# Number Systems and Progressions

## Number Systems and Progressions

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Question 1 |

The number of integers n satisfying – n + 2 ≥ 0 and 2n ≥ 4 is ?

A | 0 |

B | 1 |

C | 2 |

D | 3 |

Question 1 Explanation:

The only value that will satisfy will be 2.

Question 2 |

The sum of two integers is 10 and the sum of their reciprocals is 5/12. Then the larger of these integers is ?

A | 2 |

B | 4 |

C | 6 |

D | 8 |

Question 2 Explanation:

1⁄4 + 1/6 will give you 5/12.

Question 3 |

If x is a positive integer such that 2x + 12 is perfectly divisible by x, then the number of possible values of x is ?

A | 2 |

B | 5 |

C | 6 |

D | 12 |

Question 3 Explanation:

The possible values are 1, 2, 3, 4, 6 and 12. (i.e. the factors of 12)

Question 4 |

Let K be a positive integer such that k + 4 is divisible by 7. Then the smallest positive integer n, greater than 2, such that k + 2n is divisible by 7 equals ?

A | 9 |

B | 7 |

C | 5 |

D | 3 |

Question 4 Explanation:

k will be a number of the form 7n + 3. Hence, if you take the value of n as 9, k + 2n will become
7n + 3 + 18 = 7n + 21. This number will be divisible by 7. The numbers 3, 5 and 7 do not
provide us with this solution.

Question 5 |

2^73 – 2^72 – 2^71 is the same as ?

A | 2^69 |

B | 2^70 |

C | 2^71 |

D | 2^72 |

Question 5 Explanation:

2^73 – 2^72 – 2^71 = 2^71(4-2-1)= 2^71

Question 6 |

Three times the first of three consecutive odd integers is 3 more than twice the third. What is the third integer?

A | 15 |

B | 9 |

C | 11 |

D | 5 |

Question 6 Explanation:

Solve through options. you will get easily.

Question 7 |

x, y and z are three positive integers such that x > y > z. Which of the following is closest to the product xyz?

A | xy(z – 1) |

B | (x – 1)yz |

C | (x – y)xy |

D | x(y + 1)z |

Question 7 Explanation:

The closest value will be (x – 1)yz , since the percentage change will be lowest when the largest
number is reduced by one.

Question 8 |

A positive integer is said to be a prime number if it is not divisible by any positive integer other than itself and 1. Let p be a prime number greater than 5, then (p2 – 1) is ?

A | never divisible by 6. |

B | always divisible by 6, and may or may not be divisible by 12. |

C | always divisible by 12, and may or may not be divisible by 24. |

D | always divisible by 24. |

Question 8 Explanation:

This is a property of prime numbers greater than 5.

Question 9 |

Iqbal dealt some cards to Mushtaq and himself from a full pack of playing cards and laid the rest aside. Iqbal then said to Mushtaq “If you give me a certain number of your cards, I will have four times as many cards as you will have. If I give you the same number of cards, I will have thrice as many cards as you will have”. Of the given choices, which could represent the number of cards with Iqbal?

A | 9 |

B | 31 |

C | 12 |

D | 35 |

Question 9 Explanation:

He could have dealt a total of 40 cards, in which case Mushtaq would get 9 cards. On getting one card from Mushtaq, the ratio would become 4:1, while on giving away one card to Mushtaq, the ratio would become 3:1.

Question 10 |

In Sivakasi, each boy’s quota of match sticks to fill into boxes is not more than 200 per session. If he reduces the number of sticks per box by 25, he can fill 3 more boxes with the total number of sticks assigned to him. Which of the following is the possible number of sticks assigned to each boy?

A | 200 |

B | 150 |

C | 125 |

D | 175 |

Question 10 Explanation:

Looking at the options you realise that the correct answer should be a multiple of 25 and 50 both.The option that satisfies the condition of increasing the number of boxes by 3 is 150. (This is found through trial and error.)

Question 11 |

A lord got an order from a garment manufacturer for 480 Denim Shirts. He bought 12 sewing machines and appointed some expert tailors to do the job. However, many didn’t report for duty. As a result, each of those who did, had to stitch 32 more shirts than originally planned by Alord, with equal distribution of work. How many tailors had been appointed earlier and how many had not reported for work?

A | 12, 4 |

B | 10, 3 |

C | 10, 4 |

D | None of these |

Question 11 Explanation:

Trial and error gives you option 10, 4 as the correct answer.

Question 12 |

How many 3-digit even numbers can you form such that if one of the digits is 5, the following digit must be 7 ?

A | 5 |

B | 405 |

C | 365 |

D | 495 |

Question 12 Explanation:

Given that the number must have a 57 in it and should be even at the same time, the only numbers possible are 570, 572, 574, 576 and 578. Also, if there is no 5 in the number, you will get 360 more numbers.

Question 13 |

To decide whether a number of n digits is divisible by 7, we can define a process by which its magnitude is reduced as follows: (i1, i2 , i3…..in are the digits of the number, starting from the most significant digit).
i1,i2…in fi i1 . 3^n–1 + i2, 3^n–2 + …. + In3^0 .
e.g. 259 fi 2.3^2 + 5.3^1 + 9.3^0 = 18 + 15 + 9 = 42
Ultimately the resulting number will be seven after repeating the above process a certain number of times.
After how many such stages, does the number 203 reduce to 7?

