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31 May 2020, 06:18
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E
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Difficulty:
45%
(medium)
Question Stats:
33% (01:15) correct
67%
(00:23)
wrong
based on 9
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what is the HCF of 0.3, 0.15 and 0.06
A 0.3
B 0.18
C 0.15
D 0.06
E 0.03
A 0.3
B 0.18
C 0.15
D 0.06
E 0.03
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31 May 2020, 07:04
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Let’s take two fractions (a/b) and (c/d).
To find LCM and HCF of (a/b) and (c/d) the generalized formula will be:
H.C.F = H.C.F of numerators / L.C.M of denominators
L.C.M = L.C.M of numerators / H.C.F of denominators
=>> HCF of 0.3,0.15,0.06
Or 30/100,15/100,6/100
=>> HCF of numerator/LCM of denominator
=>> HCF of 30,15,6
=>> factors of 30 = 2*3*5
=>> factors of 15 = 5*3
=>> factors of 6 = 2*3
HCF or 30,15&6 is 3
LCM of 100,100,100 is 100
HCF of 30/100,15/100,6/100
=> HCF/LCM = 3/100 => 0.03
Answer is E
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To find LCM and HCF of (a/b) and (c/d) the generalized formula will be:
H.C.F = H.C.F of numerators / L.C.M of denominators
L.C.M = L.C.M of numerators / H.C.F of denominators
=>> HCF of 0.3,0.15,0.06
Or 30/100,15/100,6/100
=>> HCF of numerator/LCM of denominator
=>> HCF of 30,15,6
=>> factors of 30 = 2*3*5
=>> factors of 15 = 5*3
=>> factors of 6 = 2*3
HCF or 30,15&6 is 3
LCM of 100,100,100 is 100
HCF of 30/100,15/100,6/100
=> HCF/LCM = 3/100 => 0.03
Answer is E
Posted from my mobile device
31 May 2020, 08:14
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You absolutely never will need to find Greatest Common Divisors or Least Common Multiples on the GMAT of decimals or fractions. You will only ever need to find GCDs or LCMs of positive integers.
There are important reasons for that -- for one thing, it's not even clear what it would mean for a fraction to be a 'divisor' of another fraction. If you think of the definition of divisor from integers:
The integer d is a divisor of the integer a if a/d is an integer
then you might naturally think that this is the definition for fractions (by which I mean 'rational numbers') :
The fraction d is a divisor of the fraction a if a/d is a fraction
And that is, in fact, the definition any mathematician would use - it's the definition from the branch of abstract algebra known as 'ring theory' (which is way beyond the scope of the GMAT). Using this definition, the GCD concept makes no sense for fractions -- it would always be infinite. It's only if you use a non-standard definition of divisibility (Euclid's concept of 'common measure', where you need an integer result from the division) that the GCD concept can be applied to fractions. No one could be expected to guess that unless they had read texts well beyond the scope of the GMAT, so it would not be fair for the test to ask about it.
So this is not a realistic GMAT question - where is it from?
There are important reasons for that -- for one thing, it's not even clear what it would mean for a fraction to be a 'divisor' of another fraction. If you think of the definition of divisor from integers:
The integer d is a divisor of the integer a if a/d is an integer
then you might naturally think that this is the definition for fractions (by which I mean 'rational numbers') :
The fraction d is a divisor of the fraction a if a/d is a fraction
And that is, in fact, the definition any mathematician would use - it's the definition from the branch of abstract algebra known as 'ring theory' (which is way beyond the scope of the GMAT). Using this definition, the GCD concept makes no sense for fractions -- it would always be infinite. It's only if you use a non-standard definition of divisibility (Euclid's concept of 'common measure', where you need an integer result from the division) that the GCD concept can be applied to fractions. No one could be expected to guess that unless they had read texts well beyond the scope of the GMAT, so it would not be fair for the test to ask about it.
So this is not a realistic GMAT question - where is it from?
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