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Number System Questions
21. A number 18567332145x is divisible by 8. What can be the minimum value of x?
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Correct Ans:6
Explanation:
A number 18567332145x is divisible by 8. What can be the minimum value of x
Reference :
For a number to be divisible by 8; its last 3 digits should be divisible by 8
-----> So (45x) is divisible by 8
------> Thus x = 6 is the correct answer
Hence the correct answer is x = 6
Reference :
For a number to be divisible by 8; its last 3 digits should be divisible by 8
-----> So (45x) is divisible by 8
------> Thus x = 6 is the correct answer
Hence the correct answer is x = 6
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22. A fraction becomes (1/3) when 1 is subtracted from both the numerator and the denominator. The same fraction becomes (½) when 1 is added to both numerator and the denominator the sum of numerator and denominator of the fraction is"“
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Correct Ans:10
Explanation:
Let fraction be (x/y)
-----> Then,((x-1)/(y-1)) = (1/3)
-----> Or, 3x – 3 = y – 1
-----> 3x – y = 2 …………..(i)
-----> Again, ((x+1)/(y+1)) = (1/2)
-----> 2x + 2 = y + 1
-----> 2x – y = –1 ………..(ii)
-----> On solving eqn (i) and (ii)
-----> x = 3, y = 7
-----> Sum of numerator and denominator of the fraction
-----> = 3 + 7 = 10.
Hence the answer is : 10
-----> Then,((x-1)/(y-1)) = (1/3)
-----> Or, 3x – 3 = y – 1
-----> 3x – y = 2 …………..(i)
-----> Again, ((x+1)/(y+1)) = (1/2)
-----> 2x + 2 = y + 1
-----> 2x – y = –1 ………..(ii)
-----> On solving eqn (i) and (ii)
-----> x = 3, y = 7
-----> Sum of numerator and denominator of the fraction
-----> = 3 + 7 = 10.
Hence the answer is : 10
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23. If the sum of three odd natural numbers is 357, each of the number is divisible by 7. which one of the following is the largest number?
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Correct Ans:133
Explanation:
If the sum of three odd natural numbers is 357, each of the number is divisible by 7. which one of the following is the largest number
Reference :
Let the number be (x, x+14,x+28)
-----> x+x+14+x+28 = 357
-----> 3x + 42 = 357
-----> 3x = 315
-----> x =105
-----> Required,
-----> x +28 = 105 +28 = 133
Hence the answer is : 133
Reference :
Let the number be (x, x+14,x+28)
-----> x+x+14+x+28 = 357
-----> 3x + 42 = 357
-----> 3x = 315
-----> x =105
-----> Required,
-----> x +28 = 105 +28 = 133
Hence the answer is : 133
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24. The arithmetic mean of two numbers is 30 and their geometric mean is 24. What is the value of larger number?
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Correct Ans:48
Explanation:
The arithmetic mean of two numbers is 30 and their geometric mean is 24. What is the value of larger number
Reference :
Let the numbers to be ‘a’ & ‘b’.
Arithmetic mean of the numbers = ((a+b)/2)
Geometric mean of the numbers = √ab
According to the question:
----> [(a+b)/2] = 30
----> (a+b) = 60
----> And
----> √(ab) = 24
----> ab = 576
Solving both equations:
----> a(60-a) = 576
----> 60a – a2 = 576
----> a2 – 60a + 576 = 0
----> a2 – 48a - 12a + 576 = 0
----> a(a-48)-12(a-48) = 0
----> (a-12)(a-48) = 0
----> a = 12, 48
Hence larger number is = 48
Reference :
Let the numbers to be ‘a’ & ‘b’.
Arithmetic mean of the numbers = ((a+b)/2)
Geometric mean of the numbers = √ab
According to the question:
----> [(a+b)/2] = 30
----> (a+b) = 60
----> And
----> √(ab) = 24
----> ab = 576
Solving both equations:
----> a(60-a) = 576
----> 60a – a2 = 576
----> a2 – 60a + 576 = 0
----> a2 – 48a - 12a + 576 = 0
----> a(a-48)-12(a-48) = 0
----> (a-12)(a-48) = 0
----> a = 12, 48
Hence larger number is = 48
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25. The greatest among the numbers 3√2, 3√7, 6√5, 2√20 is
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Correct Ans:6√5
Explanation:
WKT, √2 = 1.4
√7 = 2.6
√5 = 2.2
3√2 = 3 x 1.4 = 4.2
3√7 = 3x 2.6 = 7.8
6√5 = 6 x 2.2 = 13.2
2√20 = 2 x 2√5
= 4√5 = 4 x 2.2 = 8.8
Hence, 6√5 is greatest.
√7 = 2.6
√5 = 2.2
3√2 = 3 x 1.4 = 4.2
3√7 = 3x 2.6 = 7.8
6√5 = 6 x 2.2 = 13.2
2√20 = 2 x 2√5
= 4√5 = 4 x 2.2 = 8.8
Hence, 6√5 is greatest.
