1. answer: easytutorialwhich one of the following is the common factor of (4743 + 4343) and (4747 +...
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Aptitude - Number series
Practice Q&A โ Easy
1. The smallest 3 digit prime number is:
Answer:
101
Explanation :
The smallest 3-digit number is 100, which is divisible by 2.
โด 100 is not a prime number.
โ101 < 11 and 101 is not divisible by any of the prime numbers 2, 3, 5, 7, 11.
โด 101 is a prime number.
Hence 101 is the smallest 3-digit prime number.
2. Which one of the following numbers is exactly divisible by 11?
Answer:
415624
Explanation :
(4 + 5 + 2) - (1 + 6 + 3) = 1, not divisible by 11.
(2 + 6 + 4) - (4 + 5 + 2) = 1, not divisible by 11.
(4 + 6 + 1) - (2 + 5 + 3) = 1, not divisible by 11.
(4 + 6 + 1) - (2 + 5 + 4) = 0, So, 415624 is divisible by 11.
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3. (?) - 19657 - 33994 = 9999
Answer:
63650
Explanation :
19657+33994=53651
Let ๐ฅ - 53651 = 9999
Then, ๐ฅ = 9999 + 53651 = 63650
4. 753ร753+247ร247โ753ร247
753ร753ร753+247ร247ร247 = ?
Answer:
1
1000
Explanation :
Given Exp. = (๐2+๐2โ๐๐)
(๐3+๐3)=
1
(๐+๐)=
1
(753+247)=
1
1000
5. (?) + 3699 + 1985 - 2047 = 31111
Answer:
27474
Explanation :
๐ฅ + 3699 + 1985 - 2047 = 31111
โ ๐ฅ + 3699 + 1985 = 31111 + 2047
โ ๐ฅ+ 5684 = 33158โ ๐ฅ= 33158 - 5684 = 27474.
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6. 107 x 107 + 93 x 93 = ?
Answer:
20098
Explanation :
107 x 107 + 93 x 93= (107)2 + (93)
= (100 + 7)2 + (100 โ 7)2
= 2 x [(100)2 + (7)2] [Ref: (a + b)2 + (a โ b)2 = 2(a2 + b2)]
= 20098
7. How many of the following numbers are divisible by 3 but not by 9 ? 2133, 2343, 3474, 4131, 5286, 5340, 6336, 7347, 8115, 9276
Answer:
6
Explanation :
Marking (/) those which are are divisible by 3 by not by 9 and the others by(๐) , by taking the sum of digits, we get:s
2133 โ 9 (๐)
2343 โ 12 (/)
3474 โ 18 (๐)
4131 โ 9 (๐)
5286 โ 21 (/)
5340 โ 12 (/)
6336 โ 18 (๐)
7347โ 21 (/)
8115 โ 15 (/)
9276 โ24 (/) Required number of numbers = 6
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8 . (963+476)2+(963โ476)2
(963ร963+476ร476) =?
Answer:
2
Explanation :
Given Exp. = (๐+๐)2+(๐โ๐)2
(๐2+๐2) =
2(๐2+๐2)
(๐2+๐2) = 2
9. 8597 - ? = 7429 - 4358
Answer:
5526
Explanation :
7429 Let 8597 - x = 3071
-4358 Then, x = 8597 - 3071
โโ- = 5526
3071
-------
10. The smallest prime number is:
Answer:
2
Explanation :
The smallest prime number is 2.
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11. 12345679 x 72 = ?
Answer:
888888888
Explanation :
12345679 x 72= 12345679 x (70 +2)
= 12345679 x 70 + 12345679 x 2
= 864197530 + 24691358
= 888888888
12. Which one of the following is the common factor of (4743 + 4343) and (4747 + 4347) ?
Answer:
(47 + 43)
Explanation :
When ๐ is odd, ( x ๐ + ๐๐ ) is always divisible by ๐ฅ + ๐ .
โด Each one of 4743 + 4343 and 4747 + 4347 is divisible by 47 + 43.
13. -84 x 29 + 65 = ?
Answer:
-2071
Explanation :
Given Exp.= -84 x (30 โ 1)+ 365 = - (84 ร 30) + 84 + 365
= -2520 + 449= -2071
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14. In a division sum, the divisor is 10 times the quotient and 5 times the remainder. If the remainder is 46, what is the dividend ?
Answer:
5336
Explanation :
Divisor = 5 x 46 = 230
โด 10 x Quotient = 230 โ = 230
10 = 23
Dividend = [Divisor x Quotient] + Remainder
= [230 x 23] + 46 = 5290 + 46 = 5336.
15. 4500 x ? = 3375
Answer:
3
4
Explanation :
4500 x ๐ฅ = 3375 โ ๐ฅ = 3375
4500 =
75
100 =
3
4
16. 9+ 3
4 +7+
2
17 - (9 +
1
15) = ?
Answer:
7 + 817
1020
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Explanation :
Given sum
= 9 + 3
4 + 7 +
2
17 - (9 +
1
15)
= (9 + 7 - 9) + (3
4+
2
17โ
1
15)
= 7 + 765+120โ68
1020 = 7 +
817
1020
17. How many prime numbers are less than 50 ?
Answer:
15
Explanation :
Prime numbers less than 50 are:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
Their number is 15
18. (800 รท 64) x (1296 รท 36) = ?
a. 420
b. 460
c. 500
d. None of these
Answer:
None of these
Explanation :
Given Exp. = 800
64 x
1296
36 = 450
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19. Which natural number is nearest to 8485, which is completely divisible by 75 ?
