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## Number System: Level 1 Test - 6

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*Number System: Level 1 Test - 6*.You scored %%SCORE%% out of %%TOTAL%%.You correct answer percentage: %%PERCENTAGE%% .Your performance has been rated as %%RATING%% Your answers are highlighted below.

Question 1 |

The number of two-digit numbers exactly divisible 3 is

A | 33 |

B | 32 |

C | 31 |

D | 30 |

Question 1 Explanation:

Required numbers are 12, 15, 18, ………., 99

This is an AP with

Tn=

99 = 12+ (n -1) x 3

n -1 = 99 -12 /3

n = 29 + 1 = 30

This is an AP with

*a*= 12 and*d*= 3Tn=

*a*+ (n - 1)*d*99 = 12+ (n -1) x 3

n -1 = 99 -12 /3

n = 29 + 1 = 30

Question 2 |

The number which when increased by 20 is equal to six times of the old number. Find the old number?

A | 7 |

B | 5 |

C | 3 |

D | 4 |

Question 2 Explanation:

Let the whole number be

x =1/6 (x + 20)

6x=x+ 20

5x=20 and x =4

*x.*x =1/6 (x + 20)

6x=x+ 20

5x=20 and x =4

Question 3 |

A number when divided by 765 leaves a remainder 42. Find the remainder if the same number is divided by 17?

A | 8 |

B | 5 |

C | 7 |

D | 6 |

Question 3 Explanation:

Let the number be

When this number is divided by 17,

then quotient will be

*(765x*+ 42).When this number is divided by 17,

then quotient will be

*(45x*+ 2) and remainder will be 8.Question 4 |

A company manufactured 6000 scooters in the third year of after establishment and 7000 scooters in the seventh year. Assuming that the production increases uniformly by in the given years, Find the production of the company in the tenth year?

A | 7850 |

B | 7650 |

C | 7750 |

D | 7950 |

Question 4 Explanation:

Production in third year =6000

Production in seventh year =7000

Production in fourth year = 1000 ie

Production increases @ 250 scooters every year.

Production in tenth year = (7000 + 250 x 3) = 7750

Production in seventh year =7000

Production in fourth year = 1000 ie

*,*Production increases @ 250 scooters every year.

Production in tenth year = (7000 + 250 x 3) = 7750

Question 5 |

The digits of a three-digit number A are written in the reverse order to form another three-digit number B. If B > A and B-A is perfectly divisible by 7, then which of the following is necessarily true?

A | 100 < A < 299 |

B | 106 < A < 305 |

C | 112 < A < 311 |

D | 118< A < 317 |

Question 5 Explanation:

Let A = abc, then B = cba

Given, B > A which implies c > a ...(1)

As B – A = (100c + 10b + a) – (100a + 10b + 1)

B – A = 100 (c – a) + (a – c)

B – A = 99 (c – a) and (B – A) is divisible by 7;

As 99 is not divisible by 7 (no factor like 7 or 7^2)

Therefore (c – a) must be divisible by 7 {i.e., (c – a)

Must be 7, 7^2 etc.} as c & a are single digits. (c – a)

Must be 7 only, the possible values (c, a) {with c > a}

Are (9, 2) & (8, 1), with this we can write A as A : abc ≡ 1b8 or 2b9

As b can take values from 0 to 9, the smallest & largest possible value of are:

A min = 108 & A max = 299

only option b satisfies the given condition, so (b) is the ans

Given, B > A which implies c > a ...(1)

As B – A = (100c + 10b + a) – (100a + 10b + 1)

B – A = 100 (c – a) + (a – c)

B – A = 99 (c – a) and (B – A) is divisible by 7;

As 99 is not divisible by 7 (no factor like 7 or 7^2)

Therefore (c – a) must be divisible by 7 {i.e., (c – a)

Must be 7, 7^2 etc.} as c & a are single digits. (c – a)

Must be 7 only, the possible values (c, a) {with c > a}

Are (9, 2) & (8, 1), with this we can write A as A : abc ≡ 1b8 or 2b9

As b can take values from 0 to 9, the smallest & largest possible value of are:

A min = 108 & A max = 299

only option b satisfies the given condition, so (b) is the ans

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