Skip links

Type and hit enter

JumpWhere
Number system and number property
Published in: Aptitude

Number system and number property

Author
Published on:

[vc_row][/vc_row][vc_column][/vc_column][vc_toggle title=”Explanation / Important formulas:” el_id=”1481454282462-60885454-0285″]

  • (a + b)(a – b) = (a2 – b2)
  • (a + b)2 = (a2 + b2 + 2ab)
  • (a – b)2 = (a2 + b2 – 2ab)
  • (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
  • (a3 + b3) = (a + b)(a2 – ab + b2)
  • (a3 – b3) = (a – b)(a2 + ab + b2)
  • (a3 + b3 + c3 – 3abc) = (a + b + c)(a2 + b2 + c2 – ab – bc – ac)
  • When a + b + c = 0, then a3 + b3 + c3 = 3abc

For more information: https://en.wikipedia.org/wiki/Number[/vc_toggle][vc_toggle title=”Instructions to take Aptitude Test” el_id=”1481454372988-cd8f0f96-30f0″]

  • Click on start to start taking the test.
  • Click on the option (A, B, C or D) to figure out the right answer.
  • You can answer multiple times till you get the right answer.
  • Once you get the right answer, explanations (if any) for the same will be showcased down.
  • On click of list, you get to see total no of questions, no of questions you answered and no of questions pending to answer.
  • On click of question number you will go to that particular question.
  • On click of END your test will end.
  • On click of ‘Get Results’ you will get to see correct answer for each questions.

[/vc_toggle][vc_toggle title=”Number system and number property – Test” open=”true” el_id=”1481454458410-9a4a39ac-c8b7″]

