**AMCAT**

If the sum of two numbers is 55 and the H.C.F. and L.C.M of these numbers are 5 and 120 respectively, then the sum of the reciprocals of the numbers is equal to:

Option 1 : 55/601

Option 2 : 601/55

Option 3 : 11/120

Option 4 : 120/11

Correct Answer :11/120

This is standard formula.

Product of any two numbers = product of their LCM and HCF

We have been asked to find the sum of reciprocals of the said numbers.

Here let number be a and b

Hence as per above formula a*b = HCF *LCM = 5 *120 =600

And also given a+b = 55.

Now reciprocals of above number will be 1/a and 1/b

Hence (1/a)+(1/b)= (a+b)/a*b= 55/600 = 11/120

Ques 2 : Choose the correct answer.

Three different containers contain 496 litres, 403 litres and 713 litres of mixtures of milk and water respectively. What biggest measure can measure all the different quantities exactly ?

Option 1 : 1 litre

Option 2 : 7 litre

Option 3 : 31 litre

Option 4 : 41 litre

Correct Answer :31 Liters

Find HCF of three numbers thus it will be 31.

Ques 3 : Choose the correct answer.

Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together ?

Option 1 : 4

Option 2 : 10

Option 3 : 15

Option 4 : 16

Correct Answer : 16

(30*60) seconds / LCM of 2,3,6,8,10,12 = 1800/120 = 15.

At starting point (at 0th second), all tolled together. This adds one more case.

So, 15+1 =16.

Ques 4 : Choose the correct answer.

Four different electronic devices make a beep after every 30 minutes, 1 hour, 3/2 hour and 1 hour 45 minutes respectively. All the devices beeped together at 12 noon. They will again beep together at:

Option 1 : 12 midnight

Option 2 : 3 a.m.

Option 3 : 6 a.m.

Option 4 : 9 a.m.

Correct Answer : 9am

Four different electronic devices make a beep after every 30 minutes, 1hours, 3/2 hours, and 1hour and 45 minutes respectively.

Time in minutes are 30 minutes , 60 minutes, 90 minutes , 105 minutes respectively.

L.C.M of 30 , 60 , 90 , 105 are 1260 minutes = 21 hrs.

All beeped together after 12 noon at 21 hrs later. i.e, (12+21) hrs = 9 am .

Therefore, Next they will beeped together at 9 am.

Ques 5 : Choose the correct answer.

The number of prime factors of (3 x 5)12 (2 x 7)10 (10)25 is:

Option 1 : 47

Option 2 : 60

Option 3 : 72

Option 4 : None of these

Correct Answer : None Of These

The equation can be facorize as 3*5*3*2*2*2*7*2*5*2*5*5*5 or 2^5*3^2*5^5*7^1 total no of prime factor =(5+1)*(5+1)*(2+1)*(1+1)=216

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