Mathmetics

ISBT Mathmetics for all banking PO,Clerk,IBPS PO,Railway,SSC,IAS,OAS Exams

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Q1.
The sum of the squares of two positive integers is 208. If the square of the larger number is 18 times the smaller number, then what would be the difference of the larger and smaller numbers ?
1) 2 2) 3
3) 4 4) 6
5)None of these
Answer : 4
Explanation : Let, the larger and smaller numbers are x and y respectively.
x2 + y2 = 208 --------- (i)
x2 = 18y 
or x2 - 18y = 0 -------- (ii)

Equating from both equation,we get 
y2 +18y - 208 = 0
or y2 + 26y - 8y - 208 = 0
or y (y+26) - 8 (y + 26) = 0
or y = 8  so, x = 12
Therefore, x-y = 12 - 8 = 4 
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Q2.
What is the remainder when 135+145 + 155 + 165  is divided  by 29 ?
1) 0 2) 3
3) 5 4) 8
5)None of these
Answer : 0
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Q3.
What  should be the remainder when 2 100 is divided by 101 ?
1) 1 2) 11
3) 99 4) 100
5)None of these
Answer : 99
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Q4.
A number consists of two digits. If the digits interchange places and the new number is added to the original number, then the resulting number will be divisible by:
1) 3 2) 5
3) 9 4) 11
5)None of these
Answer : 11
Explanation :
Let, the ten's digit be x and unit's digit be y.
Then, number = 10x + y.
Number obtained by interchanging the digits = 10y + x.
(10x + y) + (10y + x) = 11(x + y), which is divisible by 11.
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Q5.
The sum of two numbers is 28 and their difference is 4. What is the product of the two numbers ?
1) 184 2) 192
3) 196 4) 212
5)None of these
Answer : 192
Explanation :
(x + y)2 = (x - y)2  + 4xy
or x + y = 28, x - y = 4
or 4xy = (28)2 - (4)2
or 4xy = (28 + 4) (28 - 4)
or xy =  = 32 x 6 = 192
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Q6.
It is being given that (232 + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?
1) (2^16 + 1) 2) (2^16 - 1)
3) (7 x 2^23) 4) (2^96 + 1)
5)None of these
Answer : (2^96 + 1)
Explanation :
Let, 232 = x. Then, (232 + 1) = (x + 1).
Let, (x + 1) be completely divisible by the natural number N. 
Then, (296 + 1) = [(232)3 + 1] = (x3 + 1) = (x + 1)(x2 - x + 1), which is completely divisible by N, since (x + 1) is divisible by N.

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Q7.
Two-fifth of a number is two more than one-third another number.If the sum of the two numbers is 16,what is their product ?
1) 40 2) 48
3) 54 4) 60
5)None of these
Answer : 60
Explanation : Let, two numbers are x and y respectively. 
According to the questions, x + y = 16  ------- (I)     and 2x/5  - y/3 = 2 -------- (II)
or 6x -5y = 30
 Solving both equations , we get x = 10 and y = 6
So, their product = 10 X 6 = 60
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Q8.
What is value of the following expressions: 
 (51 + 52 + 53 + ... + 100) = ?
1) 2825 2) 2975
3) 3025 4) 3775
5)None of these
Answer : 3775
Explanation :
We know that,Sn = (1 + 2 + 3 + ... + 50 + 51 + 52 + ... + 100)/2 - (1 + 2 + 3 + ... + 50)/2
= 100 x (1 + 100) - 50 x (1 + 50) = (50 x 101) - (25 x 51)
= (5050 - 1275) = 3775.
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Q9.
A 3-digit number 4a3 is added to another 3-digit number 984 to give a 4-digit number 13b7, which is divisible by 11. Then, (a + b) = ?
1) 8 2) 9
3) 10 4) 12
5)None of these
Answer : 10
Explanation :
4 a 3  |
 9 8 4  }  ==> a + 8 = b  ==>  b - a = 8  
13 b 7  |
Also, 13 b7 is divisible by 11      (7 + 3) - (b + 1) = (9 - b)
 (9 - b) = 0
 or b = 9 (b = 9 and a = 1)     
So, (a + b) = 10.
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Q10.
When a number is divided by 5, we get 3 as remainder. What will the remainder when the square of the this number is divided by 5 ?

1) 1 2) 2
3) 3 4) 4
5)None of these
Answer : 4
Explanation :

We, know that , Dividend = (divisor x Quotient )+Reminder 
D = 5Q + 3
or    D2 = (5Q + 3)2 = (25Q2 + 30Q + 9) = 5(5Q2 + 6Q + 1) + 4
On dividing D2 by 5, we get 4 as remainder.
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