Number system and number property - Question and Answers

Congratulations - you have completed Number system and number property - Question and Answers. You scored %%SCORE%% out of %%TOTAL%%. Your performance has been rated as %%RATING%%
Your answers are highlighted below.
Question 1
Find next number of the following sequence 124, 62, 60, 30, 28, 14...?
A
7
B
8
C
12
D
13
Question 1 Explanation: 
To find the next sequence
=> 124/2 = 62 & 62 - 2 = 60
=> 60/2=30 & 30 - 2 =28
=> 28/2=14 & 14 - 2 =12
Question 2
Find the sum of all the terms in the series 1, ½, ¼ ……?
A
2
B
3
C
4
D
Cannot be determined
Question 2 Explanation: 
Sum of the infinite G.P = a/1 - r
(Here a = First term, r = ratio)
=1 / (1 - 1/2)
=2
Question 3
Which of the following number is divisible by 4?
A
1123346
B
10224
C
100234
D
123458
Question 3 Explanation: 
If the last two digits of the number is divisible by 4, then we can say that the number is divisible by 4
Question 4
A piece of ribbon 4 yards long is used to make a bow requiring 15 inches of ribbon for each. What is the maximum number of bows that can be made?
A
8
B
9
C
10
D
11
Question 4 Explanation: 
To find maximum number of bows that can be made
1 yard = 36 inches
4 yards = 4*36=144 inches
No.of maximum bows that can be made = 144/15 = 9.6
So maximum 9 bows can be made
Question 5
A number consist of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. The number is..?
A
145
B
253
C
370
D
352
Question 5 Explanation: 
Let the digits of the No. be x & y & z
Hence , x + y + z = 10………(1)
x + z = y………(2)
As per the condition
(100z + 10y + x) - (100x + 10y + z) = 99
Solving, the value of (z - x) =1
From equation(1) and (2)
2y = 10, y = 5
So 253 satisfies all the condition
Question 6
What is the unit digit in the product (365 x 659 x 771)?
A
1
B
2
C
4
D
6
Question 6 Explanation: 
Unit digit in 34 = 1 Unit digit in (34)16 = 1
Unit digit in 365 = Unit digit in [ (34)16 x 3 ] = (1 x 3) = 3
Unit digit in 659 = 6
Unit digit in 74 Unit digit in (74)17 is 1.
Unit digit in 771 = Unit digit in [(74)17 x 73] = (1 x 3) = 3
Required digit = Unit digit in (3 x 6 x 3) = 4.
Question 7
What is the unit digit in 7105 ?    
A
1
B
5
C
7
D
9
Question 7 Explanation: 
Unit digit in 7105 = Unit digit in [ (74)26 x 7 ]
But, unit digit in (74)26 = 1
Unit digit in 7105 = (1 x 7) = 7
Question 8
3251 + 587 + 369 - ? = 3007
A
1250
B
1300
C
1375
D
1200
Question 8 Explanation: 
3251
+ 587
369
----
4207
----
Let 4207 - x = 3007
Then, x = 4207 - 3007 = 1200
Question 9
7589 - ? = 3434
A
4242
B
4155
C
1123
D
11023
Question 9 Explanation: 
Let 7589 - x = 3434
Then, x = 7589 - 3434 = 4155
Question 10
217 x 217 + 183 x 183 =?    
A
79698
B
80578
C
80698
D
81268
Question 10 Explanation: 
(217)2 +(183)2 = (200 + 17)2 + (200 - 17)2
= 2 x [(200)2 + (17)2] [Ref: (a + b)2 + (a - b)2 = 2(a2 + b2)]
= 2[40000 + 289]
= 2 x 40289
= 80578
Question 11
The unit digit in the product (784 x 618 x 917 x 463) is:
A
2
B
3
C
4
D
5
Question 11 Explanation: 
Unit digit in the given product = Unit digit in (4 x 8 x 7 x 3) = (672) = 2
Question 12
3897 x 999 = ?
A
3883203
B
3893103
C
3639403
D
3791203
Question 12 Explanation: 
3897 x 999 = 3897 x (1000 - 1)
= 3897 x 1000 - 3897 x 1
= 3897000 - 3897
= 3893103
Question 13
Which of the following numbers will completely divide (461 + 462 + 463 + 464)?
A
3
B
10
C
11
D
13
Question 13 Explanation: 
(461 + 462 + 463 + 464) = 461 x (1 + 4 + 42 + 43) = 461 x 85
