1.) ** **Two numbers are in the ratio of 15:11. If their H.C.F. is 13, find the numbers.

**A.** 122 and 80 **B.** 87 and 190

**C.** 195 and 143 **D.** None of these

**View Answer**

**Answer:** Option** C**

**Explanation:**

Let the required numbers be 15.x and 11x.

Then, their H.C.F. is x. So, x = 13.

The numbers are (15 x 13 and 11 x 13) i.e., **195 and 143.**

2.) The H.C.F. of two numbers is 11 and their L.C.M. is 693. If one of the numbers is 77,find the other.

**A.** 80 **B.** 57

**C.** 63 **D.** 99

**View Answer**

**Answer:** Option** D **Explanation:

Other number = (11 X 693)/77 =

**99**

3.) Find the greatest possible length which can be used to measure exactly the lengths 4 m 95 cm, 9 m and 16 m 65 cm.

**A.** 45 cm **B.** 57 cm

**C.** 63 cm **D.** 99 cm

**View Answer**

**Answer:** Option** A Explanation:**

Required length = H.C.F. of 495 cm, 900 cm and 1665 cm.

495 = 3^{2} x 5 x 11, 900 = 2^{2} x 3^{2} x 5^{2}, 1665 = 3^{2} x 5 x 37.

H.C.F. = 32 x 5 = 45.

Hence, required length = **45 cm.**

4.) Find the largest number which divides 62, 132 and 237 to leave the same remainder in each case.

**A.** 35 **B.** 77

**C.** 73 **D.** 59

**View Answer**

**Answer:** Option** A Explanation:**

Required number = H.C.F. of (132 - 62), (237 - 132) and (237 - 62)

= H.C.F. of 70, 105 and 175 = **35.**

5.) **Find **the largest number of four digits exactly divisible by 12,15,18 and 27.

**A.** 5500 **B.** 9000

**C.** 7300 **D.** 9720

**View Answer**

**Answer:** Option** D Explanation: **

The Largest number of four digits is 9999.

Required number must be divisible by L.C.M. of 12,15,18,27 i.e. 540.

On dividing 9999 by 540,we get 279 as remainder .

\Required number = (9999-279) = **9720.**