Q1. A 4 Digit Number 8a43 Is Added To Another 4 Digit Number 3121 To Give A 5 Digit Number 11b64, Which Is Divisible By 11, Then (a+b)=?

a+1=b

=> ba=1.

and 11b64 is divisible by 11

=> (4+b+1)(6+1)=0

=> b2=0

=> b=2.

so, a=1

=>(a+b)= 3.

Q2. If The Number 24*32 Is Completely Divisible By

The number is divisible by 6 me it must be divisible by 2 and @Since the number has 2 as its end digit it is divisible by @Now, 2+4+x+3+2=11+x which must be divisible by @Thus x=1

Q3. The Difference Of Two Numbers Is 109

Let the smaller number be x.

Then larger number = (x + 1097)

x + 1097 = 10x + 17

9x = 1080

x = 120

Q4. If The Sum Of 1st N Integers Is 55 Then What Is N?

sum=n(n+1)/2

sum=55

n^2+n=55*2

n^2+n110=0

(n10)(n+11)=0

n=10,11,neglect negative

wer =10

Q5. A Number When Divided By The Sum Of 333 And 222 Gives Three Times Their Difference The Quotient And 62 As The Remainder. The Number Is?

Required number = (333+222)×3×111+62

= 184877

Q6. The Sum Of First 75 Natural Numbers Is?

Formula is n(n+1)/2,

Here n=75.

So the wer is 2850

Q7. How Many Natural Numbers Between 23 And 137 Are Divisible By 7?

These numbers are 28, 35, 42,…., 133.

This is in A.P. in which a= 28, d=(3528)= 7 and L=133.

Let the number of there terms be n. then, Tn=133

a+(n1)d=133 by solving this we will get n=16.

Q8. Which Of The Following Is Not A Prime Number?

133 is divisible by 7.

Rest of numbers is not divisible by any numbers except itself and 1.

Q9. The Difference Between The Place Values Of Two Eights In The Numeral 97958481 Is?

Required difference = (8000 80)

= 7920

Q10. Find The Number Which Is Nearest To 457 And Is Exactly Divisible By

On dividing 457 by 11, remainder is 6.

Required number is either 451 or 462.

Nearest to 456 is 462.

Q11. What Is The Least Number That Must Be Subtracted 2458 So That It Becomes Completely Divisible By 13?

Divide 2458 by 13 and we get remainder as 1.

Then 131=12.

Adding 12 to 2458 we get 2470 which is divisible by 13.

Thus wer is 1.

Q12. The Product Of Two Numbers Is 436 And The Sum Of Their Squares Is 18

Let the numbers be x and y.

Then, xy = 186 and x2 + y2 = 436.

=> (x y)

2 = x2 + y2 2xy

= 436 (

2 x 186)

= 64

=> x y

= SQRT(64)

= 8.

Q13. Two Times The Second Of Three Consecutive Odd Integers Is 6 More Than The Third. The Third Integer Is?

Let the three integers be x, x + 2 and x + 4.

Then, 2(x+2) = (x + 4) + 6

=> x = 6.

Third integer = x + 4 = 10.

Q14. If The Product 5465 X 6k4 Is Divisible By 15, Then The Value Of K Is

5465 is divisible by 5.

So 6K4 must be divisible by 3.

So (6+K+4) must be divisible by 3.

K = 2

Q15. Which Natural Number Is Nearest To 6475, Which Is Completely Divisible By 55 ?

(6475/55)

Remainder =40

647540=6435

Q16. How Many Natural Numbers Are There Between 17 And 84 Which Are Exactly Divisible By 6?

Required numbers are 18,24,30,…..84

This is an A.P a=18,d=6,l=84

84=a+(n1)d

n=12

Q17. How Many 4 Digit Numbers Are Completely Divisible By 7?

4digit

numbers divisible by 7 are: 1001, 1008, 1015….. 9996.

This is an A.P. in which a=1001, d=7, l=9996.

Let the number of terms be n.

Then Tn=999@.’. a+(n1)d=9996

=> 1001+(n1)7= 9996

=>(n1)7=8995

=>(n1)=8995/7= 1285

=> n=1286.

.’. number of terms =1286.

Q18. It Is Being Given That (5^32+1) Is Completely Divisible By A Whole Number. Which Of The Following Numbers Is Completely Divisible By This Number?

Let 5^32=x.

Then (5^32+1)=(x+1). Let (x+1) be completely divisible by the whole number Y.

then (5^96+1)=[(5^32)^3+1]=>(x^3+1)=(x+1)(x^2x+1) which is completely divisible by Y.

since (x+1) is divisible by Y.

Q19. 96 X 96 + 84 X 84 = ?

= 96 x 96 + 84 x 84 = (96)2 + (84)2

= (90 + 6)2 + (90 6)2

= 2 x [(90)2 + (6)2]

=16272

Q20. If The Number 13 * 4 Is Divisible By 6, Then * = ?