= 460 x (4 x 85)
= (460 x 340), which is divisible by 10
Question 14
106 x 106 - 94 x 94 =?  
A
2400
B
2000
C
1904
D
1906
Question 14 Explanation: 
106 x 106 - 94 x 94= (106)2 - (94)2
= (106 + 94)(106 - 94) [Ref: (a2 - b2) = (a + b)(a - b)]
= (200 x 12)
= 2400
Question 15
8988 ÷ 8 ÷ 4 =?
A
4494
B
561.75
C
2247
D
280.875
Question 15 Explanation: 
8988 x 1/8 x 1/4 = 2247/8 = 280.875
Question 16
3 + 33 + 333 + 3.33 =?
A
362.3
B
372.33
C
702.33
D
.702
Question 16 Explanation: 
3
+ 33
+ 333
+ 3.33
------
372.33
------
Question 17
(1000)9 ÷ 1024 =?  
A
10000
B
1000
C
100
D
10
Question 17 Explanation: 
(1000)9 / 1024 = (103 )9 / 1024 = (10)27 / 1024 = 10(27-24) = 103 = 1000
Question 18
{(476 + 424)2 - 4 x 476 x 424} = ?  
A
2906
B
3116
C
2704
D
2904
Question 18 Explanation: 
From the given expression [(a + b)2 - 4ab]
Consider a = 476 and b = 424 = [(476 + 424)2 - 4 x 476 x 424]
= [(900)2 - 807296]
= 810000 - 807296
= 2704
Question 19
A number when divided successively by 4 and 5 leaves remainders 1 and 4 respectively. When it is successively divided by 5 and 4, then the respective remainders will be
A
1, 2
B
2, 3
C
3, 2
D
4, 1
Question 19 Explanation: 
4 | x
--------
5 | y -1
--------
| 1 -4
y = (5 x 1 + 4) = 9
x = (4 x y + 1) = (4 x 9 + 1) = 37
Now, 37 when divided successively by 5 and 4, we get
5 | 37
---------
4 | 7 - 2
---------
| 1 - 3
Respective remainders are 2 and 3
Question 20
8796 x 223 + 8796 x 77 =?  
A
2736900
B
2638800
C
2658560
D
2716740
Question 20 Explanation: 
8796 x 223 + 8796 x 77= 8796 x (223 + 77) [Ref: By Distributive Law ]
= (8796 x 300)
= 2638800
Question 21
287 x 287 + 269 x 269 - 2 x 287 x 269 =?  
A
534
B
446
C
354
D
324
Question 21 Explanation: 
From the given expression[a2 + b2 - 2ab] Consider a = 287 and b = 269
= (a - b)2 = (287 - 269)2
= (182)
= 324
Question 22
Which one of the following can't be the square of natural number?
A
30976
B
75625
C
28561
D
143642
Question 22 Explanation: 
The square of a natural number never ends in 2
143642 is not the square of natural number.
Question 23
The sum of even numbers between 1 and 31 is  
A
6
B
28
C
240
D
512
Question 23 Explanation: 
Let Sn = (2 + 4 + 6 + ... + 30). This is an A.P. in which a = 2, d = 2 and l = 30
Let the number of terms be n. Then,
a + (n - 1)d = 30
2 + (n - 1) x 2 = 30
n = 15
Therefore, Sn = n/2(a + l) = 15/2 x (2 + 30) = (15 x 16) = 240
Question 24
If 60% of 3/5 of a number is 36, then the number is  
A
80
B
100
C
75
D
90
Question 24 Explanation: 
Let the number be x. Then
60% of 3/5 of x = 36
=> 60/100 * 3/5 * x = 36
=> x = (36 * 25/9) = 100
Required number = 100
Question 25
If x and y are the two digits of the number 653xy such that this number is divisible by 80, then x + y =?
A
2 or 6
B
4
C
4 or 8
D
8
Question 25 Explanation: 
80 = 2 x 5 x 8
Since 653xy is divisible by 2 and 5 both, so y = 0
Now, 653x is divisible by 8, so 13x should be divisible by 8
This happens when x = 6
x + y = (6 + 0) = 6
Question 26
The difference of the squares of two consecutive odd integers is divisible by which of the following integers?  
A
3
B
6
C
7
D
8
Question 26 Explanation: 
Let the two consecutive odd integers be (2n + 1) and (2n + 3). Then,
(2n + 3)2 - (2n + 1)2 = (2n + 3 + 2n + 1) (2n + 3 - 2n - 1)
= (4n + 4) x 2
= 8(n + 1), which is divisible by 8
Question 27
What is the unit digit in (4137)754?    
A
1
B
3
C
7
D
9
