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**Objective Questions****Tick (✔) the correct answer in each of the following :****Q.1. Which of the following numbers is divisible by 3 ?****(a) 24357806****(b) 35769812****(c) 83479560****(d) 3336433****Ans. **(c) Because sum of its digits is 8 + 3 + 4 + 7 + 9 + 5 + 6 + 0 = 42 which is divisible

by 3.**Q.2. Which of the following numbers is divisible by 9 ?****(a) 8576901****(b) 96345210****(c) 67594310****(d) none of these****Ans.**

(a) Because sum of its digits is 8 + 5 + 7 + 6 + 9 + 0 + 1 = 36 which is divisible by

9.**Q.3. Which of the following numbers is divisible by 4 ?****(a) **78653234**(b) **98765042

**(c)** 24689602**(d)** 87941032**Ans. **

(d) Because the number formed by tens and ones digits is divisible by 4 i.e. 32/4 = 8.**Q.4. Which of the following numbers is divisible by 8 ?****(a) 96354142****(b) 37450176****(c) 57064214****(d) none of these****Ans.**

(b) Because the number formed by hundred, tens and ones digits is divisible by 8 i.e. 176/8 = 22.**Q.5. Which of the following numbers is divisible by 6 ?****(a) 8790432****(b) 98671402****(c) 85492014****(d) none of these****Ans.**

(a) Because its one digit is divisible by 2 and sum of its digits is 8 + 7 + 9 + 0 + 4 + 3 + 2 =

33, which is divisible by 3.

Hence it is divisible by 6.**Q.6. Which of the following numbers is divisible by 11 ?****(a) 3333333****(b) 1111111****(c) 22222222****(d) none of these****Ans. **(c) Because the difference of the sums of its odd places digits and of its even

places digits is (2 + 2 + 2 + 2) – (2 + 2 + 2 + 2) i.e. 8 – 8 = 0, which is zero and is

divisible by 11.**Q.7. Which of the following is a prime number ?****(a) 81****(b) 87****(c) 91****(d) 97****Ans. **(d) Because 97 has no factors other than 1 and itself.**Q.8. Which of the following is a prime number ?****(a) 117****(b) 171****(c) 179****(d) none of these****Ans. **(c) Because 179 has no factors other than 1 and itself.**Q.9. Which of the following is a prime number ?****(a) 323****(b) 361****(c) 263****(d) none of these****Ans.**

(c) Because 263 has no factors other than 1 and itself.**Q.10. Which of the following are co-primes ?****(a) 8, 11****(b) 9, 10****(c) 6, 8****(d) 15, 18****Ans. **(a), (b) Because the common factors of 9 and 10 are none but 1.**Q.11. Which of the following is a composite number ?****(a) 23****(b) 29****(c) 32****(d) none of these****Ans.**

(c) Because 32 has factors which are 2,2, 2, 2, 2.**Q.12. The H.C.F. of 144 and 198 is****(a) 9****(b) 12****(c) 6****(d) 18****Ans.**

(d) Because 18 is the highest common factor of 144 and 198.**Q.13. The HCF of 144, 180 and 192 is****(a) 12****(b) 16****(c) 18****(d) 8****Ans.**

(a) Because 12 is the highest common factors of these numbers 144, 180 and 192.**Q.14. Which of the following are co-primes ?****(a) 39, 91****(b) 161, 192****(c) 385, 462****(d) none of these****Ans.**

(b) Because 161 and 192 have no common factor other than 1, i.e., HCF of 161 and 192 is 1.**Q.15. when reduced to the lowest terms is****(a) ****(b)****(c) ****(d)****Ans.**

(d) Because HCF of 289 and 391 is 17 and **Q.16. The greatest number which divides 134 and 167 leaving 2 as remainder in each ****case is****(a) 14****(b) 17****(c) 19****(d) 11**

**Ans.**

(d) Because dividing 134 and 167 by 11, remainder is 2 in each case.**Q.17. The LCM of 24, 36, 40 is****(a) 4****(b) 90****(c) 360****(d) 720****Ans.** (c) Because 360 is the least multiple of 24, 36 and 40.**Q.18. The LCM of 12, 15, 20, 27 is****(a) 270****(b) 360****(c) 480****(d) 540****Ans. **(d) Because 540 is the least multiple of 12, 15, 20 and 27.**Q.19. The smallest number which when ****diminished by 3 is divisible by 28, 36 and**

**45, is****(a) 1257****(b) 1260****(c) 1263****(d) none of these****Ans**. (c) Because 1263 – 3 = 1260 is divisible by 28, 36 and 45.**Q.20. The HCF of two co-primes is****(a) the smaller number****(b) the larger number****(c) 1****(d) none of these****Ans. **(c) Because HCF of two co-prime number is always 1.**Q.21. If a and b are co-primes, then their LCM is****(a) 1****(b)****(c) ab****(d) none of these****Ans.**

(c) Because HCF of a and b, two co-primes is 1.

∴ LCM = a × b = ab.**Q.22.The product of two numbers is 2160 and their HCF is 12. The LCM of these numbers is****(a) 12****(b) 25920****(c) 180****(d) none of these****Ans.**

(c) Because LCM of two numbers = Product of these number/their HCF i.e. 2160/12 =

180.**Q.23. The HCF of two numbers is 145 and their LCM is 2175. If one of the numbers is 725, the other number is****(a) 290****(b) 435****(c) 5****(d) none of these****Ans.**

(b) Because second number **Q.24. The least number divisible by each of the numbers 15, 20, 24, 32 and 36 is****(a) 1660****(b) 2880****(c) 1440****(d) none of these****Ans.**

(c) Because LCM of 15, 20, 24, 32 and 36 = 1440.**Q.25. Three bells toll together at intervals of 9, 12, 15 minutes. If they start tolling together, after what time will they next toll together ?****(a) 1 hour****(b) ****(c) ****(d) 3 hours****Ans.****(d)** Because LCM of 9, 12, 15 is 180.

∴ 180 minutes

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- RS Aggarwal Solutions: Whole Numbers Exercise - 3A
- RS Aggarwal Solutions: Whole Numbers Exercise - 3B
- RS Aggarwal Solutions: Whole Numbers Exercise - 3C
- RS Aggarwal Solutions: Whole Numbers Exercise - 3D
- RS Aggarwal Solutions: Whole Numbers Exercise - 3E
- RS Aggarwal Solutions: Whole Numbers Exercise - 3F