Questions and Answers Type: | MCQ (Multiple Choice Questions). |

Main Topic: | Quantitative Aptitude. |

Quantitative Aptitude Sub-topic: | Number System Aptitude Questions and Answers. |

Number of Questions: | 10 Questions with Solutions. |

- If a number is 32*54* is divisible by both 3 and 5 then find the missing digits in the number respectively?
- 1, 2
- 1, 0
- 0, 1
- 2, 1

Answer: (b) 1, 0

Solution: A number is divisible by 3 if the sum of all the digits is divisible by 3 and a number is divisible by 5 if a unit digit of any number is zero or 5.

Here if we take unit digit zero then the number will be divisible by 5.

After taking unit digit zero then the sum of all the digits $$ = 3 + 2 + * + 5 + 4 + 0 $$ $$ = 14 + * $$ if we take 1 in the missing place, the sum will be 15, which is divisible by 3. $$ = 14 + 1 $$ $$ = 15 $$ Hence 1 and zero (0) are the missing digits in the number respectively.

Solution: A number is divisible by 3 if the sum of all the digits is divisible by 3 and a number is divisible by 5 if a unit digit of any number is zero or 5.

Here if we take unit digit zero then the number will be divisible by 5.

After taking unit digit zero then the sum of all the digits $$ = 3 + 2 + * + 5 + 4 + 0 $$ $$ = 14 + * $$ if we take 1 in the missing place, the sum will be 15, which is divisible by 3. $$ = 14 + 1 $$ $$ = 15 $$ Hence 1 and zero (0) are the missing digits in the number respectively.

- Find the number which is nearest to 374 and is exactly divisible by 15?
- 375
- 370
- 380
- 385

Answer: (a) 375

Solution: If we divide 374 by 15, we get 1 as the remainder. Hence 375 is the nearest number to the 374, which is exactly divisible by 15.

Solution: If we divide 374 by 15, we get 1 as the remainder. Hence 375 is the nearest number to the 374, which is exactly divisible by 15.

- A student was asked to multiply a number by 42 but the student multiplied it by 24 and got the answer less than the correct one by 558. Find the number to be multiplied?
- 28
- 30
- 31
- 32

Answer: (c) 31

Solution: Let the number to be multiplied is \(x\) then $$ 42x - 24x = 558 $$ $$ 18x = 558 $$ $$ x = \frac{558}{18} $$ $$ x = 31 $$

Solution: Let the number to be multiplied is \(x\) then $$ 42x - 24x = 558 $$ $$ 18x = 558 $$ $$ x = \frac{558}{18} $$ $$ x = 31 $$

- What least number must be subtracted from 1000 to get a number exactly divisible by 24?
- 14
- 15
- 16
- 17

Answer: (c) 16

Solution: After dividing 1000 by 24, we get 16 as the remainder.

Hence 16 is the least number, which can be subtracted from 1000 to get a number exactly divisible by 24.

Solution: After dividing 1000 by 24, we get 16 as the remainder.

Hence 16 is the least number, which can be subtracted from 1000 to get a number exactly divisible by 24.

- The difference between the two numbers is 885, When the larger number is divided by the smaller number, the quotient is 3 and the remainder is 13 then find the smaller number?
- 428
- 431
- 433
- 436

Answer: (d) 436

Solution: Let the smaller number is \(x\) then

The larger number \(= x + 885\)

Quotient \(= 3\)

Remainder \(= 13\)

According to the question, the larger number is dividend then $$ dividend = divisor \times quotient \\ + remainder $$ $$ x + 885 = 3x + 13 $$ $$ 3x - x = 885 - 13 $$ $$ 2x = 872 $$ $$ x = \frac{872}{2} $$ $$ x = 436 $$ Hence the smaller number is 436.

Solution: Let the smaller number is \(x\) then

The larger number \(= x + 885\)

Quotient \(= 3\)

Remainder \(= 13\)

According to the question, the larger number is dividend then $$ dividend = divisor \times quotient \\ + remainder $$ $$ x + 885 = 3x + 13 $$ $$ 3x - x = 885 - 13 $$ $$ 2x = 872 $$ $$ x = \frac{872}{2} $$ $$ x = 436 $$ Hence the smaller number is 436.

Lec 1: Introduction to Number System
Lec 2: Factors of Composite Number
Questions and Answers-1
Lec 3: Basic Remainder Theorem
Questions and Answers-2
Lec 4: Polynomial Remainder Theorem
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Lec 5: LCM of Numbers
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Lec 6: HCF of Numbers
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Lec 7: Divisibility Rules of Numbers
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