YES)

The sum of first 45 natural numbers is :

natural number(1,2,3…n)

(1 2 3 …..n)=n(n 1)/2

45(45 1)/2

45*46/2

2070/2

1035

325325 is a six – digit number. It is divisible by

clearly 325325 is divisible by 7,11,13

(46)²- (?)² = 4398 – 3066

Let (46)²- (x)² = 4398 – 3066

(46)²- (x)² =1332

(x)² =(46)²-1332

(x)²= 2116-1332

(x)²= 784

x=√28

360 *17 =?

360-(20-3)

(360*20)-(360*3)

(7200-1080)

6120