Problems on Numbers.100

PROBLEMS ON NUMBERS

1. The sum of the smallest six-digit number and the greatest five-digit

number is:

a. 199999 b. 201110 c. 211110 d. 1099999

Difficulty Level : Easy Moderately easy Difficult

Basic Formula:

Answer with Explanation:

The smallest six digit number = 1,00,000

The greatest five digit number = 99,999

Therefore the sum of the smallest = 1,00,000 + 99,999six digit number and the greatest five digit number = 1,99,999

Problems on numbers Page 1 www.aptitudecoach.com

2. Which of the following has most number of divisors?

a. 99 b. 101 c. 176 d. 182


Basic Formula:


Divisiors of 99 = 1, 3, 9, 11, 33, 99

Divisors of 101 = 1,101

Divisors of 176 = 1, 2, 4, 8, 11, 22, 44, 88, 176

Divisors of 182 = 1, 2, 7, 13, 14, 26, 91, 182

Therefore 176 has most number of divisors.


3. Which of the following has fractions in ascending order?

a. b. c. d.


Basic Formula:


LCM of (1,3,7,9,8)= 1512 and

LCM of (2,3,7,8,9)= 3024

Therefore For (a) we have , , Not in ascending order

For (b) we have , , Not in ascending order

For (c) we have , , , ,

The fractions are in ascending order.

For (d), we have , , , ,

Not in ascending order.

Therefore the answer is (c)


4. If one-third of one-fourth of a number is 15, then three-tenth of that

number is:

a. 35 b. 36 c. 45 d. 54


Basic Formula:


Given one third of one fourth of a number (x) is 15.

( ( x x)) = 15

x = 15 x 12

x = 180

Three benth of x = x x

= x 180 = 54


5. (8 ÷ 88) × 8888088 =?

a. 808008 b. 808080 c. 808088 d. 8008008


Basic Formula:


x 8888088 =

= 808008

Note :

808008 x 11 = 8888088


6. The value of is:

a. 4 b. 5 c. 8 d. 10


Basic Formula:


= Therefore = 15

= Therefore =13

= Therefore = 11

= Therefore = 6

=

=

=4


7. 9548 + 7314 = 8362 + ?

a. 8230 b. 8410 c. 8500 d.

8600


Basic Formula:


9548 + 7314 = 9548 7314

___________ 16862 (-) 8362

___________ 8500

____________

Ans = 8500

(i.e) 9548 + 7314 = 8362 + 8500


8. The H.C.F of 24 × 33 × 55 × 24, 23 × 32 × 52 × 7 and 24 × 34 × 5 × 72 × 11 is a. 22 ×32 × 5 b. 22 ×32 ×5 ×7 ×11 c. 24 ×34 ×54

d. 24 ×34×55×7×77


Basic Formula:

Answer with Explanation:Among the three factors

HCF of 24 x 24, 23, 24 is = 23

HCF of 33, 32, 34 is = 32

HCF of 55, 52, 5 = 5

7 & 11 are not in three terms

So we leave the values 7, 72, 11

HCF of three terms = 23 x 32 x 5


9. What is the difference between the biggest and the smallest fraction

among ?

a. b. c. d.


Basic Formula:


The biggest among , , , is =

The Smallest among , , , is =

The difference between the biggest and the smallest fraction = -

=

=

=


10. Find the number which when multiplied by 15 increased by 196.

a. 14 b. 20 c. 26 d. 28


Basic Formula:


15 x 14 = 210

Which is increased by 196 210 – 14

196 since we multiply it by 15

So the number is 14


11.

a. 1 b. 2 c. 6.65 d. 7.75


Basic Formula:


=

=

=

= 7.75


12. In the following sum, ‘?’ stands for which digit?

? + 1? + 2? + ?3 + ?1 = 21?

a. 4 b. 6 c. 8 d. 9


Basic Formula:


8+81+28+83+81 = 218

Answer is 8


13. Which of the following is a pair of co-primes?

a. (16, 62) b. (18, 25) c. (21, 35) d. (23, 92)


Basic Formula:

Two numbers are said to be co-prime if their H.C.F is 1.


H.C.F of 16, 62 is 2

H.C.F of 18, 25 is 1

H.C.F. of 21, 35 is 7

Co-prime = (18, 25).


14. 34.95 + 240.016 + 23.98 = ?

a. 298.0946 b. 298.111 c. 298.946 d. 299.09


Basic Formula:

Ordinary Addition


34.95

240.016

23.98 (+)

_________________

298.946

_________________


15. If the sum of one-half and one-fifth of a number exceeds one-third

of that number by , the number is:

a. 15 b. 18 c. 20 d. 30


Basic Formula:


Let the unknown number be x

x + x – (7 ) = x

+ - =

+ - =

30

10615 xxx =

3

22

=

= 2

x = 20


16. is equal to:

a. b. c. d. None of these


Basic Formula:


+

= +

= +

=

= 1

The Answer is None of these.


