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07 Sep 2019, 18:03
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Three lines intersect at point \(O\), creating 6 angles. Three adjacent angles are \(19X, 3Y,\) and \(19Z\). If \(X, Y,\) and \(Z\) are positive integers, how many different values of \(X\) can have?
A. 2
B. 3
C. 5
D. 8
E. 13
Source: All questions I posted are adapted or enhanced from OG or OG Quant.
Kudos for a good or creative solution. Also, give +1 kudos if you think this is a good question.
A. 2
B. 3
C. 5
D. 8
E. 13
Source: All questions I posted are adapted or enhanced from OG or OG Quant.
Kudos for a good or creative solution. Also, give +1 kudos if you think this is a good question.
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07 Sep 2019, 18:46
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Sum of any 3 adjacent angle is 180 degrees
19X+3Y+19Z=180
19(X+Z)+3Y=180
19(X+Z)= 3(60-Y)
Hence, X+Z is a multiple of 3.
As X, Y and Z are positive integers, X+Z can be 3, 6 or 9
When X+Z=9
X can take any integral value from 1 to 8 (both inclusive)
D
19X+3Y+19Z=180
19(X+Z)+3Y=180
19(X+Z)= 3(60-Y)
Hence, X+Z is a multiple of 3.
As X, Y and Z are positive integers, X+Z can be 3, 6 or 9
When X+Z=9
X can take any integral value from 1 to 8 (both inclusive)
D
chondro48
Three lines intersect at point \(O\), creating 6 angles. Three adjacent angles are \(19X, 3Y,\) and \(19Z\). If \(X, Y,\) and \(Z\) are positive integers, how many different values of \(X\) can have?
A. 2
B. 3
C. 5
D. 8
E. 13
Source: All questions I posted are adapted or enhanced from OG or OG Quant.
Kudos for a good or creative solution. Also, give +1 kudos if you think this is a good question.
A. 2
B. 3
C. 5
D. 8
E. 13
Source: All questions I posted are adapted or enhanced from OG or OG Quant.
Kudos for a good or creative solution. Also, give +1 kudos if you think this is a good question.
07 Sep 2019, 18:59
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Given, 19(x+z)+3y=180, maximum value x+z can take is 9, we know that 3y is a multiple of 3 ,for 3y to be a multiple of 3 ,x+z should be multiple of three remember x+z max value is nine ,so x+z = 3,6,9 , substituting integers which add up to 9 , we get x=1,2,3,4,5,6,7,8 total possible values of x=8 , it took me more than four minutes can anyone suggest shorter method
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