Question 27 Explanation: 
Unit digit in (4137)754 = Unit digit in {[(4137)4]188 x (4137)2}
=Unit digit in { 292915317923361 x 17114769 }
= (1 x 9) = 9
Question 28
A number was divided successively in order by 4, 5 and 6. The remainders were respectively 2, 3 and 4. The number is:
A
214
B
476
C
954
D
1908
Question 28 Explanation: 
4 | x
-----------
5 | y -2
-----------
6 | z - 3
-----------
| 1 - 4
z = 6 x 1 + 4 = 10
y = 5 x z + 3 = 5 x 10 + 3 = 53
x = 4 x y + 2 = 4 x 53 + 2 = 214
Hence, required number = 214.
Question 29
The smallest 6 digit number exactly divisible by 111 is?
A
111111
B
110011
C
100011
D
110101
Question 29 Explanation: 
The smallest 6-digit number 100000
111) 100000 (900
999
-----
100
-------
Required number = 100000 + (111 - 100)
= 100011
Question 30
The largest 5 digit number exactly divisible by 91 is:
A
99921
B
99918
C
99981
D
99971
Question 30 Explanation: 
Largest 5-digit number = 99999
91) 99999 (1098
91
----
899
819
----
809
728
-----
81
---
Required number = (99999 - 81)
= 99918
Question 31
How many terms are there in the G.P. 3, 6, 12, 24, ... , 384 ?    
A
8
B
9
C
10
D
11
Question 31 Explanation: 
Here a = 3 and r = 6/3 =2 Let the number of terms be n
Then, tn = 384 arn-1 = 384
=>3 x 2n - 1= 384 =>2n-1 = 128 = 27
=>n - 1 = 7
=> n = 8
Number of terms = 8
Question 32
If x and y are positive integers such that (3x + 7y) is a multiple of 11, then which of the following will be divisible by 11?  
A
4x+6y
B
x+y+4
C
9x+4y
D
4x-9y
Question 32 Explanation: 
By hit and trial, we put x = 5 and y = 1 so that (3x + 7y) = (3 x 5 + 7 x 1) = 22, which is divisible by 11
(4x + 6y) = ( 4 x 5 + 6 x 1) = 26, which is not divisible by 11
(x + y + 4 ) = (5 + 1 + 4) = 10, which is not divisible by 11
(9x + 4y) = (9 x 5 + 4 x 1) = 49, which is not divisible by 11
(4x - 9y) = (4 x 5 - 9 x 1) = 11, which is divisible by 11
Question 33
9548 + 7314=8362 + (?)
A
8230
B
8410
C
8500
D
8600
Question 33 Explanation: 
9548
+ 7314
-----
16862
-----
16862 = 8362 + x
x = 16862 - 8362
x = 8500
Question 34
In a division sum, the remainder is 0. As student mistook the divisor by 12 instead of 21 and obtained 35 as quotient. What is the correct quotient?
A
0
B
12
C
13
D
20
Question 34 Explanation: 
Number = (12 x 35)
Correct Quotient = 420 ÷ 21 = 20
Question 35
2 + 22 + 23 + ... + 29 =?  
A
2044
B
1022
C
1056
D
None of these
Question 35 Explanation: 
This is a G.P. in which a = 2, r = 22 = 2 and n = 9
Sn= a(rn-1) / (r-1) = 2 *(29 -1) / (2-1) = 2 *(512 - 1) = 2*511 = 1022
Question 36
The difference of the squares of two consecutive even integers is divisible by which of the following integers?
A
3
B
4
C
6
D
7
Question 36 Explanation: 
Let the two consecutive even integers be 2n and (2n + 2). Then,
(2n + 2)2 = (2n + 2 + 2n)(2n + 2 - 2n)
= 2(4n + 2)
= 4(2n + 1), which is divisible by 4
Question 37
Which of the following numbers will completely divide (325 + 326 + 327 + 328)?  
A
11
B
16
C
25
D
30
Question 37 Explanation: 
325 + 326 + 327 + 328) = 325 x (1 + 3 + 32 + 33) = 325 x 40
= 324 x 3 x 4 x 10
= (324 x 4 x 30), which is divisible by 30
Question 38
A number when divide by 6 leaves a remainder 3. When the square of the number is divided by 6, the remainder is
A
0
B
1
C
2
D
3
Question 38 Explanation: 
Let x = 6q + 3
Then, x2 = (6q + 3)2
= 36q2 + 36q + 9
= 6(6q2 + 6q + 1) + 3
Thus, when x2 is divided by 6, then remainder = 3
Question 39