17.

a. b. c. d.


Basic Formula:


=

= = 4/9


18. The value of 112 × 54 is:

a. 6700 b. 70000 c. 76500 d.

77200


Basic Formula:


54 = 5 x 5 x 5 x 5 = 25 x 25

= 625

112 x 54 = 112 x 625 _______________

560 224 672

________________ 70000 _________________

The Answer is 70000


19. The L.C.M of 23 × 32 × 5 × 11, 24 ×34 × 52 × 7 and 25 × 33 × 53 × 72 × 11

is :

a. 23 × 32 × 5 b. 25 ×34 × 53

c. 23 ×32 × 5 × 7 × 11 d. 25 ×34 × 53 ×72 × 11


Basic Formula:


Since the multipliers are all in multiplication we can take the L.C.M. of each

number separately.

LCM of 23, 24, 25 = 25

LCM of 32, 34, 33 = 34

LCM of 5, 52, 53 = 53

LCM of 7, 72 = 72

LCM of 11, 11 = 11

LCM of 23 x 32 x 5 x 11, 24 x 34 x 52 x 7, 25 x 33 x 53 x 72 x 11 is

= 25 x 34 x 53 x 72 x 11


20. 12.1212 + 17.0005 – 9.1102 = ?

a. 20.0015 b. 20.0105 c. 20.0115 d. 20.1015


Basic Formula:


12.1212 +

17.0005

______________

29.1217

9.1102

______________

20.0115

______________


21. The sum of a number and its reciprocal is one-eight of 34. What is

the product of the number and its square root?

a. 8 b. 27 c. 32 d. None of these


Basic Formula:

Answer with Explanation:Let the unknown number be x

The sum of a number x & its reciprocal is (34)

Given x + = (34) x =

= a = 4, b= -17, c=4

4x2 – 17x + 4 = 0 x =

Taking x = 4 =

The product of x & it’s square root = x x =

= 4 x = ,

= 4 x 2 = x = 4,

= 8


22. of 168 × 15 ÷ 5 + ? = 549 ÷ 9 + 235

a. 107 b. 174 c. 189 d. 296


Basic Formula:


R.H.S. = + 235

= 61 + 235

R.H.S. = 296

L.H.S. = ( x168) x + x Where x has to be found

L.H.S. = 189 = x

L.H.S. = R.H.S. 189 + x = 296

x = 296 – 189

x = 107


23. equals:

a. 0.00069 b. 0.0069 c. 0.0609 d. 0.069


Basic Formula:


=

= ( = 69 )

=

=

= 0.0069


24. The average of five consecutive odd numbers is 61. What is the

difference between of these highest and lowest numbers?



Basic Formula:


Let the Consecutive odd numbers be

x, x +2, x +4, x +6, x +8

Given = 61

= 61

x+4 =61

x = 57

The numbers are 57, 59, 61, 63, 65

Difference between the highest and lowest number is 65 – 57 = 8.


25. A positive integer, which when added to 1000, gives a sum which is

greater than when it is multiplies by 1000. This positive integer is:

a. 1 b. 3 c. 5 d. 7


Basic Formula:


Let us take the positive integes as x.

Then x+1000 1000 x (Given)

1000 x x+1000

1000 x- x 1000

(1000-1) x 1000

999 x 1000

x

x 1.00

x = 1


26. The H.C.F of is:

a. b. c. d.


Basic Formula:


The numerators are : 9, 12, 18, 21.

3, 9, 12, 18, 21

3, 4, 6, 7 Here common divisor = 3

The denominators are : 10, 25, 35, 40

5 10, 25, 35, 40

2, 5, 7, 8

5 x 2 x 5 x 7 x 8 = 2800

H.C.F =



27. Which of the following is equal to 3.14 × 106 ?

a. 314 b. 3140 c. 3140000 d. None of

these


Basic Formula:


3.14 x 10 6

= 3.14 x 10,00,000

= 31,40,000


28. The product of two natural numbers is 17. Then, the sum of the

reciprocals of their squares is:

a. b. c. d. 289


Basic Formula:


Let the take the natural numbers as 1 and 17.

Given that, xy = 17 where x = 1 y = 17

+ =

=

=


29. If a * b = , fine the value of 3 * (3 * -1).

a. -3 b. -1.5 c. -1 d. 2 /

3


Basic Formula:

a*b = (given)


Now 3 * (3 * -1) = ?

