problems on numbers.100
TRANSCRIPT
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
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
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.
Problems on numbers Page 2 www.aptitudecoach.com
3. Which of the following has fractions in ascending order?
a. b. c. d.
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
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)
Problems on numbers Page 3 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
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
Problems on numbers Page 4 www.aptitudecoach.com
5. (8 ÷ 88) × 8888088 =?
a. 808008 b. 808080 c. 808088 d. 8008008
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
x 8888088 =
= 808008
Note :
808008 x 11 = 8888088
Problems on numbers Page 5 www.aptitudecoach.com
6. The value of is:
a. 4 b. 5 c. 8 d. 10
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
= Therefore = 15
= Therefore =13
= Therefore = 11
= Therefore = 6
=
=
=4
Problems on numbers Page 6 www.aptitudecoach.com
7. 9548 + 7314 = 8362 + ?
a. 8230 b. 8410 c. 8500 d.
8600
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
9548 + 7314 = 9548 7314
___________ 16862 (-) 8362
___________ 8500
____________
Ans = 8500
(i.e) 9548 + 7314 = 8362 + 8500
Problems on numbers Page 7 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
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
Problems on numbers Page 8 www.aptitudecoach.com
9. What is the difference between the biggest and the smallest fraction
among ?
a. b. c. d.
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
The biggest among , , , is =
The Smallest among , , , is =
The difference between the biggest and the smallest fraction = -
=
=
=
Problems on numbers Page 9 www.aptitudecoach.com
10. Find the number which when multiplied by 15 increased by 196.
a. 14 b. 20 c. 26 d. 28
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
15 x 14 = 210
Which is increased by 196 210 – 14
196 since we multiply it by 15
So the number is 14
Problems on numbers Page 10 www.aptitudecoach.com
11.
a. 1 b. 2 c. 6.65 d. 7.75
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
=
=
=
= 7.75
Problems on numbers Page 11 www.aptitudecoach.com
12. In the following sum, ‘?’ stands for which digit?
? + 1? + 2? + ?3 + ?1 = 21?
a. 4 b. 6 c. 8 d. 9
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
8+81+28+83+81 = 218
Answer is 8
Problems on numbers Page 12 www.aptitudecoach.com
13. Which of the following is a pair of co-primes?
a. (16, 62) b. (18, 25) c. (21, 35) d. (23, 92)
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Two numbers are said to be co-prime if their H.C.F is 1.
Answer with Explanation:
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).
Problems on numbers Page 13 www.aptitudecoach.com
14. 34.95 + 240.016 + 23.98 = ?
a. 298.0946 b. 298.111 c. 298.946 d. 299.09
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Ordinary Addition
Answer with Explanation:
34.95
240.016
23.98 (+)
_________________
298.946
_________________
Problems on numbers Page 14 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
Let the unknown number be x
x + x – (7 ) = x
+ - =
+ - =
30
10615 xxx =
3
22
=
= 2
x = 20
Problems on numbers Page 15 www.aptitudecoach.com
16. is equal to:
a. b. c. d. None of these
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
+
= +
= +
=
= 1
The Answer is None of these.
Problems on numbers Page 16 www.aptitudecoach.com
17.
a. b. c. d.
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
=
= = 4/9
Problems on numbers Page 17 www.aptitudecoach.com
18. The value of 112 × 54 is:
a. 6700 b. 70000 c. 76500 d.
77200
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
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
Problems on numbers Page 18 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
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
Problems on numbers Page 19 www.aptitudecoach.com
20. 12.1212 + 17.0005 – 9.1102 = ?
a. 20.0015 b. 20.0105 c. 20.0115 d. 20.1015
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
12.1212 +
17.0005
______________
29.1217
9.1102
______________
20.0115
______________
Problems on numbers Page 20 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
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
Problems on numbers Page 21 www.aptitudecoach.com
22. of 168 × 15 ÷ 5 + ? = 549 ÷ 9 + 235
a. 107 b. 174 c. 189 d. 296
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
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
Problems on numbers Page 22 www.aptitudecoach.com
23. equals:
a. 0.00069 b. 0.0069 c. 0.0609 d. 0.069
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
=
= ( = 69 )
=
=
= 0.0069
Problems on numbers Page 23 www.aptitudecoach.com
24. The average of five consecutive odd numbers is 61. What is the
difference between of these highest and lowest numbers?
a. 2 b. 5 c. 8 d. None of these
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
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.
Problems on numbers Page 24 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
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
Problems on numbers Page 25 www.aptitudecoach.com
26. The H.C.F of is:
a. b. c. d.
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
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 =
Problems on numbers Page 26 www.aptitudecoach.com
Problems on numbers Page 27 www.aptitudecoach.com
27. Which of the following is equal to 3.14 × 106 ?
a. 314 b. 3140 c. 3140000 d. None of
these
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
3.14 x 10 6
= 3.14 x 10,00,000
= 31,40,000
Problems on numbers Page 28 www.aptitudecoach.com
28. The product of two natural numbers is 17. Then, the sum of the
reciprocals of their squares is:
a. b. c. d. 289
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
Let the take the natural numbers as 1 and 17.
