### Mathmetics

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

## Q571. | ## 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, x

^{2}+ y

^{2}+ z

^{2}= 138 and (xy + yz + zx) = 131.

or (x + y + z)

^{2}= x

^{2}+ y

^{2}+ z

^{2}+ 2(xy + yz + zx) = 138 + 2 x 131 = 400.

or (x + y + z) = 20.

**View Answer**

## Q572. | ## 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.

**View Answer**

## Q573. | ## 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.

**View Answer**

## Q574. | ## 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 x

^{2}+ 17x - 60 = 0

or (x + 20) (x - 3) = 0 or x = 3.

**View Answer**

## Q575. | ## 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.

**View Answer**

## Q576. | ## 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.

**View Answer**

## Q577. | ## 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.

**View Answer**

## Q578. | ## 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.

**View Answer**

## Q579. | ## 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.

**View Answer**

## Q580. | ## 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**

**View Answer**