# H.C.F and L.C.M Aptitude Test Paper 2

6) If the HCF of two numbers is 27, and their sum is 216, find these numbers.

1. 27, 189
2. 154, 162
3. 108, 108
4. 81, 189

Explanation:

Let the numbers be 27x and 27y.

Then, 27x + 27y = 216
27 (x+ y) = 216
(x + y) = 216/27
X + y = 8

co-prime numbers with sum 8 are (1, 7) and (3, 5).

Therefore we can say that the required numbers are (27 x1, 27 x 7) and (27 x 3, 27x 5), i.e. (27, 189) and (81, 135).
Out of the above two answers, the given one in the answer is the pair (27, 189).

7) Two numbers are in the ratio of 15:11. If the HCF of numbers is 13, find the numbers.

1. 75, 55
2. 105, 77
3. 15, 11
4. 195, 143

Explanation:

Let the two numbers are 15x and 11x
HCF = x
x = 13
Therefore, the numbers are (15 x 13 and 11 x 13), i.e. 195 and 143.

8) Find the greatest integer that divides 358, 376, and 334 and leaves the same remainder in each case.

1. 6
2. 7
3. 8
4. 9

Explanation:

Take the difference between two numbers

376 - 358 = 18;
376 - 334 = 42;
358 - 334 = 24;

By taking the HCF of 18, 42, 24.

18 = 2 x3 x 3
42 = 2 x 3 x 7
24 = 2 x 2 x 2 x 3
HCF = 2 x 3 = 6

Hence the required number is 6.

9) Three bells toll at intervals of 36 sec, 40 sec, and 48 sec respectively. They start singing together at a particular time. When will they toll next together?

1. 6 minutes
2. 12 minutes
3. 18 minutes
4. 24 minutes

Explanation:

Firstly find the LCM of 36, 40, and 48

LCM = 2 x 2 x 2 x 2 x 3 x 3 x 5 = 720 seconds

Hence, after 720 seconds or 12 minutes three bells will toll together.

10) The LCM of two numbers is 7700, and their HCF is 11. If one of these numbers is 275, what is the other number?

1. 279
2. 283
3. 308
4. 318

Explanation:

Apply Formula: HCF x LCM = first number x Second number 11 x 7700 = 275 x second number

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