Given that, xy = 17 where x = 1 y = 17
+ =
=
=
Problems on numbers Page 29 www.aptitudecoach.com
29. If a * b = , fine the value of 3 * (3 * -1).
a. -3 b. -1.5 c. -1 d. 2 /
3
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
a*b = (given)
Answer with Explanation:
Now 3 * (3 * -1) = ?
Here a = 3 b=3 *-1 = =
3* (3*-1) = ( by given)
=
= -
= - 3
Problems on numbers Page 30 www.aptitudecoach.com
30. = ?
a. 1.05 b. 1.25 c. 1.45
d. 1.55
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
= 1.25
Problems on numbers Page 31 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
-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.
Problems on numbers Page 32 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
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
Problems on numbers Page 33 www.aptitudecoach.com
33. 40.83 × 1.02 × 1.2 = ?
a. 41.64660 b. 49.97592 c. 42.479532 d.
58.7952
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
x x
= x
=
= 49.97592
Problems on numbers Page 34 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
x+y+z = 264
2y+y+ (2y) = 264
3y+ y = 264
= 264
11y =792
y=72
Problems on numbers Page 35 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
= = x =
The answer is
i.e. - = = =
Ans: None of these.
Problems on numbers Page 36 www.aptitudecoach.com
36. Which number can replace both the question marks in the equation?
?
a. 12 b. 7 c. 6 d. None of these
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
=
X2 = x 32 16
X2 = 144
x = 12
Problems on numbers Page 37 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
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
Answer with Explanation:
n3 = n .n2
n3 is odd = n .n2 is odd
= both n & n2 are odd.
Problems on numbers Page 38 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
95.75 x 0.2554
= 24.45455
Ans: 5
Problems on numbers Page 39 www.aptitudecoach.com
39. The sum of two numbers is 25 and their difference is 13. Find their
product.
a. 104 b. 114 c. 315 d. 325
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
(x + y)2 = (x-y)2 + 4xy
Answer with Explanation:
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
Problems on numbers Page 40 www.aptitudecoach.com
40. On simplification, 3034 – (1002÷20.04) is equal to:
a. 2543 b. 2984 c. 2993
d. 3029
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
3034 – (1002 -20.04)
= 3034 -
= 3034 – 1002 x 100
20.04 x 100
= 3034 – 1002 x 100
2004
= 3034 -
= 3034 – 50
= 2984
Problems on numbers Page 41 www.aptitudecoach.com
41. If , then the value of n is:
a. 6 b. 8 c. 10 d. 12
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
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
Problems on numbers Page 42 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
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
Problems on numbers Page 43 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Given x + y = 528 Greatest common divisor of x, y i.e HCF of (x, y) = 33
Answer with Explanation:
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 .
Problems on numbers Page 44 www.aptitudecoach.com
44.
a. .0009 b. 009 c. 9 d. 9
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
Let = 0.1
x =
x = x
x =
x = 0.09
Problems on numbers Page 45 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
(x+y)2 = (x-y)2 + 4xy
Answer with Explanation:
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
Problems on numbers Page 46 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
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
Problems on numbers Page 47 www.aptitudecoach.com
47. If , then the value of x is:
a. 0.1764 b. 1.764 c. 1.64 d.
2.64
Difficulty Level : Easy Moderately easy Difficult
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
Problems on numbers Page 48 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
+ (number-1) = same number
(i.e.) +(x-1) = x where (x-1) is remainder here.
Answer with Explanation:
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.
Problems on numbers Page 49 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
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
Problems on numbers Page 50 www.aptitudecoach.com
50. The value of is:
a. 0.08 b. 0.2 c. 0.8 d. 1
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
= = a+b
Answer with Explanation:
=
=
= 0.5 + 0.3
= 0.8
Problems on numbers Page 51 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
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.
Problems on numbers Page 52 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
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
Problems on numbers Page 53 www.aptitudecoach.com
53.
a. b. c. d.
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
=
=
=
= 1
Problems on numbers Page 54 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
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.
Problems on numbers Page 55 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
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
Problems on numbers Page 56 www.aptitudecoach.com
56. The value of is:
a. 0 b. 1.6 c. 2 d. 3.4
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
=
= a-b
=
a = 2.3, b=.3
a-b = 2.3 – 0.3
= 2.
Problems on numbers Page 57 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
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.
Problems on numbers Page 58 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
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.
Problems on numbers Page 59 www.aptitudecoach.com
59.
a. 3 b. c. 6 d. None of these
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
=
=
= x
=
=
=
None of these.
Problems on numbers Page 60 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
x = Quotient x Dividend + Remainder
Answer with Explanation:
x = 366 x 999+103
= 365634 +103
x = 365737
Problems on numbers Page 61 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
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
Problems on numbers Page 62 www.aptitudecoach.com
62. is equal to:
a. 30 b. 60 c. 80 d. 100
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
(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
Problems on numbers Page 63 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
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
Problems on numbers Page 64 www.aptitudecoach.com
Problems on numbers Page 65 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Trial and Error Method
Answer with Explanation:
When A = 50 shots
By Trial and error methods A Shots 30 birds
and B Shots 20 birds.