Here a = 3 b=3 *-1 = =

3* (3*-1) = ( by given)

=

= -

= - 3


30. = ?

a. 1.05 b. 1.25 c. 1.45

d. 1.55


Basic Formula:


= 1.25


31. If -1 < x < 2 and 1 < x < 3, then least possible value of (2y – 3x) is:

a. 0 b. -3 c. -4 d. -5


Basic Formula:


-1 x 2 1 y 3-3 3x 6 2 2y 63 -3x -6

i.e. -6 -3x 3 -4 2y - 3 x 9

The least possible value of

(2y – 3x) is -4.


32. The G.C.D. of 1.08, 0.36 and 0.9 is

a. 0.03 b. 0.9 c. 0.18

d. 0.108


Basic Formula:


0.2 1.08, 0.36, 0.9 (or) 2 108, 36, 90

3 54, 18, 45

0.9 5.4, 1.8, 4.5 3 18, 6, 15

6, 2, 5 6, 2, 5

G.C.D = 0.2 x 0.9 = 0.18 2 x 3 x 3 = = 0.18


33. 40.83 × 1.02 × 1.2 = ?

a. 41.64660 b. 49.97592 c. 42.479532 d.

58.7952


Basic Formula:


x x

= x

=

= 49.97592


34. The sum of three numbers is 264. If the first number be twice the second

and third number be one-third of the first, then the second number is:

a. 48 b. 54 c. 84 d. 72


Basic Formula:


x+y+z = 264

2y+y+ (2y) = 264

3y+ y = 264

= 264

11y =792

y=72


35. A student was asked to solve the fraction and his answer was

. By how much was his answer wrong?

a. 1 b. c. d. None of these


Basic Formula:


= = x =

The answer is

i.e. - = = =

Ans: None of these.


36. Which number can replace both the question marks in the equation?

?



Basic Formula:


=

X2 = x 32 16

X2 = 144

x = 12


37. For the integer n, if n3 is odd, then which of the following statements are

true?

I. n is odd II. n2 is odd II. n2 is even

a. I only b. II only c. I and II only d. I and III

only382. Three numbers are in the ratio 1 : 2 : 3 and their H.C.F. is 12. The

numbers are:

a. 4, 8, 12 b. 5, 10, 15 c. 10, 20, 30 d. 12, 24, 36


Basic Formula:

Product of two odd number is oddProduct of an old and an even number is even Product of two even numbers is even


n3 = n .n2

n3 is odd = n .n2 is odd

= both n & n2 are odd.


38. How many digits will be there to the right of the decimal point in the

product of 95.75 and 0.2554?

a. 5 b. 6 c. 7 d. 9


Basic Formula:


95.75 x 0.2554

= 24.45455

Ans: 5


39. The sum of two numbers is 25 and their difference is 13. Find their

product.

a. 104 b. 114 c. 315 d. 325


Basic Formula:

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


Given x +y = 25 & x-y = 13

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

252 = 132 + 4xy

4xy = 252 - 132

=625-169

4xy = 456

xy =

xy = 114


40. On simplification, 3034 – (1002÷20.04) is equal to:

a. 2543 b. 2984 c. 2993

d. 3029


Basic Formula:


3034 – (1002 -20.04)

= 3034 -

= 3034 – 1002 x 100

20.04 x 100

= 3034 – 1002 x 100

2004

= 3034 -

= 3034 – 50

= 2984


41. If , then the value of n is:

a. 6 b. 8 c. 10 d. 12


Basic Formula:


Given = 729

i.e) 3 n/2 = 729

Taking log on both sides,

log 3 n/2 = log 729

n/2 log 3 = log 729

n/2 = = =

n/2 = 6

n= 2 x 6

n = 12


42. There are four prime numbers written in ascending order. The product of

the first three is 385 and that of the last three is 1001. The last number is:

a. 11 b. 13 c. 17 d. 19


Basic Formula:


Let a, b, c, d be the Four Prime numbers

Then abc = 385 1 & bcd = 1001 2

Now gcd of abc & bcd i.e., (abc, bcd)

= bc (a,d)

= bc x 1 ( a & d are prime)

Also (abc, bcd) = (gcd 385, 1001 ) = 77

bc = 77

From 2 bcd = 1001

d = = = 13

IIIly From 1, a = = = 5

Four Prime no’s are 5, 7, 11, 13

The last no. is 13


43. The sum of two numbers is 528 and their H.C.F. is 33. The number of

pairs of numbers satisfying the above conditions is:

a. 4 b. 6 c. 8 d. 12


Basic Formula:

Given x + y = 528 Greatest common divisor of x, y i.e HCF of (x, y) = 33


Considering the multiples of 33 we have (33, 66, 99, 132, 165, 198, 231,

264, 297, 330, 363, 396, 429, 462, 495) we can stop here because the next

factor of 33 is 528.

