6
Q:

The H.C.F and L.C.M of two numbers are  84 and 21 respectively.  If the ratio of the two numbers is 1 : 4 , then the larger of the two numbers is 

A) 12 B) 48
C) 84 D) 108

Answer:   C) 84

Explanation:

Let the numbers be x and 4x. Then,  \inline \fn_jvn x\times 4x =84\times 21\: \: \Leftrightarrow \: \: x^{2}=\frac{84\times 21}{4} \: \: \Leftrightarrow \: \: x=21

Hence Larger Number = 4x = 84

Q:

Find the greatest number that will divide 964, 1238 and 1400 leaving remainder of 41,31 and 51 respectively ?

A) 64 B) 69
C) 71 D) 58
 
Answer & Explanation Answer: C) 71

Explanation:

To find the greatest number which divides the numbers 964, 1238 and 1400 leaving the remainders 41, 31 and 51 is nothing but the HCF of (964 - 41), (1238 - 31), (1400 - 51).

Therefore, HCF of 923, 1207 and 1349 is 71.

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2 34
Q:

A student can divide her books into groups of 5, 9 and 13. what is the smallest possible number of the books ?

A) 487 B) 585
C) 635 D) 705
 
Answer & Explanation Answer: B) 585

Explanation:

The smallest possible number of books = L.C.M of 5, 9 and 13.
Therefore, L.C.M of 5,9 and 13 is = 5 x 9 x 13 = 585.

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4 35
Q:

If HCF of two numbers is 8,which of the following can never be their LCM?

A) 32 B) 48
C) 60 D) 152
 
Answer & Explanation Answer: C) 60

Explanation:

60 is not a multiple of 8

 

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6 52
Q:

In a palace, three different types of coins are there namely gold, silver and bronze. The number of gold, silver and bronze coins is 18000, 9600 and 3600 respectively. Find the minimum number of rooms required if in each room should give the same number of coins of the same type ?

A) 26 B) 24
C) 18 D) 12
 
Answer & Explanation Answer: A) 26

Explanation:

Gold coins = 18000 , Silver coins = 9600 , Bronze coins = 3600

Find a number which exactly divide all these numbers 

That is HCF of 18000, 9600& 3600

 

All the value has 00 at end so the factor will also have 00.

HCF for 180, 96 & 36.

 

Factors of  

180 = 3 x 3 x 5 x 2 x 2

96 = 2 x 2 x 2 x 2 x 2 x 3

36 = 2 x 2 x 3 x 3

Common factors are 2x2×3=12

 Actual HCF is 1200

 

Gold Coins  will be in 15 rooms

Silver Coins  will be in 8 rooms

Bronze Coins  will be in 3 rooms

Total rooms will be (15+8+3)  =  26 rooms.

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5 240
Q:

Three numbers are in the ratio of 3:4:5 and their L.C.M is 3600.Their HCF is:

A) 40 B) 60
C) 100 D) 120
 
Answer & Explanation Answer: B) 60

Explanation:

Let the numbers be 3x, 4x, 5x.

Then, their L.C.M = 60x.

So, 60x=3600 or x=60.

 The numbers are (3 x 60), (4 x 60), (5 x 60).

Hence,required H.C.F=60

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7 194