Answer:
8475
Explanation :
On dividing, we get
75) 8485 (113
75 ----
98
75 ---- 235
225
---- 10 ----
Required number = (8485 - 10) // Because 10 < (75 - 10) = 8475.
20. Which of the following numbers is divisible by each one of 3, 7, 9 and 11 ?
Answer:
2079
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Explanation :
639 is not divisible by 7
2079 is divisible by each of 3, 7, 9, 11.
21. Which natural number is nearest to 9217, which is completely divisible by 88 ?
Answer:
9240
Explanation :
On dividing we get,
88) 9217 (104
88
---------------
417
352
--------------
65
--------------
Therefore, Required number = 9217 + (88 - 65) // Because (88 - 65) < 65.
= 9217 + 23 = 9240.
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22. 4300731 - ? = 2535618
Answer:
1765113
Explanation :
Let 4300731 โ ๐ฅ = 2535618
Then ๐ฅ , = 4300731 - 2535618 = 1765113
23. (489+375)2โ(489โ375)2
(489ร375) =?
Answer:
4
Explanation :
Given Exp. = (๐+๐)2โ(๐โ๐)2
๐๐ =
4๐๐
๐๐ = 4
24. 397 x 397 + 104 x 104 + 2 x 397 x 104 = ?
Answer:
251001
Explanation :
Given Exp.= (397)2 + (104)2
+ 2 x 397 x 104
= (397 + 104)2
= (501) 2
= (500 + 1)2
= (500)2 +(1)2 + (2 ร 500 ร 1)
= 250000 + 1 + 1000= 251001
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25. (35423 + 7164 + 41720) - (317 ร 89) = ?
Answer:
28213
Explanation :
35423
โข 7164
โข 41720
-----------------
84307
โข 28213
-----------------
56094
-----------------
317 x 89 = 317 x (90 โ 1)
= (317 ร 90 โ 317)
= (28530 โ 317)
= 28213
26. (xn - an) is completely divisible by (x - a), when
Answer:
n is any natural number
Explanation :
For every natural number ๐ , (xn - an) is completely divisible by (x - a).
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27. A number when divide by 6 leaves a remainder 3. When the square of the number is divided by 6, the remainder is:
Answer:
3
Explanation :
Let ๐ฅ = 6 ๐ + 3.
Then, ๐ฅ2= (6q + 3)2
= 36 q2 + 36 ๐ + 9
= 6(6 q2 + 6 ๐ + 1) + 3
Thus, when ๐ฅ 2 is divided by 6, then remainder = 3.
28. What will be remainder when 17200 is divided by 18 ?
Answer:
1
Explanation :
When ๐ is even. (๐ฅ๐ โ ๐๐)
is completely divisibly by ( x + a )
(17200 - 1200)is completely divisible by (17 + 1), i.e., 18.
โ (17200 - 1) is completely divisible by 18.
โ On dividing 17200 by 18, we get 1 as remainder.
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29. If 1400 x ๐ฅ = 1050. Then, ๐ฅ = ?
Answer:
3
4
Explanation :
1400 x ๐ฅ = 1050 โ ๐ฅ = 1050
1400 =
3
4
30. Which one of the following numbers is completely divisible by 99?
Answer:
114345
Explanation :
99 = 11 x 9, where 11 and 9 are co-prime.
By hit and trial, we find that 114345 is divisible by 11 as well as 9. So, it is divisible by 99.
31. (51 + 52 + 53+. . . +100) = ?
Answer:
3775
Explanation :
This is an A.P. in which ๐ = 51, ๐ = 100 and ๐ = 50.
โด Sum = ๐
2(๐ + ๐) =
50
2 x (51 + 100) = 25 x 151 = 3775.
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32. 1904 x 1904 = ?
Answer:
3625216
Explanation :
1904 x 1904= (1904)2 = (1900 + 4)2
= (1900)2 + (4)2 + (2 ร 1900 ร 4)
= 3610000 + 16 + 15200.= 3625216.
33. 1 + 2 + 3 + โฆ + 40 = ?
Answer:
820
Explanation :
Sum of first n natural numbers = ๐ร(๐+1)
2
Sum of first 40 natural numbers = 40ร41
2
= 20 ร 41 = 820
34. What is sum of first 17 natural numbers?
Answer:
153
Explanation :
Sum of first n natural numbers = ๐ร(๐+1)
2
Sum of first 17 natural numbers = 17ร18
2
= 17 ร 9 = 153
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35. Find the sum of first 25 natural numbers.
Answer:
325
Explanation :
Sum of first n natural numbers = ๐ร(๐+๐)
๐
Sum of first 25 natural numbers = 25ร(25+1)
2
= 25ร26
2 = 25 ร 13 = 325
36. Find the sum of first 100 natural numbers.
Answer:
5050
Explanation :
Sum of first n natural numbers = ๐ร(๐+1)
2
Sum of first 25 natural numbers = 100ร(100+1)
2
= 100ร101
2
= 50 ร 101 = 5050
37. Find the sum of first 25 even numbers.
Answer: 650
Explanation :
Sum of first 25 even numbers = n ร (n + 1) = 25 ร 26 = 650
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38. Find the sum of first 100 even numbers.
Answer:
10100
Explanation :
Sum of first 100 even numbers = n ร (n + 1) = 100 ร 101 = 10100
39. Find the sum of first 20 odd numbers.
Answer:
400
Explanation :
Sum of first 20 odd numbers = 20 ร 20 = 400
40. Find the sum of first 500 odd numbers.
Answer:
250000
Explanation :
Sum of first 500 odd numbers = 500 ร 500 = 250000
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