A | 1 |

B | 2 |

C | 3 |

D | 4 |

Question 13 Explanation:

203 becomes → 2.3^2 + 0 + 3.3^0 = 21 → 2.3^1 +1.3^0 = 7. Hence, clearly two steps are required.

Question 14 |

A teacher teaching students of third standard gave a simple multiplication exercise to the kids. But one kid reversed the digits of both the numbers and carried out the multiplication and found that the product was exactly the same as the one expected by the teacher. Only one of the following pairs of numbers will fit in the description of the exercise. Which one is that?

A | 14, 22 |

B | 13, 62 |

C | 19, 33 |

D | 42, 28 |

Question 14 Explanation:

Trial and error will give option (13, 62) as the correct answer, since 13 × 62 = 26 × 31

Question 15 |

If 8 + 12 = 2, 7 + 14 = 3 then 10 + 18 =?

A | 10 |

B | 4 |

C | 6 |

D | 18 |

Question 15 Explanation:

The solutions are defined as the sum of digits of the answer. Hence, 10 is correct.

Question 16 |

Find the minimum integral value of n such that the division 55n/124 leaves no remainder.
(a) 124 (b) 123
(c) 31 (d) 62

A | 124 |

B | 123 |

C | 31 |

D | 62 |

Question 16 Explanation:

There are no common factors between 55 and 124. Hence the answer should be 124.

Question 17 |

What is the value of k for which the following system of equations has no solution: 2x – 8y = 3; and kx + 4y = 10. ?

A | -2 |

B | -1 |

C | 1 |

D | 2 |

Question 17 Explanation:

At k = –1, the two equations become inconsistent with respect to each other and there will then be no solution to the system of equations.

Question 18 |

A positive integer is said to be a prime if it is not divisible by any positive integer other than itself and one. Let p be a prime number strictly greater than 3. Then, when p 2 + 17 is divided by 12, the remainder is ?

A | 6 |

B | 1 |

C | 0 |

D | 8 |

Question 18 Explanation:

Try with 5, 7, 11. In each case the remainder is 6.

Question 19 |

A man sells chocolates that come in boxes. Either full boxes or half a box of chocolates can be bought from him. A customer comes and buys half the number of boxes the seller has plus half a box. A second customer comes and buys half the remaining number of boxes plus half a box. After this, the seller is left with no chocolates box. How many chocolates boxes did the seller have before the first customer came?

A | 2 |

B | 3 |

C | 4 |

D | 5 |

Question 19 Explanation:

Trial and error gives you the answer as 3 .

Question 20 |

X and Y are playing a game. There are eleven 50 paise coins on the table and each player must pick up at least one coin but not more than five. The person picking up the last coin loses. X starts. How many should he pick up at the start to ensure a win no matter what strategy Y employs?

A | 2 |

B | 3 |

C | 4 |

D | 5 |

Question 20 Explanation:

Picking up 4 coins will ensure that he wins the game.

Question 21 |

If a < b, which of the following is always true?

A | a < (a + b) / 2 < b |

B | a < ab/2 < b |

C | a < b^2 – a^2 < b |

D | a < ab < b |

Question 21 Explanation:

(Snce the average of any two numbers lies between the numbers.

Question 22 |

The money order commission is calculated as follows. From ` X to be sent by money order, subtract 0.01 and divide by 10. Get the quotient and add 1 to it, if the result is Y, the money order commission is ` 0.5Y. If a person sends two money orders to Aurangabad and Bhatinda for ` 71 and ` 48 respectively, the total commission will be ?

A | ` 7.00 |

B | ` 6.50 |

C | ` 6.00 |

D | ` 7.50 |

Question 22 Explanation:

8/2 + 5/2 = 6.5.

Question 23 |

The auto fare in Ahmedabad has the following formula based upon the meter reading. The meter reading is rounded up to the next higher multiple of 4. For instance, if the meter reading is 37 paise, it is rounded up to 40 paise. The resultant is multiplied by 12. The final result is rounded off to nearest multiple of 25 paise. If 53 paise is the meter reading what will be the actual fare?
(a) ` 6.75 (b) ` 6.50
(c) ` 6.25 (d) ` 7.50

A | ` 6.75 |

B | ` 6.50 |

C | ` 6.25 |

D | ` 7.50 |

Question 23 Explanation:

The answer will be 56 × 12 = 672 → 675. Hence, ` 6.75.

Question 24 |

Juhi and Bhagyashree were playing simple mathematical puzzles. Juhi wrote a two digit number and asked Bhayashree to guess it. Juhi also indicated that the number is exactly thrice the product of its digits. What was the number that Juhi wrote ?

A | 36 |

B | 24 |

C | 12 |

D | 48 |

Question 24 Explanation:

The given condition is satisfied only for 24.

Question 25 |

It is desired to extract the maximum power of 3 from 24!, where n! = n.(n – 1) . (n – 2) … 3.2.1. What will be the exponent of 3 ?

A | 8 |

B | 9 |

C | 10 |

D | 11 |

Question 25 Explanation:

The answer will be given by 8 + 2 = 10.

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