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. |

- The HCF and LCM of two numbers are 22 and 2400 respectively. If one number is 264 then find another number?
- 100
- 150
- 200
- 250

Answer: (c) 200

Solution: Given, HCF = 22

LCM = 2400

First number = 264

Let the second number is \(x\) then $$ Product \ of \ two \ numbers = HCF \times LCM $$ $$ 264 \times x = 22 \times 2400 $$ $$ x = \frac{22 \times 2400}{264} $$ $$ x = \frac{52800}{264} $$ $$ x = 200 $$ Hence the second number is 200.

Solution: Given, HCF = 22

LCM = 2400

First number = 264

Let the second number is \(x\) then $$ Product \ of \ two \ numbers = HCF \times LCM $$ $$ 264 \times x = 22 \times 2400 $$ $$ x = \frac{22 \times 2400}{264} $$ $$ x = \frac{52800}{264} $$ $$ x = 200 $$ Hence the second number is 200.

- Find the smallest sum of rupees which contains Rs 1.25, Rs 15, Rs 2.50, and Rs 10?
- 30
- 35
- 40
- 45

Answer: (a) 30

Solution: Given, Rs 1.25, Rs 15, Rs 2.50, and Rs 10 then

LCM of 1.25, 15, 2.50, and 10

It can be also written

\((LCM \ of \ 125, 1500, 250, 1000) \times 0.01\) $$ = 3000 \times 0.01 $$ $$ = 30 $$ Hence Rs 30 is the smallest sum of rupees.

Solution: Given, Rs 1.25, Rs 15, Rs 2.50, and Rs 10 then

LCM of 1.25, 15, 2.50, and 10

It can be also written

\((LCM \ of \ 125, 1500, 250, 1000) \times 0.01\) $$ = 3000 \times 0.01 $$ $$ = 30 $$ Hence Rs 30 is the smallest sum of rupees.

- Three women start walking together to the same way around a circular track of 15 km. If their speeds are 3, 4, and 5 km per hour respectively then find how much time they will take to meet together again?
- 10 hours
- 12 hours
- 15 hours
- 18 hours

Answer: (c) 15 hours

Solution: Time taken by the women to complete one revolution of the circular way $$ = \frac{15}{3}, \frac{15}{4}, \ and \ \frac{15}{5} \ hours $$ $$ = \frac{5}{1}, \frac{15}{4}, \ and \ \frac{3}{1} \ hours $$ Taking LCM of \(\frac{5}{1}, \frac{15}{4}, \ and \ \frac{3}{1}\) $$ = \frac{LCM \ of \ 5, 15, 3}{HCF \ of \ 1, 4, 1} $$ $$ = \frac{15}{1} $$ $$ 15 \ hours $$ Hence the women will meet together again after 15 hours.

Solution: Time taken by the women to complete one revolution of the circular way $$ = \frac{15}{3}, \frac{15}{4}, \ and \ \frac{15}{5} \ hours $$ $$ = \frac{5}{1}, \frac{15}{4}, \ and \ \frac{3}{1} \ hours $$ Taking LCM of \(\frac{5}{1}, \frac{15}{4}, \ and \ \frac{3}{1}\) $$ = \frac{LCM \ of \ 5, 15, 3}{HCF \ of \ 1, 4, 1} $$ $$ = \frac{15}{1} $$ $$ 15 \ hours $$ Hence the women will meet together again after 15 hours.

- The LCM and HCF of two numbers are 1350 and 25 respectively. If one number is 125 then find another number?
- 200
- 270
- 290
- 300

Answer: (b) 270

Solution: Given, LCM = 1350

HCF = 25

First number = 125

Let the second number is \(x\) then $$ Product \ of \ two \ numbers = HCF \times LCM $$ $$ 125 \times x = 25 \times 1350 $$ $$ x = \frac{25 \times 1350}{125} $$ $$ x = \frac{33750}{125} $$ $$ x = 270 $$ Hence the second number is 270.

Solution: Given, LCM = 1350

HCF = 25

First number = 125

Let the second number is \(x\) then $$ Product \ of \ two \ numbers = HCF \times LCM $$ $$ 125 \times x = 25 \times 1350 $$ $$ x = \frac{25 \times 1350}{125} $$ $$ x = \frac{33750}{125} $$ $$ x = 270 $$ Hence the second number is 270.

- If HCF of 575 and 325 is 65 then find the LCM of the same numbers?
- 2525
- 2775
- 2825
- 2875

Answer: (d) 2875

Solution: Given, first number = 575

second number = 325

HCF = 65 then $$ Product \ of \ two \ numbers = HCF \times LCM $$ $$ LCM = \frac{Product \ of \ two \ numbers}{HCF} $$ $$ LCM = \frac{575 \times 325}{65} $$ $$ LCM = \frac{186,875}{65} $$ $$ LCM = 2875 $$

Solution: Given, first number = 575

second number = 325

HCF = 65 then $$ Product \ of \ two \ numbers = HCF \times LCM $$ $$ LCM = \frac{Product \ of \ two \ numbers}{HCF} $$ $$ LCM = \frac{575 \times 325}{65} $$ $$ LCM = \frac{186,875}{65} $$ $$ LCM = 2875 $$

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
Questions and Answers-3
Questions and Answers-4
Questions and Answers-5
Lec 5: LCM of Numbers
Questions and Answers-6
Lec 6: HCF of Numbers
Questions and Answers-7
Questions and Answers-8
Lec 7: Divisibility Rules of Numbers
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Questions and Answers-10
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