If x,y and z are positive integers and 3x=4y=7z, then the least possible value of x+y+z is
A)33
B)40
C)49
D)61
E)84
OA is D
The way I approached problem was to assume the smallest possible value for x. Since x must be a positive integer, then x =1, from that we get y=3/4 and z=3/7
when we add those up we don't get anywhere close to the answer choices
if you were to take y=1 and solve with that or z=1 and solve from there - you would get a higher value for x+y+z
Can an instructor please advise what am i missing here??
thanks in advance
least possible value from old GMAT Prep test
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The condition mentioned in the stem is 3x=4y=7z, so you need to find the LCM among 3,4,7 and that is 84, then you divide 84 by 3,4,7 to get values of x,y,z (28,21,12) and then x+y+z(61).
I am not sure though how to clarify your method, but if you add the fractions, you do get a 61 in the numerator.
I am not sure though how to clarify your method, but if you add the fractions, you do get a 61 in the numerator.
- selango
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If you put only x=1 it means you are assuming least value only for 1.y and z can be of maximum values.
Similarly for y=1 or z=1
To get the least value of x+y+z,we need to substitute x,y and z values as 1(ie) x=1,y=1 and z=1.
We need to find the ratios of x,y,z so that we can get all the values.
Hope this clarify
Similarly for y=1 or z=1
To get the least value of x+y+z,we need to substitute x,y and z values as 1(ie) x=1,y=1 and z=1.
We need to find the ratios of x,y,z so that we can get all the values.
Hope this clarify
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Hi San,san2009 wrote:If x,y and z are positive integers and 3x=4y=7z, then the least possible value of x+y+z is
A)33
B)40
C)49
D)61
E)84
OA is D
The way I approached problem was to assume the smallest possible value for x. Since x must be a positive integer, then x =1, from that we get y=3/4 and z=3/7
when we add those up we don't get anywhere close to the answer choices
if you were to take y=1 and solve with that or z=1 and solve from there - you would get a higher value for x+y+z
Can an instructor please advise what am i missing here??
thanks in advance
The question stem tells us that x, y and z are positive integers. As you wrote yourself, if x=1 then "we get y=3/4 and z=3/7". This contradicts the question stem because y and z must be positive integers.
My approach is to focus on 3x=4y=7z. Since the variables are integers, 3x, 4y and 7z must also be integers. They all equal some mystery number. This mystery number is a multiple of 3, 4 and 7. The smallest values of x, y, z will result in the smallest possible mystery number. Thus this number is the least common multiple (LCM) of 3, 4, and 7. This is 84. Thus 3x=4y=7z=84. x=28, y=21, z=12. x+y+z=61
Hope that helps,
-Patrick
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