What will be remainder when 17200 is divided by 18?
A
17
B
16
C
1
D
2
Question 39 Explanation: 
When n is even. (xn - an) is completely divisibly by (x + a)
(17200 - 1200) is completely divisible by (17 + 1), i.e., 18
(17200 - 1) is completely divisible by 18
On dividing 17200 by 18, we get 1 as remainder
Question 40
A number when divide by 6 leaves a remainder 3. When the square of the number is divided by 6, the remainder is
A
0
B
1
C
2
D
3
Question 40 Explanation: 
Let x = 6q + 3
Then, x2 = (6q + 3)2
= 36q2 + 36q + 9
= 6(6q2 + 6q + 1) + 3
Thus, when x2 is divided by 6, then remainder = 3
Question 41
When a number is divided by 13, the remainder is 11. When the same number is divided by 17, then remainder is 9. What is the number?    
A
339
B
349
C
369
D
Data inadequate
Question 41 Explanation: 
x = 13p + 11 and x = 17q + 9
13p + 11 = 17q + 9
17q - 13p = 2 q= 2+13p / 17
The least value of p for which q = 2+13p / 17 is a whole number is p = 26
Therefore,x = (13 x 26 + 11)
= (338 + 11)
= 349
Question 42
(51 + 52 + 53 + ... + 100) = ?
A
2654
B
2975
C
3225
D
3775
Question 42 Explanation: 
Sn = (1 + 2 + 3 + ... + 50 + 51 + 52 + ... + 100) - (1 + 2 + 3 + ... + 50)
= 100/2 * (1 + 100) – 50/2 * (1 + 50)
= (50 x 101) - (25 x 51)
= (5050 - 1275)
= 3775
Question 43
n is a whole number which when divided by 4 gives 3 as remainder. What will be the remainder when 2n is divided by 4?
A
3
B
2
C
1
D
0
Question 43 Explanation: 
Let n = 4q + 3. Then 2n = 8q + 6 = 4(2q + 1 ) + 2
Thus, when 2n is divided by 4, the remainder is 2
Question 44
[(489 + 375)2–(489 – 3752)] / [(489 * 375)] = ?
A
144
B
864
C
2
D
4
Question 44 Explanation: 
From the given equation = [(a+b)2-(a-b)2] / ab = 4ab /ab = 4
Question 45
476**0 is divisible by both 3 and 11. The non-zero digits in the hundred's and ten's places are respectively
A
7 and 4
B
7 and 5
C
8 and 5
D
None of these
Question 45 Explanation: 
Let the given number be 476xy0
Then (4 + 7 + 6 + x + y + 0) = (17 + x + y) must be divisible by 3
And, (0 + x + 7) - (y + 6 + 4) = (x - y -3) must be either 0 or 11
x - y - 3 = 0 y = x - 3
(17 + x + y) = (17 + x + x - 3) = (2x + 14)
x= 2 or x = 8
x = 8 and y = 5
Question 46
On dividing 2272 as well as 875 by 3-digit number N, we get the same remainder. The sum of the digits of N is:
A
10
B
11
C
12
D
13
Question 46 Explanation: 
Clearly, (2272 - 875) = 1397, is exactly divisible by N
Now, 1397 = 11 x 127
The required 3-digit number is 127, the sum of whose digits is 10
Question 47
A boy multiplied 987 by a certain number and obtained 559981 as his answer. If in the answer both 9 are wrong and the other digits are correct, then the correct answer would be:
A
553681
B
555181
C
555681
D
556581
Question 47 Explanation: 
987 = 3 x 7 x 47
So, the required number must be divisible by each one of 3, 7, 47
553681 (Sum of digits = 28, not divisible by 3)
555181 (Sum of digits = 25, not divisible by 3)
555681 is divisible by 3, 7, 47
Question 48
On dividing a number by 357, we get 39 as remainder. On dividing the same number 17, what will be the remainder?
A
0
B
3
C
5
D
11
Question 48 Explanation: 
Let x be the number and y be the quotient. Then,
x = 357 x y + 39
= (17 * 21 x y) + (17 * 2) + 5
= 17 * (21y + 2) + 5)
Required remainder = 5
Question 49
If the product 4864 x 9 P 2 is divisible by 12, then the value of P is
A
1
B
5
C
6
D
8
Question 49 Explanation: 
Clearly, 4864 is divisible by 4
