Mathmetics

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

Q551.
What is the sum of two consecutive even numbers, the difference of whose squares is 84  ?
1) 34 2) 38
3) 42 4) 46
5)None of these
Answer : 42
Explanation : Let the numbers be x and x + 2.
    Then, (x + 2)2 - x2 = 84
    or 4x + 4 = 84   or  4x = 80
    or x = 20. The required sum = x + (x + 2) = 2x + 2 = 42.
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Q552.
The product of two numbers is 9375 and the quotient, when the larger one is divided by the smaller, is 15. The sum of the numbers is:
  
1) 380 2) 395
3) 400 4) 425
5)None of these
Answer : 400
Explanation : Let the numbers be x and y.
    Then, xy = 9375 and     x/y  = 15.
    X = 15y
   So, y x 15y = 15y2 = 9375
    or y2 = 625.          y = 25.
    x = 15y = (15 x 25) = 375.
    Thus, Sum of the numbers = x + y = 375 + 25 = 400.
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Q553.
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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Q554.
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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Q555.
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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Q556.
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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Q557.
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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Q558.
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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Q559.
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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Q560.
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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