Since we have the sum of multiples of 33 are 528, we will combine these

multiples as to get their sum as 528.

we get (33, 495) (66, 462) (99, 429) (132, 396) (165, 363) (198, 330)

(231,297)

But we have a condition that HCF of (x, y) = 33

Eliminating the one’s which does not satisfies the condition we get (33,

495) (99, 429) (165, 363) (231, 297)

The number of pairs of numbers satisfying the above condition is 4 .


44.

a. .0009 b. 009 c. 9 d. 9


Basic Formula:


Let = 0.1

x =

x = x

x =

x = 0.09


45. Two numbers differ by 5. If their product is 336, then the sum of the two

numbers is:

a. 21 b. 28 c. 37 d. 51


Basic Formula:

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


Given x-y = 5 and xy =336

We know that

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

= 52 +4 (336)

= 25+1344

(x+y)2 = 1369

x+y = 37


46. 3 – [1.6 – {3.2 – (3.2 + 2.25 ÷ X)}] = .65. The value of X is:

a. 0.3 b. 0.7 c. 3 d. 7


Basic Formula:


Given 3-[1.6-{3.2-(3.2+2.25 ÷ x)}] = 0.65

-[1.6-{3.2-(3.2+2.25÷ x)}] = 0.65-3

-1.6+{3.2-(3.2+2.25÷ x)} = 0.65-3

3.2- (3.2+2.25÷ x) = - 0.75

- 3.2-2.25÷ x = -0.75-3.2

-2.25÷ x = -0.75-3/2 + 3/2

-2.25÷ x = - 0.75

= -0.75

x =

x = 3


47. If , then the value of x is:

a. 0.1764 b. 1.764 c. 1.64 d.

2.64


Basic Formula:

Answer with Explanation: ÷ = 0.02

= 0.02

Squaring on both sides

= (0.02)2

= 0.004

x = 0.004 x 441

x = 0.1764


48. In dividing a number by 585, a student employees the method of short

division. He divided the number successively by 5, 9 and 13 (factors of 585)

and got the remainders 4, 8 and 12. If he had divided the number by 585, the

remainder would have been:

a. 24 b. 144 c. 292 d. 584


Basic Formula:

+ (number-1) = same number

(i.e.) +(x-1) = x where (x-1) is remainder here.


Given a unknown number x when divided by 5,9,13. We get remainders 4,8

&12 .

(i.e.) +4 = x x = 5 & 4 = x-1 (remainder)

+8 = x x = 9 & 8 = x-1 (remainder)

+12 = x x =13 & 12 = x-1 (remainder)

IIIly +(585-1) = x (i.e.) +(x-1) = x x-1 = 584 (remainder)

The remainder would have been 584.


49. The least number which when divided by 5, 6, 7 and 8 leaves a

remainder 3, but when divided by 9 leaves no remainder, is:

a. 1677 b. 1683 c. 2523

d. 3363


Basic Formula:

Answer with Explanation: 336 28 24 21 187

5 1683 6 1683 7 1683 8 1683 9 1683

15 12 14 16 9

18 48 28 8 78

15 48 28 8 72

33 3 3 3 63

30 63

3 0

Ans: L.C.M of 5,6,7,8 is 840

Let the required number be 840k+3,

Which is divisible by 9.

Least value of k for which (90k+4)

is divisible by 9 is k=2

840 x 2 +3 = 1680 +3

= 1683


50. The value of is:

a. 0.08 b. 0.2 c. 0.8 d. 1


Basic Formula:

= = a+b


=

=

= 0.5 + 0.3

= 0.8


51. What will be the sum of two numbers?

I. Among the two numbers, the bigger number is greater than the smaller

number by 6

II. 40% of the smaller number is equal to 30% of the bigger number

III. The ratio between half of the bigger number and one-third of the smaller number

is 2 : 1

a. I and II only b. II and III only c. All I, II and III d. None of these


Basic Formula:


Let x be bigger number and y be smaller number I x –y = 6

II x = y

3x = 4y

III - = 2 3x-4y = 0

Ans I & II only.


