Mathmetics

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

Q531.
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:
 
1) 20 2) 30
3) 40 4) 24
5)None of these
Answer : 20
Explanation : Let the numbers be x, y and z.
 Then, x2 + y2 + z2 = 138   and  (xy + yz + zx) = 131.
 or  (x + y + z)2 = x2 + y2 + z2 + 2(xy + yz + zx)  = 138 + 2 x 131 = 400.
 or  (x + y + z) = 20.
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Q532.
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 ?
  
1) 69 2) 78
3) 96 4) D.I
5)None of these
Answer : D.I
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.
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Q533.
The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?
 
1) 3 2) 4
3) 9 4) D.I
5)None of these
Answer : 4
Explanation : Let the ten's digit be x and unit's digit be y.
   Then, (10x + y) - (10y + x) = 36
   or 9(x - y) = 36   or x - y = 4.
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Q534.
Find a positive number which when increased by 17 is equal to 60 times the reciprocal of the number.

1) 3 2) 10
3) 17 4) 20
5)None of these
Answer : 3
Explanation :   Let the number be x.
  Then, x + 17 =  60/x       or   x2 + 17x - 60 = 0
  or  (x + 20) (x - 3) = 0    or    x = 3.
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Q535.
On dividing a number by 56, we get 29 as remainder. On dividing the same number by 8, what will be the remainder ?
1) 4 2) 5
3) 6 4) 7
5)None of these
Answer : 5
Explanation : Dividend = ( 56 x  Q ) + 29         (Q = Quotient )
    Dividend = ( 87 x Q ) + (8 x 3) +5
    All Parts are divisible by 8 except 5.
    So,5 should be the reminder.
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Q536.
The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?
1) 240 2) 270
3) 295 4) 360
5)None of these
Answer : 270
Explanation : Let the smaller number be x.
    Then larger number = (x + 1365).
    x + 1365 = 6x + 15
    5x = 1350   or  x = 270
    Thus , Smaller number = 270.
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Q537.
Which one of the following numbers is exactly divisible by 11 ?
1) 235641 2) 245642
3) 315624 4) 415624
5)None of these
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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Q538.
If the number 517 * 324 is completely divisible by 3, then the smallest whole number in the place of * will be:

1) 0 2) 1
3) 2 4) 3
5)None of these
Answer : 2
Explanation : Explanation:
    Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = (22 + x),   which is not must be divisible by 3.
     So, x = 2.
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Q539.
The sum of two number is 25 and their difference is 13. Find their product.
1) 104 2) 114
3) 315 4) 325
5)None of these
Answer : 114
Explanation : Explanation:

    Let the numbers be x and y.
    Then, x + y = 25 and x - y = 13.
    4xy = (x + y)2 - (x- y)2  = (25)2 - (13)2
     = (625 - 169) = 456
   So,  xy = 114.
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Q540.
Find the two natural numbers whose sum is 85 and the LCM is 102
         

1) 1) 30 and 55 2) 2) 17 and 68
3) 3) 35 and 55 4) 4) 51 and 34
5)5) None of these
Answer : 4) 51 and 34
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