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Integers

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Source: — Data Sufficiency |
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by narik11 » Wed Oct 06, 2010 10:17 am
danjuma wrote:The LCM of 2 numbers is 630. What is the difference between the 2 numbers?

1. The HCF of the 2 numbers is 9.

2.The sum of the 2 numbers is 153.
Let the two numbers be a and b
asked a-b=?

Option 1: HCF*LCM=ab=9*630
not sufficient

option 2: a+b=153
not sufficient

From 1 and 2 u can find the values of a and b

So its C
Whats OA?
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by limestone » Wed Oct 06, 2010 10:18 am
Let call those 2 numbers: x and y
LCM: least common multiple ---- HCF: highest common factor
Given information : LCM of x and y is 630
or xy/HCF = 630 (as LCM*HCF = x*y)

1. HCF = 9 then xy = 630*9
2 unknowns with only 1 equation => Cannot define x and y => insuf.

2. x+y = 153 and xy = 630*HCF
However, we haven't got the HCF value yet, then cannot define x and y => insuf.

1&2
x*y=9*630 = 5670
x+y = 153
=> suf.

Then pick C.
"There is nothing either good or bad - but thinking makes it so" - Shakespeare.
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by shovan85 » Wed Oct 06, 2010 10:21 am
IMO C.

LCM(x,y) = 630

1: HCF(x,y) = 9 => x-y = ? Not Sufficient

But we can get x*y = LCM(x,y) * GCF(x,y)

2: x+y = 153 => x-y = ? Not Suff.

Combine 1 and 2 you get xy and x+y. Thus you can get x-y .
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by Yanat » Thu Oct 07, 2010 7:11 am
I feel C is correct.

Using the concept of HCF * LCM = number
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