52. The taxi charges in a city comprise of a fixed charge, together with the

charge of the distance covered. For a journey of 16 km, the charges paid are

Rs.156 and for a journey of 24 km, the charges paid are Rs.204. What will a

person have to pay for traveling a distance of 30 km?

a. Rs.236 b. Rs.240 c. Rs.248 d. Rs.252


Basic Formula:


For 16 km the charge = Rs.156

1 km the charge = Rs.9.75

For 24 Km the charge = Rs.204

1 Km the charge = Rs.8.5

For 1 Km the fixed charge = Rs.8

For 30 the charge = 30 x 8

= Rs.240


53.

a. b. c. d.


Basic Formula:


=

=

=

= 1


54. A number when divided by 114 leaves the remainder 21. If the same

number is divided by 19, then the remainder will be:

a. 1 b. 2 c. 7 d. 21


Basic Formula:

Answer with Explanation:Given

114 x 19 x

21 ?

114 is a Multiple of 19 (19 x 6 = 114)

So the remainder obtained by when divided by 114 is subtracted from 19

will give the remainder when the same number is divided by 19.

(i.e.) 21 – 19 gives 2.


55. The least multiple of 7, which leaves a remainder of 4, when divided by

6, 9, 15 and 18 is:

a. 74 b. 94 c. 184 d. 364


Basic Formula:

Answer with Explanation:L.C.M of 6,9,15 & 18 is 90

Let required number be 90 k + 4,

which is a multiple of 7

Least value of k for which (90k+4) is divisible by 7 is k = 4

Required number = 90 x 4 +4

= 360 + 4

= 364


56. The value of is:

a. 0 b. 1.6 c. 2 d. 3.4


Basic Formula:


=

= a-b

=

a = 2.3, b=.3

a-b = 2.3 – 0.3

= 2.


57. What is the two-digit number?

I. Sum of the digits is 7.

II. Difference between the number and the number obtained by interchanging the

digits is 9.

III. Digit in the ten’s place is bigger than the digit in the unit’s place by 1.

a. I & II only b. II & III only c. All I, II & III d.

None of these


Basic Formula:

Answer with Explanation:I x +y= 7

II (10x +y) – (10y +x) = 9

9(x-y) = 9

x-y =1

III x-y =1

I & III, I & II

Ans: None of these.


58. In and examination, a student scores 4 marks for every correct answer

and loses 1 mark for every wrong answer. If he attempts in all 60 questions

and secures 130 marks, the number of questions he attempts correctly, is:

a. 35 b. 38 c. 40 d. 42


Basic Formula:

Answer with Explanation:x be the correct answer

y be the wrong answer

x+y = 60

4x –y = 130

x+y = 60

4x-y=130

_____________

5x =190 x = 38

_____________

y= 60-38 y = 22

The number of correct question is 38.


59.

a. 3 b. c. 6 d. None of these


Basic Formula:


=

=

= x

=

=

=

None of these.


60. On dividing a number by 999, the quotient is

366 and the remainder is 103. The number is:

a. 364724 b. 365387 c. 365737 d. 366757


Basic Formula:

x = Quotient x Dividend + Remainder


x = 366 x 999+103

= 365634 +103

x = 365737


61. The smallest number which when diminished by 7, is divisible by 12, 16,

18, 21 and 28 is:

a. 1008 b. 1015 c. 1022

d. 1032


Basic Formula:


1015-7 = 1008

1008 is divisible by 12, 16, 18, 21 & 28

i.e.

12 1008 (84 16 1008 18) 1008 (56 21) 1008 (48

96 63 90 84

48 36 108 168

48 28 ) 1008 108 168

0 84 0 0

168

168

0 1008-7 = 1001 which is not divisible by 2.

Hence which is not divisible by 12, 16, 18, 21 & 28

Similarly, 1022-7 = 1015 also. 1032-7 = 1025


62. is equal to:

a. 30 b. 60 c. 80 d. 100


Basic Formula:


(7.5 x 7.5 + 37.5 + 2.5 x 2.5)

= 7.5 x 7.5 + 2 x 7.5 x 2.5 + 2.5 x 2.5

= (7.5) 2 + 2 x 7.5 x 2.5 + (2.5) 2

Which is in the form of a2 + 2ab + b2 = (a+b)2

Here a = 7.5 & b=2.5

(a+b)2 = (7.5 + 2.5)2

= 10 2

= 100


63. 54 is to be divided into two parts such that the sum of 10 times the first

and 22 times the second is 780. The bigger part is:

a. 24 b. 34 c. 30 d. 32


Basic Formula:


Here a+b = 54 1

54 is divided in to two parts

Hence = 27

10 times the first part is 27 x a = 27a

22 times the second part is 27 x b = 27b

their sum = 780

Hence 10a + 22b = 780 2

1 x 10 10a + 10b = 540

2

b = = 20

put b = 20 in 1,

a +b = 54 a + 20 = 54

a = 54-20 = 34



64. A fires 5 shots to B’s 3 but A kills only once in 3 shots while B kills

once in 2 shots. When B has missed 27 times, A has killed:

a. 30 birds b. 60 birds c. 72 birds d. 90 birds


Basic Formula:

Trial and Error Method


When A = 50 shots

By Trial and error methods A Shots 30 birds

and B Shots 20 birds.


