Tag: Basic Arithmetic

Question: (?) + 2763 + 1254 1967 =26988

Answer :

x = 28955 4017

= 24938.

Question: (11/n)+( 12/n)+(13/n)+…… Up To N Terms=?

Answer :

Given sum=(1+1+1+…. to n terms)(1/n+2/n+3/n+…. to n terms)

= n(n(n+1)/2)/n

= n(n+1)/2=1/2(n1).

Question: 1004*1004+996*996=

Answer :

= (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

Question: 3621 X 137 + 3621 X 63 = ?

Answer :

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

= (3621 x 200)

= 724200

Question: 597**6 Is Divisible By Both 3 And 11. The Nonzero Digits In The Hundred’s And Ten’s Places Are Respectively?

Answer :

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 11. xy+3=0

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

=>(27+x+x+3)

=>(30+2x)

=> x = 3 and y = 6.

Question: 96 X 96 + 84 X 84 = ?

Answer :

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

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

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

=16272

Question: 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)=?

Answer :

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.

Question: 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?

Answer :

Required number = (333+222)×3×111+62

= 184877

Question: A Two Digit Number Is Such That The Product Of The Digits Is 6. When 45 Is Added To The Number, Then The Digits Are Reversed. The Number Is:

Answer :

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

Question: Find The Number Which Is Nearest To 457 And Is Exactly Divisible By 11.

Answer :

On dividing 457 by 11, remainder is 6.

Required number is either 451 or 462.

Nearest to 456 is 462.

Question: Find The Remainder When 3^27 Is Divided By 5?

Answer :

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 7. now, 7 when divided by 5 gives 2 as remainder.

Question: Here The Sum Of The Series Is 4+8+12+16+….. =612. Find How Many Terms Are There In The Series?

Answer :

This is an A.P. in which a=4, d=4 and Sn=612

Then, n/2[2a+(n1)d]=612 => n/2[2*4+(n1)*4]=612

=> 4n/2(n+1)=612

=> n(n+1)=306

=> n^2+n306=0

=> n^2+18n17n306=0

=> n(n+18)17(n+18)=0

=> (n+18)(n17)=0

=> n=17.

Number of terms=17.

Question: How Many 4 Digit Numbers Are Completely Divisible By 7?

Answer :

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=9996. .’. a+(n1)d=9996

=> 1001+(n1)7= 9996

=>(n1)7=8995

=>(n1)=8995/7= 1285

=> n=1286.

.’. number of terms =1286.

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

Answer :

Required numbers are 18,24,30,…..84

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

84=a+(n1)d

n=12

Question: How Many Natural Numbers Between 23 And 137 Are Divisible By 7?

Answer :

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.

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

Answer :

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 answer =3

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

Answer :

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

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

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

Answer :

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

Question: If The Number 13 * 4 Is Divisible By 6, Then * = ?

Answer :

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.

Question: If The Number 24*32 Is Completely Divisible By 6. What Is The Smallest Whole Number In The Place Of *?

Answer :

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

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

Answer :

5465 is divisible by 5.

So 6K4 must be divisible by 3.

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

K = 2

Question: If The Sum Of 1st N Integers Is 55 Then What Is N?

Answer :

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 ans

answer =10

Question: 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?

Answer :

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.

Question: 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?

Answer :

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.

Question: 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 ?

Answer :

Let P = 5x + 2.

Then 3P = 15x + 6

= 5(3x + 1 ) + 1

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

Question: The Difference Between The Place Values Of Two Eights In The Numeral 97958481 Is?

Answer :

Required difference = (8000 80)

= 7920

Question: The Difference Of The Cubes Of Two Consecutive Even Integers Is Divisible By Which Of The Following Integers?

Answer :

let take 2 consecutive even numbers 2 and 4.

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

Question: The Difference Of Two Numbers Is 1097. On Dividing The Larger Number By The Smaller, We Get 10 As Quotient And The 17 As Remainder. What Is The Smaller Number ?

Answer :

Let the smaller number be x.

Then larger number = (x + 1097)

x + 1097 = 10x + 17

9x = 1080

x = 120

Question: The Product Of Two Numbers Is 20. The Sum Of Squares Of The Two Numbers Is 81.find The Sum Of The Numbers.?

Answer :

Let the numbers be x,y.

=> x2+y2=81,

=> 2(x+y)=40,

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

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

Question: The Product Of Two Numbers Is 436 And The Sum Of Their Squares Is 186. The Difference Of The Numbers Is:

Answer :

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.

Question: The Sum Of Digits Of A Two Digit Number Is 13,the Difference Between The Digits Is 5. Find The Number.?

Answer :

=> x+y=13, xy=5

Adding these 2x =18

=> x=9, y=4.

Thus the number is 94

Question: The Sum Of First 75 Natural Numbers Is?

Answer :

Formula is n(n+1)/2,

Here n=75.

So the answer is 2850

Question: The Sum Of Two Numbers Is 30. The Difference Between The Two Numbers Is 20. Find The Product Of Two Numbers?

Answer :

=> x+y=30
=> xy=20
=> (x+y)2(xy)2 = 4xy
=> 4xy=302202=500
=> xy=500/4=125

Question: Two Third Of Three Fourth Of A Number Is 24. Then One Third Of That Number Is?

Answer :

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

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

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

Answer :

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.

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

Answer :

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 answer is 1.

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

Answer :

Divide 5377 with 7 we get remainder as 1. so, add 6 to the given number so that it will divisible by 7.

Question: Which Natural Number Is Nearest To 6475, Which Is Completely Divisible By 55 ?

Answer :

(6475/55)

Remainder =40

647540=6435

Question: Which Of The Following Is Not A Prime Number?

Answer :

133 is divisible by 7.

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

Question: Which Of The Following Numbers Will Completely Divide (36^11 1) ?

Answer :

=> (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.