1. Two numbers are in the ratio 2 : 3. If their L.C.M. is 48. what is sum of the numbers?
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A. 28
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B. 40
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C. 64
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D. 42
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Answer : Option B
Explanation :
Let the numbers be 2x and 3x
LCM of 2x and 3x = 6x (∵ LCM of 2 and 3 is 6. Hence LCM
of 2x and 3x is 6x)
Given that LCM of 2x and 3x is 48
=> 6x = 48
=> x = 48⁄6 = 8
Sum of the numbers = 2x + 3x = 5x = 5 × 8 = 40
LCM of 2x and 3x = 6x (∵ LCM of 2 and 3 is 6. Hence LCM
of 2x and 3x is 6x)
Given that LCM of 2x and 3x is 48
=> 6x = 48
=> x = 48⁄6 = 8
Sum of the numbers = 2x + 3x = 5x = 5 × 8 = 40
2. What is the greatest number of four digits which is divisible by 15, 25, 40 and 75 ?
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A. 9800
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B. 9600
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C. 9400
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D. 9200
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Answer : Option B
Explanation :
Greatest number of four digits = 9999
LCM of 15, 25, 40 and 75 = 600
9999 ÷ 600 = 16, remainder = 399
Hence, greatest number of four digits which is divisible by 15, 25, 40 and 75
= 9999 - 399 = 9600
LCM of 15, 25, 40 and 75 = 600
9999 ÷ 600 = 16, remainder = 399
Hence, greatest number of four digits which is divisible by 15, 25, 40 and 75
= 9999 - 399 = 9600
3. Three numbers are in the ratio of 2 : 3 : 4 and their L.C.M. is 240. Their H.C.F. is:
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A. 40
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B. 30
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C. 20
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D. 10
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Answer : Option C
Explanation :
Let the numbers be 2x, 3x and 4x
LCM of 2x, 3x and 4x = 12x
=> 12x = 240
=> x = 240⁄12 = 20
H.C.F of 2x, 3x and 4x = x = 20
LCM of 2x, 3x and 4x = 12x
=> 12x = 240
=> x = 240⁄12 = 20
H.C.F of 2x, 3x and 4x = x = 20
4. What is the lowest common multiple of 12, 36 and 20?
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A. 160
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B. 220
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C. 120
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D. 180
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Answer : Option D
Explanation :
LCM = 2 × 2 × 3 × 1 × 3 × 5 = 180
5. What is the least number which when divided by 5, 6, 7 and 8 leaves a remainder 3,
but when divided by 9 leaves no remainder?
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A. 1108
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B. 1683
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C. 2007
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D. 3363
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Answer : Option B
Explanation :
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Solution 1
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LCM of 5, 6, 7 and 8 = 840
Hence the number can be written in the form (840k + 3) which is divisible by 9
If k = 1, number = (840 × 1) + 3 = 843 which is not divisible by 9
If k = 2, number = (840 × 2) + 3 = 1683 which is divisible by 9
Hence 1683 is the least number which when divided by 5, 6, 7 and 8 leaves a remainder 3,
but when divided by 9 leaves no remainder
-------------------------------------------------------------------------------- Solution 2 - Hit and Trial Method
--------------------------------------------------------------------------------
Just see which of the given choices satisfy the given condtions
Take 3363. This is not even divisible by 9. Hence this is not the answer
Take 1108. This is not even divisible by 9. Hence this is not the answer
Take 2007. This is divisible by 9.
2007 ÷ 5 = 401, remainder = 2 . Hence this is not the answer
Take 1683. This is divisible by 9.
1683 ÷ 5 = 336, remainder = 3
1683 ÷ 6 = 280, remainder = 3
1683 ÷ 7 = 240, remainder = 3
1683 ÷ 8 = 210, remainder = 3
Hence 1683 is the answer
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LCM of 5, 6, 7 and 8 = 840
Hence the number can be written in the form (840k + 3) which is divisible by 9
If k = 1, number = (840 × 1) + 3 = 843 which is not divisible by 9
If k = 2, number = (840 × 2) + 3 = 1683 which is divisible by 9
Hence 1683 is the least number which when divided by 5, 6, 7 and 8 leaves a remainder 3,
but when divided by 9 leaves no remainder
-------------------------------------------------------------------------------- Solution 2 - Hit and Trial Method
--------------------------------------------------------------------------------
Just see which of the given choices satisfy the given condtions
Take 3363. This is not even divisible by 9. Hence this is not the answer
Take 1108. This is not even divisible by 9. Hence this is not the answer
Take 2007. This is divisible by 9.
2007 ÷ 5 = 401, remainder = 2 . Hence this is not the answer
Take 1683. This is divisible by 9.
1683 ÷ 5 = 336, remainder = 3
1683 ÷ 6 = 280, remainder = 3
1683 ÷ 7 = 240, remainder = 3
1683 ÷ 8 = 210, remainder = 3
Hence 1683 is the answer