65. The greatest four-digit perfect square number is:

a. 9000 b. 9801 c. 9900 d.

9981


Basic Formula:

Answer with Explanation:To find the square root of 9000

3 9000 9000 = 3 x 3 x 10 x 10 x 10

3 3000 = 3 x 10

10 1000 = 30

10 100

10

which is not a perfect square

To find the square root of 9900

3 9900

3 3300 9900 = 3 x 3 x 10 x 10 x 11

10 1100 = 3 x 10 x

10 110 = 30

11 which is also not a perfect square 3 9981

To find 9981 3 3327

1109

Which is also not a perfect square


66. What least number must be subtracted from 427398 so that the

remaining number is divisible by 15?

a. 3 b. 6 c. 11 d. 16


Basic Formula:

Answer with Explanation 15 427398 (28493

30

127

120

73

60

139

135

48

45

3

Remainder is 3.

When we subtract the remainder from 427398. We will get 427395

which is divisible by 15.


67. The greatest number of hour digits which is divisible by 15, 25, 40 and

75 is:

a. 1008 b. 1015 c. 1022 d.

1032


Basic Formula:


The largest number of four digits is 9999

Required number must be divisible by L.C.M of 15, 25, 40 and 75 by 600

on dividing 9999 by 600 we get 399

Required number = (9999-399) = 9600


68.

a. 3.308 b. 4 c. 33.08 d. 330.8


Basic Formula:


Let = 40

= x

x =

x =

x = 33.08

Answer is 33.08


69. The denominator of a fraction is 3 more than the numerator. If the

numerator as well as the denominator is increased by 4, the fraction becomes

. What was the original fraction?

a. b. c. d.


Basic Formula:


Let the fraction be

Now, =

5(x+4) = 4 (x+7)

5x + 20 = 4x +28

x= 28-20

x=8

The fraction is = =

The Answer is


70. A boy read th of a book on one day and th of the remainder on

another day. If there were 30 pages unread, how many pages did the book

contain?

a. 240 b. 300 c. 600 d. None of

these


Basic Formula:


Let x be the total number of pages in a book (i) (x) read on 1st day

Remaining page = (x- )

th of those remaining page read on 2nd day

(i.e) (x - ) = pages on 2nd time

The Remaining page left = - = 30 (given)

= 30

x = 240


71. The least number by which 1470 must be divided to get a number which

is a perfect square, is:

a. 5 b. 6 c. 15 d. 30


Basic Formula:


1470 = 7x7x5x6

To make it a perfect square it must be divided by 5x6 (i.e) 30

Required number = 30

The Answer is 30


72. If x and y are positive integers such that (3x+7y) is a multiple of 11, then

which of the following will also be divisible by 11?

a. 4x + 6y b. x + y + 4 c. 9x + 4y d. 4x – 9y


Basic Formula:


Keeping y=1, for x=5, we have 3x + 7y=22

which is divisible by 11

Now, substitute x = 5 and y=1 in each alternative and find out which

expression becomes a multiple of 11.

Now, 4x + 6y = 4x5+6 = 26

x+y+4 = 5+1+4 = 10

9x +4y = 9x5+4 =49

4x-9y= 4x5-9 = 20-9 = 11

Which is divisible by 11.

4x-9y is the answer.


73. Which of the following fraction is the largest?

a. b. c. d.


Basic Formula:


We have = 0.875

= 0.8125

= 0.775

= 0.7875

The largest of these is


74. The value of (4.7 × 13.26 + 4.7 × 9.43 + 4.7 × 7731) is:

a. 0.47 b. 47 c. 470 d.

4700


Basic Formula:


(4.7 x 13.26 + 4.7 x 9.43 + 4.7 x 77.31)

= 4.7 (13.26 + 9.43 + 77.31)

= 4.7 x 100

= 470


75. The denominator of a fraction is 3 more than the numerator. If the

numerator as well as the denominator is increased by 4, the fraction becomes

. What was the original fraction?

a. b. c. d.


Basic Formula:


Let the fraction be

Now =

5 (x+4) = 4 (x+7)

5x +20 = 4x +28

x = 28-20

x = 8

The fraction is = =

The Answer is


76. A sum of Rs.1360 has been divided among A B and C such that A gets

of what B gets and B gets of what C gets. B’s share is:

a. Rs.120 b. Rs.160 c. Rs.240 d. Rs.300


Basic Formula:


Let c= x then B= x and A = x x = x

A : B : C = x : x : x

A : B : C = 2 : 3: 12

B’s share = Rs. (1360 x )

= Rs.

