Basic Arithmetic MCQ Questions with Answers
Question: 1. On Dividing A Certain Number By 234, We Get 43 As Remainder. If The Same Number Is Divided By thirteen, What Will Be The Remainder?
Answer:
assume that on dividing the given range by 234,
we get quotient=x and the rest= 43
then, quantity= 234*x+43—–>(1).
=> (thirteen*18x)+(thirteen*three)+4
=> thirteen*(18x+3)+four.
So, the wide variety while divided through 13 gives remainder=four.
Question: 2. Find The Remainder When 3^27 Is Divided By 5?
Answer:
three^27= ((3^4)^6) * (3^three) = (eighty one^6) * 27 then unit digit of (81^6) is 1 so on multiplying with 27, unit digit inside the end result might be 7. Now, 7 whilst divided through five gives 2 as the rest.
Question: 3. 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 range of there terms be n. Then, Tn=133
a+(n1)d=133 through solving this we are able to get n=sixteen.
Question: 4. 597**6 Is Divisible By Both 3 And eleven. The Nonzero Digits In The Hundred’s And Ten’s Places Are Respectively?
Answer:
Let the given wide variety be 597xy6.
Then (five+9+7+x+y+6)=(27+x+y) have to be divisible by way of three
And, (6+x+9)(y+7+5)=(xy+3) must be both zero or divisible by using 11. Xy+three=zero
=> y=x+3 27+x+y)
=>(27+x+x+3)
=>(30+2x)
=> x = 3 and y = 6.
Question: 5. 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 the rest as 1. So, add 6 to the given quantity a good way to divisible by using 7.
Question: 6. The Difference Of The Cubes Of Two Consecutive Even Integers Is Divisible By Which Of The Following Integers?
Answer:
permit take 2 consecutive even numbers 2 and 4.
=> (four*four*4)(2*2*2)=648=fifty six that is divisible via 4.
Question: 7. If The Sum Of 1st N Integers Is 55 Then What Is N?
Answer:
sum=n(n+1)/2
sum=fifty five
n^2+n=fifty five*2
n^2+n110=0
(n10)(n+11)=0
n=10,eleven,neglect terrible ans
answer =10
Question: 8. 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 five^32=x.
Then (five^32+1)=(x+1). Let (x+1) be absolutely divisible by means of the entire number Y.
Then (five^ninety six+1)=[(5^32)^3+1]=>(x^three+1)=(x+1)(x^2x+1) which is completely divisible by way of Y.
For the reason that (x+1) is divisible through Y.
Question: 9. A 4 Digit Number 8a43 Is Added To Another four Digit Number 3121 To Give A five Digit Number 11b64, Which Is Divisible By 11, Then (a+b)=?
Answer:
a+1=b
=> ba=1.
And 11b64 is divisible by 11
=> (four+b+1)(6+1)=zero
=> b2=0
=> b=2.
So, a=1
=>(a+b)= three.
Question: 10. How Many 4 Digit Numbers Are Completely Divisible By 7?
Answer:
4digit
numbers divisible by means of 7 are: 1001, 1008, 1015….. 9996.
This is an A.P. In which a=1001, d=7, l=9996.
Let the wide variety of phrases be n.
Then Tn=9996. .’. A+(n1)d=9996
=> 1001+(n1)7= 9996
=>(n1)7=8995
=>(n1)=8995/7= 1285
=> n=1286.
.’. Quantity of phrases =1286.
Question: 11. (eleven/n)+( 12/n)+(13/n)+…… Up To N Terms=?
Answer:
Given sum=(1+1+1+…. To n phrases)(1/n+2/n+3/n+…. To n phrases)
= n(n(n+1)/2)/n
= n(n+1)/2=half of(n1).
Question: 12. Here The Sum Of The Series Is four+eight+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=zero
=> n^2+18n17n306=0
=> n(n+18)17(n+18)=zero
=> (n+18)(n17)=zero
=> n=17.
Number of terms=17.
Question: 13. If (fifty five^fifty five+55) Is Divided By fifty six, Then The Remainder Is:?
Answer:
(x^n+1) is divisible by using (x+1), while n is peculiar.
.’. (55^55+1) is divisible by way of (fifty five+1)=fifty six. When (55^fifty five+1)+54 is divided by means of 56, the the rest is fifty four.
Question: 14. Two Third Of Three Fourth Of A Number Is 24. Then One Third Of That Number Is?
Answer:
=> (2/three)*(three/four)*x = 24
=> x=forty eight,1/3x = sixteen
Question: 15. 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 those 2x =18
=> x=9, y=4.
Thus the variety is ninety four
Question: 16. The Product Of Two Numbers Is 20. The Sum Of Squares Of The Two Numbers Is 81.Discover The Sum Of The Numbers.?
Answer:
Let the numbers be x,y.
=> x2+y2=81,
=> 2(x+y)=40,
=> (x+y)2=eighty one+40=121,
=> x+y=sqrt(121)=11
Question: 17. 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: 18. Which Of The Following Is Not A Prime Number?
Answer:
133 is divisible by means of 7.
Rest of numbers isn’t always divisible by way of any numbers except itself and 1.
