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### Mathmetics

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

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##### 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
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 View Answer
##### 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 View Answer
##### What  should be the remainder when 2 100 is divided by 101 ?
 1) 1 2) 11 3) 99 4) 100 5) None of these View Answer
##### 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
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. View Answer
##### 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
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 View Answer
##### 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
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. View Answer
##### 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
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 View Answer
##### What is value of the following expressions:  (51 + 52 + 53 + ... + 100) = ?
 1) 2825 2) 2975 3) 3025 4) 3775 5) None of these
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. View Answer
##### 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
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. View Answer
##### 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 View Answer