= Rs.240

Answer is Rs.240


77. if = 2.236, then the value of is equal to :

a. 5.59 b. 7.826 c. 98.994 d.

10.062


Basic Formula:

Answer with Explanation:Given = 2.236

- +

= - +5

= - + 5 x 2.236

= 1.118 – 4.4727 + 11.18

= 7.826

Ans is 7.826


78. The sum of three consecutive odd numbers is always divisible by:

I. 2 II. 3 III. 5 IV. 6

a. Only I b. Only II c. III. Only I & II d. Only II and IV


Basic Formula:


For example, the first three consecutive odd numbers in natural numbers are

1, 3, 5 and their sum is 9

Which is divisible by 3 alone.

Ans is 3

In general the first three odd consecutive numbers are n, n+2, n+4 then their

sum is 3n +6 which is equal to 3 (n+2)

Which is always divisible by 3.


79. A rectangular courtyard 3.78 metres long and 5.25 metres wide is to be

paved exactly with square tiles, all of the same size. What is the largest size

of the tile which could be used for the purpose?

a. 14 cms b. 21 cms c. 42 cms d. None of these


Basic Formula:

G.C.D


Length of the rectangular courtyard = 3.78 m

= 378 cm

breadth = 5.25 m

= 525 cm

GCD =

3 525, 378

7 175, 126

25, 18

3 x 7 = 21 cms.


80.

a. 0.8 b. 1.45 c. 2.40

d. 3.25


Basic Formula:


=

= 0.8


81. The different between a tow-digit number and the number obtained by

interchanging the digits is 36. What is the difference between the sum and

the difference of the digits of the number if the ratio between the digits of

the number is 1 : 2 ?

a. 4 b. 8 c. 16 d. 18


Basic Formula:

Let the two digit number be 10x + y


10y + x – 10x –y = 36

9y-9x = 36

y-x = 4

ratio x : y = 1:2

y = 2x

2x-x = 4

x = 4

Sub x = 4 in y-x = 4

y-4 = 4

y = 8

x+y - (x-y) = 12+4

= 16


82. A person travels 3.5 km form place A to place B. Out of this distance, he

travels km on bicycle, km on scooter and the rest on foot. What

portion of the whole distance does he cover on foot?

a. b. c. d.


Basic Formula:


The distance travels by

bicycle is = 1 =

Scooter is = 1 =

Foot is = 3.5 – ( + )

= 3.5 – ( )

= 3.5 -

= 0.6633


83. The value of is close to:

a. 0.6 b. 1.1 c. 1.6 d. 1.7


Basic Formula:


=

=

= 1.6


84. The digits indicated * and $ in 3422213*$ so that this number is

divisible by 99, are respectively:

a. 1, 9 b. 3, 7 c. 4, 6 d. 5, 5


Basic Formula:

Trial and Error Method.

Answer with Explanation: 345678

99 3422213 xy 9

297 1

452

396

562

495

671

594

773

693

801

792

99 Ans. is 1, 9 99

0


85. The greatest possible length which can be used to measure exactly the

lengths 7 m, 3 m 85 cm, 12 m 95 cm is :

a. 15 cm b. 25 cm c. 35 cm d. 42 cm


Basic Formula:


Convert cm to m

1 m = 100 cm

85 cm = 0.85 m

95 cm = 0.95 m

To find the LCM of 7m, 3.85m and 12.95m

7 7, 3.85, 12.95

5 1, 0.55, 1.85

1, 0.11, 0.37

LCM of 7, 3.85 and 12.95 is

7 x 5 = 35


86. If 1.5 x = 0.04y, then the value of is:

a. b. c. d. None of these


Basic Formula:


x=

=

=

=

= = =


87. The difference between a two-digit number and the number obtained by

interchanging the two digits is 63. Which is the smaller of the two numbers?



Basic Formula:


70-7 = 63 (i.e) two digit No. = 70

The interchanged No. = 07

Then 70-07 = 63

But smallest of those two No. (70, 07) is 07.

Since it is not here.

Ans is None of these.


88. A pineapple costs Rs.7 each. A watermelon costs Rs.5 each. X spends

Rs.38 on these fruits. The number f pineapples and purchased is:

a. 2 b. 3 c. 4 d. 5


Basic Formula:


Given Pineapple costs = Rs.7

Watermelon costs = Rs.5

Suppose 2 Pineapples are purchased the remaining amount is 24. From this

amount we can get 4 watermelons. The remaining amount is 4.