Problems on numbers Page 66 www.aptitudecoach.com
65. The greatest four-digit perfect square number is:
a. 9000 b. 9801 c. 9900 d.
9981
Difficulty Level : Easy Moderately easy Difficult
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
Problems on numbers Page 67 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
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.
Problems on numbers Page 68 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
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
Problems on numbers Page 69 www.aptitudecoach.com
68.
a. 3.308 b. 4 c. 33.08 d. 330.8
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
Let = 40
= x
x =
x =
x = 33.08
Answer is 33.08
Problems on numbers Page 70 www.aptitudecoach.com
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.
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
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
Problems on numbers Page 71 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
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
Problems on numbers Page 72 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
1470 = 7x7x5x6
To make it a perfect square it must be divided by 5x6 (i.e) 30
Required number = 30
The Answer is 30
Problems on numbers Page 73 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
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.
Problems on numbers Page 74 www.aptitudecoach.com
73. Which of the following fraction is the largest?
a. b. c. d.
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
We have = 0.875
= 0.8125
= 0.775
= 0.7875
The largest of these is
Problems on numbers Page 75 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
(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
Problems on numbers Page 76 www.aptitudecoach.com
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.
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
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
Problems on numbers Page 77 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
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
Problems on numbers Page 78 www.aptitudecoach.com
77. if = 2.236, then the value of is equal to :
a. 5.59 b. 7.826 c. 98.994 d.
10.062
Difficulty Level : Easy Moderately easy Difficult
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
Problems on numbers Page 79 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
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.
Problems on numbers Page 80 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
G.C.D
Answer with Explanation:
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.
Problems on numbers Page 81 www.aptitudecoach.com
80.
a. 0.8 b. 1.45 c. 2.40
d. 3.25
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
=
= 0.8
Problems on numbers Page 82 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Let the two digit number be 10x + y
Answer with Explanation:
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
Problems on numbers Page 83 www.aptitudecoach.com
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.
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
The distance travels by
bicycle is = 1 =
Scooter is = 1 =
Foot is = 3.5 – ( + )
= 3.5 – ( )
= 3.5 -
= 0.6633
Problems on numbers Page 84 www.aptitudecoach.com
83. The value of is close to:
a. 0.6 b. 1.1 c. 1.6 d. 1.7
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
=
=
= 1.6
Problems on numbers Page 85 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
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
Problems on numbers Page 86 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
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
Problems on numbers Page 87 www.aptitudecoach.com
86. If 1.5 x = 0.04y, then the value of is:
a. b. c. d. None of these
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
x=
=
=
=
= = =
Problems on numbers Page 88 www.aptitudecoach.com
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?
a. 29 b. 70 c. 92 d. None of these
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
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.
Problems on numbers Page 89 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
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.
Problems on numbers Page 90 www.aptitudecoach.com
89. Which one of the following numbers has rational square root?
a. 0.4 b. 0.09 c. 0.9 d.
0.025
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
= __ not rational
= __ 0.3 which is rational
= __ not rational
= __ not rational
Ans is 0.09
Problems on numbers Page 91 www.aptitudecoach.com
90. Which of the following numbers is divisible by 3, 7, 9 and 11?
a. 639 b. 2079 c. 3791 d.
37911
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
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
Problems on numbers Page 92 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
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.
Problems on numbers Page 93 www.aptitudecoach.com
92.
a. 10-2 b. 10-1 c. 10 d. None of these
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
÷
= ÷
= 0.0371166 ÷ 3.71166
= 0.010000
= 10-2
Problems on numbers Page 94 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
x+y =15
x-y =3
2x = 18
x = 9
x + y = 15
y = 15-9
y = 6
The two digit number = 96
Problems on numbers Page 95 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
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
Problems on numbers Page 96 www.aptitudecoach.com
95. If a = 0.1039, then the value of is:
a. 0.1039 b. 0.2078 c. 1.1039 d. 2.1039
Difficulty Level : Easy Moderately easy Difficult
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
Problems on numbers Page 97 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
A number is divisible by 8, if the number formed by the last 3 digitsof the given number is divisible by 8.
Answer with Explanation:
6 * 2 must be divisible by 8
So * must be replaced by 3
Problems on numbers Page 98 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
(a, b) [a,b] = ab
Answer with Explanation:
ab = 1320, (a, b) = 6
[a, b] = ?
6 x [a, b] = 1320
[a,b] = = 220
Problems on numbers Page 99 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:1.6 x 21.3
= 16 x 10-1 x 213 x 10-1
= x
=
=
= 34.08
Problems on numbers Page 100 www.aptitudecoach.com
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
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
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?
Problems on numbers Page 101 www.aptitudecoach.com
a. 22 b. 44 c. 24 d. 48
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
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.
Problems on numbers Page 102 www.aptitudecoach.com