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26. What is the least value of K so that the number 6735K1 is divisible by 9?
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Correct Ans:5
Explanation:
Given: 6735K1
6 + 7 + 3 + 5 + K + 1 = 22 + K
Here, the least number K should be greater than 22 and divisible by 9.
Therefore, the least number is27.
27 = 22 + K
K = 5
6 + 7 + 3 + 5 + K + 1 = 22 + K
Here, the least number K should be greater than 22 and divisible by 9.
Therefore, the least number is27.
27 = 22 + K
K = 5
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27. A 4-digit number is formed by repeating a 2-digit number such as 2525, 3232, etc., Any number of this form is always exactly divisible by
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Correct Ans:Smallest 3-digit prime number
Explanation:
Let the unit digit be x and ten's digit be y.
Number = 1000y + 100x + 10y + x
= 1010y + 101x
= 101(10y + x)
Hence, this number is divisible by 101, which is the smallest three-digit prime number.
Number = 1000y + 100x + 10y + x
= 1010y + 101x
= 101(10y + x)
Hence, this number is divisible by 101, which is the smallest three-digit prime number.
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28. In a zoo there are rabbits and pigeons. If their heads are counted, they are 90 while their legs are 224. Find the number of pigeons in the zoo?
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Correct Ans:68
Explanation:
Let number of pigeons be 'X'.
Number of rabbits and pigeons = 90
Therefore, number of rabbits = 90 - X
According to the question,
2X + 4(90 - X) = 224
2X + 360 - 4X = 224
360 - 224 = 2X
136 = 2X
X = 68
Hence, there are 68 pigeons in the zoo.
Number of rabbits and pigeons = 90
Therefore, number of rabbits = 90 - X
According to the question,
2X + 4(90 - X) = 224
2X + 360 - 4X = 224
360 - 224 = 2X
136 = 2X
X = 68
Hence, there are 68 pigeons in the zoo.
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29. Five-eight of three-tenth of four-ninth of a number is 60. What is the number?
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Correct Ans:720
Explanation:
Let the number be Y.
(5/8)x(3/10)x(4/9)x Y = 60
Y = 60 x (8/5) x (10/3) x (9/4)
Y = 720
(5/8)x(3/10)x(4/9)x Y = 60
Y = 60 x (8/5) x (10/3) x (9/4)
Y = 720
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30. What is the sum of first 12 terms of an arithmetic progression, if the first term is -19 and the last term is 36?
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Correct Ans:102
Explanation:
Given: First term, a = -19; Last term, an = 36; n =12
WKT, Required sum = (n/2)[a + an]
= (12/2)[(-19 + 36)]
= 102
WKT, Required sum = (n/2)[a + an]
= (12/2)[(-19 + 36)]
= 102
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31. The sum of three consecutive odd numbers is 20 more than the smallest number. What is the middle number?
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Correct Ans:9
Explanation:
Let the three consecutive odd numbers be x, x + 2, x + 4.
As per the question,
x + x + 2 + x + 4 = x + 20
3x + 6 = x + 20
3x - x = 20 - 6
2x = 14
x = 7
Therefore, three odd numbers are 7, 9, 13 and the middle number is 9.
As per the question,
x + x + 2 + x + 4 = x + 20
3x + 6 = x + 20
3x - x = 20 - 6
2x = 14
x = 7
Therefore, three odd numbers are 7, 9, 13 and the middle number is 9.
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32. The 4th and 7th term of an arithmetic progression are 11 and -4, respectively. What is the 15th term?
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Correct Ans:-44
Explanation:
WKT, aâ‚™ = a + (n - 1)d
where a - first term; d - difference
Given 4th term of AP is 11,
a + (4 - 1)d = 11
a + 3d = 11 .....(1)
Also given that 7th term of AP is -4,
a + (7 - 1)d = -4
a + 6d = -4 .....(2)
On solving (1) and (2),
a = 26; d = -5
Therefore, 15th term = a + (15 - 1)d
= 26 + 14(-5)
= 26 - 70
= -44
where a - first term; d - difference
Given 4th term of AP is 11,
a + (4 - 1)d = 11
a + 3d = 11 .....(1)
Also given that 7th term of AP is -4,
a + (7 - 1)d = -4
a + 6d = -4 .....(2)
On solving (1) and (2),
a = 26; d = -5
Therefore, 15th term = a + (15 - 1)d
= 26 + 14(-5)
= 26 - 70
= -44
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33. What is the 507th term of the sequence 1, -1, 2, -2, 1, -1, 2, -2, 1,...........?
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Correct Ans:2
Explanation:
Given sequence: 1, -1, 2, -2, 1, -1, 2, -2, 1,.......
From the sequence it is clear that repetition take place for each set of four terms.
Hence, remainder of 507/4 = 3.
