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## Number System: Level 1 Test - 5

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Question 1 |

How many numbers are there between 500 and 600 in which 9 occurs only once?

19 | |

18 | |

20 | |

21 |

Question 1 Explanation:

The required numbers are 509, 519, 529, 539, 549, 559, 569, 579, 589, 590, 591, 592…..598.

So, there are 18 such numbers.

A shorter method for this question:

Since the number has to be between 500 and 600,

the first position (out of three available) will be filled by 5 only.

Now we have two cases:

Case-1:

5 9 _ if we fix number 5 and 9 in 1 and 10th place we are left with only 9

i.e 0 to 8 options for the ones place.

5 _ 9 if we fix number 5 and 9 in 1 and 100th place we are left with only 9

i.e 0 to 8 options for tens place.

Thus, the answer is 18.

So, there are 18 such numbers.

A shorter method for this question:

Since the number has to be between 500 and 600,

the first position (out of three available) will be filled by 5 only.

Now we have two cases:

Case-1:

5 9 _ if we fix number 5 and 9 in 1 and 10th place we are left with only 9

i.e 0 to 8 options for the ones place.

5 _ 9 if we fix number 5 and 9 in 1 and 100th place we are left with only 9

i.e 0 to 8 options for tens place.

Thus, the answer is 18.

Question 2 |

If 6 yr are subtracted from the present age of Randheer and then it is divided by 18, then the quotient is the present age of his grandson Anup is obtained. If Anup is 2 yr younger to Mahesh whose age is 5 yr, what is the age of Randheer?

84 yr | |

48 yr | |

60 yr | |

96 yr |

Question 2 Explanation:

Given: (Randheer-6)/18=Anup,

Given, Mahesh = 5 yr

Anup = 3 yr

R = 18 x 3 + 6 = 60 yr

Given, Mahesh = 5 yr

Anup = 3 yr

R = 18 x 3 + 6 = 60 yr

Question 3 |

A clock strikes 4 taking 9s. In order to strike 12 at the same rate, the time taken is

36 s | |

27 s | |

30 s | |

33 s |

Question 3 Explanation:

A clock strikes 4 taking 9 s.

There are 3 intervals when the clock strikes 4

one strike time 9/3=3 , ie, 12 strike 11 x 3 = 33

Therefore the right answer is option d

There are 3 intervals when the clock strikes 4

one strike time 9/3=3 , ie, 12 strike 11 x 3 = 33

Therefore the right answer is option d

Question 4 |

A driver unloaded 2/5 of the packages in his van at the first stop on his route. After he unloaded another three packages at his next stop, 1/2 of the original number of packages remained. How many packages were in the van before the first delivery?

25 | |

10 | |

30 | |

36 |

Question 4 Explanation:

Let the total number of packages be x.

So, 2x/5+3=x/2,

x/10=3

X=30

So, 2x/5+3=x/2,

x/10=3

X=30

Question 5 |

An Army Commander wishing to draw up his 5180 men in the form of a solid square found that he had 4 men less. If he could get four more men and form the solid square, the number of men in the front row

72 | |

68 | |

78 | |

82 |

Question 5 Explanation:

Total number of men = 5180 + 4 = 5184

Number of men in first row = square root of5184 = 72

Number of men in first row = square root of5184 = 72

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Can somebody explain Solution 3 more clearly?

we are actually calculating the space in between(that is the actual time)

so let us represent strikes by “|” and time between them by as single space

so when clock strikes 4: it is : | | | | notice that there are 3 spaces between 4 “|”.likewise for 12