So the answer 2 is impossible.

It is similar for the case 3 and 5.

If 4 Pineapples are purchased the remaining amount is 10. From this we can

get 2 watermelons.

So the answer is 4.


89. Which one of the following numbers has rational square root?

a. 0.4 b. 0.09 c. 0.9 d.

0.025


Basic Formula:


= __ not rational

= __ 0.3 which is rational

= __ not rational

= __ not rational

Ans is 0.09


90. Which of the following numbers is divisible by 3, 7, 9 and 11?

a. 639 b. 2079 c. 3791 d.

37911


Basic Formula:


Since 3, 7 and 11 are Prime numbers

9 is not a Prime number

So, we multiply all the given numbers

3 x 7 x 9 x 11 = 2079


91. About the number of pairs which have 16 as their H.C.F. and 136 as their

L.C.M., we can definitely say that:

a. No such pair exists b. Only one such pair exists

c. Only two such pairs exist d. Many such pairs exist


Basic Formula:


H.C.F of two numbers divides their L.C.M exactly.

Since 16 is not a factor of 136, it follows that there does not exist any pair of

numbers with H.C.F. 16 and L.C.M. 136.


92.

a. 10-2 b. 10-1 c. 10 d. None of these


Basic Formula:


÷

= ÷

= 0.0371166 ÷ 3.71166

= 0.010000

= 10-2


93. The sum of the digits of a two-digit number is 15 and the difference

between the digits is 3. What is the two-digit number?

a. 69 b. 78 c. 96 d. 87


Basic Formula:


x+y =15

x-y =3

2x = 18

x = 9

x + y = 15

y = 15-9

y = 6

The two digit number = 96


94. Income of a company doubles after every one year. If the initial income

was Rs.4 lakhs, what would be the income after 5 years?

a. Rs.1.24 crores b. Rs.1.28 crores c. Rs.2.56 crores d. None of these


Basic Formula:

Answer with Explanation:Income in 1st year = Rs.4 Lakhs

( Income of a company doubles every 1 year)

Income in 2nd year = Rs.8 Lakhs

” in 3rd year = Rs.16 Lakhs

” in 4th year = Rs.32 Lakhs

” in 5th year = Rs.64 Lakhs

” in 6th year = Rs.12.8 Lakhs

(i.e.) after 5 year = Rs.1.28 crores


95. If a = 0.1039, then the value of is:

a. 0.1039 b. 0.2078 c. 1.1039 d. 2.1039


Basic Formula:

Answer with Explanation:Let a = 0.1039 then

+ 3a = +3a

= +3(0.1039)

= +0.3117

= + 0.3117

= 0.79220 + 0.3117

= 1.1039


96. What least value must be assigned to * so that the number 63576*2 is

divisible by 8?

a. 1 b. 2 c. 3 d. 4


Basic Formula:

A number is divisible by 8, if the number formed by the last 3 digitsof the given number is divisible by 8.


6 * 2 must be divisible by 8

So * must be replaced by 3


97. The product of two numbers is 1320 and their H.C.F. is 6. The L.C.M. of

the numbers is:

a. 220 b. 1314 c. 1326 d.

7920


Basic Formula:

(a, b) [a,b] = ab


ab = 1320, (a, b) = 6

[a, b] = ?

6 x [a, b] = 1320

[a,b] = = 220


98. If 213 × 16 = 3408, then the 1.6 × 21.3 is equal to:

a. 0.3408 b. 3.408 c. 34.08 d. 340.8


Basic Formula:

Answer with Explanation:1.6 x 21.3

= 16 x 10-1 x 213 x 10-1

= x

=

=

= 34.08


99. The sum of the squares of three consecutive natural numbers is 2030.

What is the middle number?

a. 25 b. 26 c. 27 d. 28


Basic Formula:


Let a = x b = x+1 c = x +2

Given a2 + b2 +c2 = 2030 x2 + (x +1)2 + (x+2)2 = 2030 x2 + x2 + 2x+1+x2 +4+4x = 2030

3x2 + 6x + 5 = 2030

3x2 + 6x – 2025 = 0

x2 + 2x – 675 = 0

x =

=

x =

x = = = 25

x =25; x+1 = 26 ; x+2 = 27

100. How many times are the hands of a clock at right angel in a day?


a. 22 b. 44 c. 24 d. 48


Basic Formula:


The hands of a clock at right angle comes twice in an hour.

For a day (i.e) for 24 hours. The hands of a clock at right angle comes

24 x 2 = 48 times.


Date post:	24-Oct-2014
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