In the given sequence, we know that four terms are repeated again and again. In that 3rd term is 2.
Therefore, 507th term is 2.
From the sequence it is clear that repetition take place for each set of four terms.
Hence, remainder of 507/4 = 3.
In the given sequence, we know that four terms are repeated again and again. In that 3rd term is 2.
Therefore, 507th term is 2.
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34. What number must be subtracted from both the numerator and the denominator of the fraction 27/35 so that it becomes 2/3?
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Correct Ans:11
Explanation:
Let the number be 'X'.
(27 - X)/(35 - X) = 2/3
3(27 - X) = 2(35 - X)
81 - 3X = 70 - 2X
81 - 70 = 3X - 2X
X = 11
(27 - X)/(35 - X) = 2/3
3(27 - X) = 2(35 - X)
81 - 3X = 70 - 2X
81 - 70 = 3X - 2X
X = 11
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35. Sum of a fraction and thrice its reciprocal is 31/6. What is the fraction?
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Correct Ans:9/2
Explanation:
Let the fraction be x/1.
Accoroding to the question,
(x/1) + 3(1/x) = 31/6
(x2) + 3)/x = 31/6
6x2 + 18 = 31x
6x2 -31x + 81 = 0
6x2 -4x - 27x + 18 = 0
2x(3x - 2) - 9(3x -2) = 0
(2x - 9) (3x - 2) = 0
x = 9/2, 2/3
From the options, 9/2 is the correct answer.
Accoroding to the question,
(x/1) + 3(1/x) = 31/6
(x2) + 3)/x = 31/6
6x2 + 18 = 31x
6x2 -31x + 81 = 0
6x2 -4x - 27x + 18 = 0
2x(3x - 2) - 9(3x -2) = 0
(2x - 9) (3x - 2) = 0
x = 9/2, 2/3
From the options, 9/2 is the correct answer.
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36. Which one of the following is the minimum value of the sum of two integers whose product is 24?
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Correct Ans:10
Explanation:
Let the two integers be 'x' and 'y'.
Given: Product of two integers, xy = 24
The possible integers are (1, 24) or (2, 12) or (3, 8) or (4, 6)
Therefore, mininmum value of (x + y) = 4 + 6 = 10.
Given: Product of two integers, xy = 24
The possible integers are (1, 24) or (2, 12) or (3, 8) or (4, 6)
Therefore, mininmum value of (x + y) = 4 + 6 = 10.
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37. A man plants 5184 orange trees in his garden and arrange them,so that there are as many rows as there are orange trees in a row. How many rows are there in the garden?
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Correct Ans:72
Explanation:
Given, number of rows and columns of trees are same.
So, let the number of rows and columns be 'Y'.
As per the question,
Y x Y = 5184
Y2 = 5184
Y = 72 rows.
So, let the number of rows and columns be 'Y'.
As per the question,
Y x Y = 5184
Y2 = 5184
Y = 72 rows.
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38. In a division problem, the divisor is 4 times the quotient and 3 times the remainder. If remainder is 4, then the dividend is
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Correct Ans:40
Explanation:
Given: Remainder = 4
As per the question,
Divisor = 3 x Remainder = 3 x 4 = 12
Also, Divisor = 4 x Quotient
12 = 4 x Quotient
Quotient = 12/4
Quotient = 3
WKT, Dividend = Quotient x Divisor + Remainder
Dividend = 3 x 12 + 4
Dividend = 40.
As per the question,
Divisor = 3 x Remainder = 3 x 4 = 12
Also, Divisor = 4 x Quotient
12 = 4 x Quotient
Quotient = 12/4
Quotient = 3
WKT, Dividend = Quotient x Divisor + Remainder
Dividend = 3 x 12 + 4
Dividend = 40.
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39. The first term of an Arithmetic Progression is 22 and the last term is 11. If the sum is 66, the number of terms in the sequences are
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Correct Ans:12
Explanation:
Given: s - 66, a - 22, l - 11
The sum of Arithmetic Progression is given by
s = (n/2)(a + l)
66 = (n/2)(22 - 11)
66 = (n/2)(11)
n = (66 x 2)/11
n = 12
The sum of Arithmetic Progression is given by
s = (n/2)(a + l)
66 = (n/2)(22 - 11)
66 = (n/2)(11)
n = (66 x 2)/11
n = 12
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40. Find the number lying between 900 and 1000 which when divided by 38 and 57 leaves in each case a remainder 23.
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Correct Ans:935
Explanation:
Here, LCM of 38 and 57 is 114.
Where 114 is divisible by both 38 and 57.
Therefore, the required number is multiple of 114.
Number divisible by 114 between 900 and 1000 is 912.
Required number = 912 + 23 = 935.
Where 114 is divisible by both 38 and 57.
Therefore, the required number is multiple of 114.
Number divisible by 114 between 900 and 1000 is 912.
Required number = 912 + 23 = 935.
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