6 = 3 x 2.

Clearly, 13 * 4 is divisible by 2.

Replace * by x.

Then, (1 + 3 + x + 4) must be divisible by 3.

So, x = 1.

Q21. (?) + 2763 + 1254 1967 =26988

x = 28955 4017

= 24938.

Q22. Two Third Of Three Fourth Of A Number Is 2

=> (2/3)*(3/4)*x = 24

=> x=48,1/3x = 16

Q23. 1004*1004+996*996=

= (1004)2+(996)2=(1000+4)2+(10004)2

= (1000)2 + (4)2 + 2*1000*4 + (1000)2 + (4)2 2*100*4

= 2000000 +32 = 2000032

Q24. If N Is A Natural Number, Then (7(n2) + 7n) Is Always Divisible By:

(7n2 + 7n) = 7n(n + 1), which is always divisible by 7 and 14 both, since n(n + 1) is always even.

Q25. What Is The Smallest Number Should Be Added To 5377 So That The Sum Is Completely Divisible By 7?

Divide 5377 with 7 we get remainder as @so, add 6 to the given number so that it will divisible by 7.

Q26. Which Of The Following Numbers Will Completely Divide (36^11 1) ?

=> (xn 1) will be divisible by (x + 1) only when n is even.

=> (36^11 1)

= {(6^2)^11 1}

= (6^22 1),which is divisible by (6 +1)

i.e., 7.

Q27. The Product Of Two Numbers Is 2

Let the numbers be x,y.

=> x2+y2=81,

=> 2(x+y)=40,

=> (x+y)2=81+40=121,

=> x+y=sqrt(121)=11

Q28. 597**6 Is Divisible By Both 3 And

Let the given number be 597xy6.

Then (5+9+7+x+y+6)=(27+x+y) must be divisible by 3

And, (6+x+9)(y+7+5)=(xy+3) must be either 0 or divisible by @xy+3=0

=> y=x+3 27+x+y)

=>(27+x+x+3)

=>(30+2x)

=> x = 3 and y = 6.

Q29. How Many Of The Following Numbers Are Divisible By 132 ? 264, 396, 462, 792, 968, 2178, 5184, 6331

132 = 4 x 3 x 11

So, if the number divisible by all the three number 4, 3 and 11, then the number is divisible by 132 also.

264,396,792 are divisible by 132.

Required wer =3

Q30. If (55^55+55) Is Divided By 56, Then The Remainder Is:?

(x^n+1) is divisible by (x+1), when n is odd.

.’. (55^55+1) is divisible by (55+1)=5@when (55^55+1)+54 is divided by 56, the remainder is 54.

Q31. P Is A Whole Number Which When Divided By 5 Gives 2 As Remainder. What Will Be The Remainder When 3p Is Divided By 5 ?

Let P = 5x + 2.

Then 3P = 15x + 6

= 5(3x + 1 ) + 1

Thus, when 3P is divided by 5, the remainder is 1.

Q32. The Difference Of The Cubes Of Two Consecutive Even Integers Is Divisible By Which Of The Following Integers?

let take 2 consecutive even numbers 2 and 4.

=> (4*4*4)(2*2*2)=648=56 which is divisible by 4.

Q33. A Two Digit Number Is Such That The Product Of The Digits Is

Let the ten’s and unit digit be x and 8/x respectively.

Then, 10x + 6/x + 45 = 10 x 6/x + x

=> 10×2 + 6 + 45x = 60 + x2

=> 9×2 + 45x 54

= 0

=> x2 + 5x 6

= 0

=> (x + 6)(x 1)

= 0

=> x = 1

So the number is 16

Q34. The Sum Of Digits Of A Two Digit Number Is 13,the Difference Between The Digits Is

=> x+y=13, xy=5

Adding these 2x =18

=> x=9, y=4.

Thus the number is 94

Q35. Find The Remainder When 3^27 Is Divided By 5?

3^27= ((3^4)^6) * (3^3) = (81^6) * 27 then unit digit of (81^6) is 1 so on multiplying with 27, unit digit in the result will be @now, 7 when divided by 5 gives 2 as remainder.

Q36. 3621 X 137 + 3621 X 63 = ?

3621 x 137 + 3621 x 63 = 3621 x (137 + 63)

= (3621 x 200)

= 724200

Q37. On Dividing A Certain Number By 234, We Get 43 As Remainder. If The Same Number Is Divided By 13, What Will Be The Remainder?

suppose that on dividing the given number by 234,

we get quotient=x and remainder= 43

then, number= 234*x+43—–>(1).

=> (13*18x)+(13*3)+4

=> 13*(18x+3)+4.

So, the number when divided by 13 gives remainder=4.

Q38. The Sum Of Two Numbers Is 3

=> x+y=30

=> xy=20

=> (x+y)2(xy)2 = 4xy

=> 4xy=302202=500

=> xy=500/4=125