Question: 19. What Is The Least Number That Must Be Subtracted 2458 So That It Becomes Completely Divisible By thirteen?
Answer:
Divide 2458 by 13 and we get remainder as 1.
Then 131=12.
Adding 12 to 2458 we get 2470 which is divisible via thirteen.
Thus answer is 1.
Question: 20. If The Number 24*32 Is Completely Divisible By 6. What Is The Smallest Whole Number In The Place Of *?
Answer:
The variety is divisible via 6 approach it must be divisible via 2 and three. Since the range has 2 as its stop digit it is divisible with the aid of 2. Now, 2+four+x+3+2=11+x which have to be divisible by means of three. Thus x=1
Question: 21. 1004*1004+996*996=
Answer:
= (1004)2+(996)2=(a thousand+4)2+(10004)2
= (one thousand)2 + (four)2 + 2*a thousand*four + (one thousand)2 + (four)2 2*one hundred*4
= 2000000 +32 = 2000032
Question: 22. 3621 X 137 + 3621 X sixty three = ?
Answer:
3621 x 137 + 3621 x sixty three = 3621 x (137 + 63)
= (3621 x two hundred)
= 724200
Question: 23. 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 wide variety be x.
Then larger wide variety = (x + 1097)
x + 1097 = 10x + 17
9x = 1080
x = one hundred twenty
Question: 24. If N Is A Natural Number, Then (7(n2) + 7n) Is Always Divisible By:
Answer:
(7n2 + 7n) = 7n(n + 1), that is continually divisible by using 7 and 14 each, in view that n(n + 1) is always even.
Question: 25. 96 X 96 + eighty four X eighty four = ?
Answer:
= ninety six x 96 + eighty four x 84 = (ninety six)2 + (84)2
= (90 + 6)2 + (ninety 6)2
= 2 x [(90)2 + (6)2]
=16272
Question: 26. How Many Of The Following Numbers Are Divisible By 132 ? 264, 396, 462, 792, 968, 2178, 5184, 6331
Answer:
132 = four x 3 x 11
So, if the quantity divisible by all of the 3 range four, 3 and 11, then the wide variety is divisible by using 132 additionally.
264,396,792 are divisible via 132.
Required answer =3
Question: 27. (?) + 2763 + 1254 1967 =26988
Answer:
x = 28955 4017
= 24938.
Question: 28. How Many Natural Numbers Are There Between 17 And 84 Which Are Exactly Divisible By 6?
Answer:
Required numbers are 18,24,30,…..Eighty four
This is an A.P a=18,d=6,l=84
84=a+(n1)d
n=12
Question: 29. If The Product 5465 X 6k4 Is Divisible By 15, Then The Value Of K Is
Answer:
5465 is divisible by way of 5.
So 6K4 must be divisible by three.
So (6+K+4) need to be divisible by way of three.
K = 2
Question: 30. If The Number 13 * 4 Is Divisible By 6, Then * = ?
Answer:
6 = three x 2.
Clearly, thirteen * 4 is divisible by using 2.
Replace * by x.
Then, (1 + three + x + 4) must be divisible by means of 3.
So, x = 1.
Question: 31. Which Of The Following Numbers Will Completely Divide (36^11 1) ?
Answer:
=> (xn 1) will be divisible through (x + 1) most effective whilst n is even.
=> (36^11 1)
= (6^2)^eleven 1
= (6^22 1),which is divisible by way of (6 +1)
i.E., 7.
Question: 32. Which Natural Number Is Nearest To 6475, Which Is Completely Divisible By 55 ?
Answer:
(6475/55)
Remainder =forty
647540=6435
Question: 33. P Is A Whole Number Which When Divided By five Gives 2 As Remainder. What Will Be The Remainder When 3p Is Divided By five ?
Answer:
Let P = 5x + 2.
Then 3P = 15x + 6
= 5(3x + 1 ) + 1
Thus, while 3P is divided by five, the remainder is 1.
Question: 34. The Sum Of First 75 Natural Numbers Is?
Answer:
Formula is n(n+1)/2,
Here n=75.
So the answer is 2850
Question: 35. The Difference Between The Place Values Of Two Eights In The Numeral 97958481 Is?
Answer:
Required distinction = (8000 80)
= 7920
Question: 36. 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 wide variety = (333+222)×three×111+62
= 184877
Question: 37. Find The Number Which Is Nearest To 457 And Is Exactly Divisible By 11.
Answer:
On dividing 457 through 11, remainder is 6.
Required number is either 451 or 462.
Nearest to 456 is 462.
Question: 38. Two Times The Second Of Three Consecutive Odd Integers Is 6 More Than The Third. The Third Integer Is?
Answer:
Let the 3 integers be x, x + 2 and x + four.
Then, 2(x+2) = (x + 4) + 6
=> x = 6.
Third integer = x + four = 10.
Question: 39. A Two Digit Number Is Such That The Product Of The Digits Is 6. When forty five Is Added To The Number, Then The Digits Are Reversed. The Number Is:
Answer:
Let the 10’s and unit digit be x and 8/x respectively.
Then, 10x + 6/x + forty five = 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 quantity is sixteen
Question: 40. 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)
= sixty four
=> x y
= SQRT(64)
= eight.