So, 9P2 must be divisible by 3. So, (9 + P + 2) must be divisible by 3
P = 1.
Question 50
Which one of the following is the common factor of (4743 + 4343) and (4747 + 4347)?
A
(47 - 43)
B
(47 + 43)
C
(4743 + 4343)
D
None of these
Question 50 Explanation: 
When n is odd, (xn + an) is always divisible by (x + a)
Each one of (4743 + 4343) and (4747 + 4347) is divisible by (47 + 43).
Question 51
On dividing a number by 5, we get 3 as remainder. What will the remainder when the square of the this number is divided by 5?
A
0
B
1
C
2
D
4
Question 51 Explanation: 
Let the number be x and on dividing x by 5, we get k as quotient and 3 as remainder
x = 5k + 3
x2 = (5k + 3)2
= (25k2 + 30k + 9)
= 5(5k2 + 6k + 1) + 4
On dividing x2 by 5, we get 4 as remainder
Question 52
What will be remainder when (6767 + 67) is divided by 68?
A
1
B
63
C
66
D
67
Question 52 Explanation: 
(xn + 1) will be divisible by (x + 1) only when n is odd
(6767 + 1) will be divisible by (67 + 1)
(6767 + 1) + 66, when divided by 68 will give 66 as remainder
Question 53
The sum of first 45 natural numbers is
A
1035
B
1280
C
2070
D
2140
Question 53 Explanation: 
Let Sn =(1 + 2 + 3 + ... + 45). This is an A.P. in which a =1, d =1, n = 45
Sn= n/2[2a+(n-1)d] = 45/2 * [2*1+(45 - 1)*1)] = (45/2*46) =(45 x 23)
= 45 x (20 + 3)
= 45 x 20 + 45 x 3
= 900 + 135
= 1035
Question 54
Which one of the following is not a prime number?
A
31
B
61
C
71
D
91
Question 54 Explanation: 
91 is divisible by 7. So, it is not a prime number
Question 55
Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is
A
9
B
11
C
13
D
15
Question 55 Explanation: 
Let the three integers be x, x + 2 and x + 4
Then, 3x = 2(x + 4) + 3 x = 11
Third integer = x + 4 = 15
Question 56
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
Cannot be determined
Question 56 Explanation: 
Let the ten's digit be x and unit's digit be y
Then, x + y = 15 and x - y = 3 or y - x = 3
Solving x + y = 15 and x - y = 3, we get: x = 9, y = 6
Solving x + y = 15 and y - x = 3, we get: x = 6, y = 9
So, the number is either 96 or 69
Hence, the number cannot be determined
Question 57
The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is
A
20
B
30
C
40
D
None of these
Question 57 Explanation: 
Let the numbers be a, b and c
Then, a2 + b2 + c2 = 138 and (ab + bc + ca) = 131
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) = 138 + 2 x 131 = 400
(a + b + c) = 400 = 20
Question 58
The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is
A
20
B
23
C
169
D
None of these
Question 58 Explanation: 
Let the numbers be x and y
Then, xy = 120 and x2 + y2 = 289
(x + y)2 = x2 + y2 + 2xy = 289 + (2 x 120) = 529
x + y = 529 = 23
Question 59
A number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. The number is
A
145
B
253
C
370
D
352
Question 59 Explanation: 
Let the middle digit be x
Then, 2x = 10 or x = 5. So, the number is either 253 or 352
Since the number increases on reversing the digits,so the hundred's digits is smaller than the unit's digit.
Hence, required number = 253
Once you are finished, click the button below. Any items you have not completed will be marked incorrect. Get Results
There are 59 questions to complete.

[/vc_toggle][vc_empty_space][vc_btn title=”More Aptitude Question” color=”warning” size=”lg” align=”center” button_block=”true” link=”url:https%3A%2F%2Fjumpwhere.com%2Faptitude%2F||”]

You may also like

Explore
Drag