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A Learning Portal from Recruitment India

There are four prime numbers written in ascending order of magnitude. The product of the first three is 7429 and of the last three is 12673. Find the fourth number?

A.

17

B.

23

C.

31

D.

29

Answer with explanation

Answer: Option DExplanation

(7429/12673) = 17/29 Fourth Number is 29

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John, Smith and Kate start at same time, same point and in same direction to run around a circular ground. John completes a round in 250 seconds, Smith in 300 seconds and Kate in 150 seconds. Find after what time will they meet again at the starting point?

A.

30 min

B.

25 min

C.

20 min

D.

15 min

Answer with explanation

Answer: Option BExplanation

L.C.M. of 250, 300 and 150 = 1500 sec Dividing 1500 by 60 we get 25, which mean 25 minutes. John, Smith and Kate meet after

25 minutes.

Workspace

The traffic lights at three different road crossings change after every 40 sec, 72 sec and 108 sec respectively. If they all change simultaneously at 5 : 20 : 00 hours, then find the time at which they will change simultaneously.

A.

5 : 28 : 00 hrs

B.

5 : 30 : 00 hrs

C.

5 : 38 : 00 hrs

D.

5 : 40 : 00 hrs

Answer with explanation

Answer: Option CExplanation

Traffic lights at three different road crossings change after every 40 sec, 72 sec and 108 sec respectively.

Therefore, find the L.C.M. of 40, 72 and 108.

L.C.M. of 40, 72 and 108 = 1080

The traffic lights will change again after 1080 seconds = 18 min

The next simultaneous change takes place at 5 : 38 : 00 hrs.

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A man was employed on the promise that he will be paid the highest wages per day. The contract money to be paid was Rs. 1189. Finally he was paid only Rs. 1073. For how many days did he actually work?

A.

39

B.

40

C.

37

D.

35

Answer with explanation

Answer: Option CExplanation

HCF of 1189, 1073 = 29

1073/29 = 37

Workspace

On dividing a number by 4, the remainder is 2. The quotient so obtained when divided by 5, leaves the remainder 3. Now the quotient so obtained when divided by 6, leaves the remainder 5. The last quotient is 7. The number was

A.

962

B.

954

C.

946

D.

938

Answer with explanation

Answer: Option BExplanation

WKT,

Divisor x Quotient + Remainder = Number

6 x 7 + 5 = 47

5 x 47 + 3 = 238

4 x 238 + 2 = 954

Therefore, required number is 954.

Workspace

Find the side of the largest square slab which can be paved on the floor of a room 5 meters 44cm long and 3 meters 74 cm broad?

A.

56 cm

B.

42 cm

C.

38 cm

D.

34 cm

Answer with explanation

Answer: Option DExplanation

The side of the square slab is the H.C.F. of 544 and 374 cm i.e. 34.

Workspace

Three different containers contain 1365 litres, 1560 litres and 1755 litres of mixtures of milk and water respectively. What biggest measure that can measure all the different quantities exactly ?

A.

97 lit

B.

129 lit

C.

195 lit

D.

37 lit

Answer with explanation

Answer: Option CExplanation

containers contain mixtures of milk and water as 1365 lit, 1560 lit and 1755 lit.

Biggest measure that can measure all these different quantities exactly can be given by

HCF of (1365, 1560, 1755)

That can be found as

HCF of 1365, 1755 = 195

Now, HCF of 195 and 1560 = 195

Hence, biggest measure that can measure all the given different quantities exactly is 195 lit

Workspace

Given : Three numbers 17, 42 and 93

Find the largest number to divide all the three numbers leaving the remainders 4, 3, and 15 respectively at the end?

A.

13

B.

17

C.

21

D.

78

Answer with explanation

Answer: Option AExplanation

Here greatest number that can divide means the HCF

Remainders are different so simply subtract remainders from numbers

17 – 4 = 13; 42 – 3 = 39; 93 – 15 = 78

Now let’s find HCF of 13, 39 and 78

By direct observation we can see that all numbers are divisible by 13.

∴ HCF = 13 = required greatest number

Workspace

A milkman has 75 litres milk in one cane and 45 litres in another. The maximum capacity of container which can measure milk of either container exact number ?

A.

25 litres

B.

15 litres

C.

5 litres

D.

1 litre

Answer with explanation

Answer: Option BExplanation

75 litres, 45 litres

For maximum capacity take HCF (75, 45) = 15

Workspace

The product of two 2 digit numbers is 2028 and their HCF is 13. What are the numbers?

A.

26, 78

B.

39, 52

C.

13, 156

D.

36, 68

Answer with explanation

Answer: Option BExplanation

Let the numbers be 13x and 13y (∵ HCF of the numbers = 13)

13x×13y=2028⇒xy=12 co-primes with product 12 are (1, 12) and (3, 4) (∵ we need to take only co-primes with product 12. If we take two numbers with product 12,

but not co-prime, the HCF will not remain as 13)

Hence the numbers with HCF 13 and product 2028

= (13 × 1, 13 × 12) and (13 × 3, 13 × 4)

= (13, 156) and (39, 52)

Given that the numbers are 2 digit numbers. Hence numbers are 39 and 52.

Workspace

Find the least number which when divided by 2, 3, 4 and 5 leaves a remainder 3. But when divided by 9 leaves no remainder?

A.

B.

63

C.

183

D.

153

Answer with explanation

Answer: Option BExplanation

LCM of 2, 3, 4 and 5 is 30,

let number be 30k + 3 put k = 2,

we get 63 which is divisible by 9

Workspace

The least number, which when divided by 12, 15, 20 and 54 leaves in each case a remainder of 8 is:

A.

216

B.

389

C.

443

D.

548

Answer with explanation

Answer: Option DExplanation

Required number = (L.C.M. of 12, 15, 20, 54) + 8

= 540 + 8

= 548.

**(OR)**

Given numbers are 12, 15, 20, 54

To Find: least no. which is divided by given nos. and leaves remainder 8

Least no which is divisible by all given no is LCM of all nos.

LCM means the least common multiple.

First, we find LCM of 12, 15, 20, 54 by prime factorization method

12 = 2 × 2 × 3

15 = 3 × 5

20 = 2 × 2 × 5

54 = 2 × 3 × 3 × 3

LCM ( 12, 15 , 20 , 54 ) = 2 × 2 × 3 × 3 × 3 × 5 = 540

To find the required no. we add 8 to LCM

⇒ Required No. = 540 + 8 = 548

Thus, 548 is the least no which when divided by 12 15 20 and 54 leaves in each case a remainder of 8.

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