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The LCM of 24,36 and third number is 2016 and their GCD is 4

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Kudos [?]: 16 [0], given: 16

The LCM of 24,36 and third number is 2016 and their GCD is 4 [#permalink] New post 13 May 2013, 18:57
The LCM of 24,36 and third number is 2016 and their GCD is 4. What is the smallest possible value of the third number.
A) 48
B)224
C)288
D)63
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Kudos [?]: 36 [0], given: 25

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Re: The LCM of 24,36 and third number is 2016 and their GCD is 4 [#permalink] New post 13 May 2013, 19:56
The fact that 2016 is the LCM of the number means that all the factors of 2016 mus be present within the three numbers.

Now 2016 is 32 X 7 X 9

Since 32 and 9 can be accommodated within 24 and 36, 7 must be present in the third number

So it can be either 224 or 63

It is also given that the GCD of the number is 4, which is not possible in case of 63 therefore the third number can only be 224

B
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Kudos [?]: 16 [0], given: 16

if 0<a<1 and 0<b<1 and a>b, then which among the given expre [#permalink] New post 14 May 2013, 00:29
Given
(aMb) = a-b
(aDb) = a+b
(aHb) = a*b
(aPb) = a/b

Question: if 0<a<1 and 0<b<1 and a>b, then which among the given expression has highest value
a)(aMB)
b)(aDb)
c)(aPb)
d)Cant be determined
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Kudos [?]: 16 [0], given: 16

When the same number of track suits were distributed [#permalink] New post 14 May 2013, 00:31
When the same number of track suits were distributed among 2 groups of athletes comprising 4 and 6 athletes, 2 suits were left in each case. What is the smallest number of suits distributed to each group.
a) 12
b)14
c)16
d)18
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Number Theory [#permalink] New post 15 May 2013, 19:47
A milkman has three different qualities of milk. 403 gallons of 1st quality, 465 gallons of 2nd quality and 496 gallons of 3rd quality. Find the least possible number of bottles of equal size in which different milk of different qualities can be filled without mixing

a)34
b)46
c)26
d)44


OA: d
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Re: Number Theory [#permalink] New post 15 May 2013, 22:36
Vamshiiitk wrote:
A milkman has three different qualities of milk. 403 gallons of 1st quality, 465 gallons of 2nd quality and 496 gallons of 3rd quality. Find the least possible number of bottles of equal size in which different milk of different qualities can be filled without mixing

a)34
b)46
c)26
d)44


OA: d

Hi,

We have to find the least number of bottle, given, the size of all bottles is same.
The HCF of all the quantities would be the maximum capacity of each bottle, thus,
403 = 13x31
465 = 15x31
496 = 16x31
31 gallons would be the size, so, the total number of bottles required = 13+15+16 = 44
Answer (D)

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Re: The LCM of 24,36 and third number is 2016 and their GCD is 4 [#permalink] New post 19 May 2013, 00:14
63 is out as it is not divisible by 4

48 , 288 have another Multiple in in 12 : 12 x 48 =288

Only option remains 224 and that is not divisible by 12 but by 4. hence B
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Re: if 0<a<1 and 0<b<1 and a>b, then which among the given expre [#permalink] New post 19 May 2013, 00:21
Vamshiiitk wrote:
Given
(aMb) = a-b
(aDb) = a+b
(aHb) = a*b
(aPb) = a/b

Question: if 0<a<1 and 0<b<1 and a>b, then which among the given expression has highest value
a)(aMB)
b)(aDb)
c)(aPb)
d)Cant be determined


Easy one , since a > b and both are +ve a/b is goign to be greatest . answer C
Re: if 0<a<1 and 0<b<1 and a>b, then which among the given expre   [#permalink] 19 May 2013, 00:21
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The LCM of 24,36 and third number is 2016 and their GCD is 4

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