sanju09 wrote:If x, y, and z are positive integers, and x is a multiple of 3, for which of the following must z and 18 have a common factor greater than 1?
I. (x/9) + (y/6) = (z/18)
II. (x/6) + (y/9) = (z/18)
III. (x/6) + (y/5) = (z/30)
A. I only
B. II only
C. I and II only
D. I an III only
C. I, II, and III
To see the situation more clearly, we can plug in values.
Be sure to satisfy the constraint that x is multiple of 3.
Since statement I is included in four of the five answer choices, it is almost certain that statement I must be included in the correct answer choice.
To save time, start with statement II.
II: (x/6) + (y/9) = (z/18)
To clear the fractions, multiply both sides of the equation by the GREATEST of the 3 denominators (18).
18 (x/6 + y/9) = 18 (z/18)
3x + 2y = z.
Case 1: If x=3 and y=1, then z = 3(3) + 2(1) = 11.
z=11 and 18 do not have a common factor greater than 1.
Here, it does not have to be true that z and 18 have a common factor greater than 1.
Eliminate any answer choice that includes statement II.
Eliminate B, C and E.
III: (x/6) + (y/5) = (z/30)
To clear the fractions, multiply both sides of the equation by the GREATEST of the 3 denominators (30).
30 (x/6 + y/5) = 30 (z/30)
5x + 6y = z.
Case 1: If x=3 and y=1, then z = 5(3) + 6(1) = 21.
z=21 and 18 are both divisible by 3.
Case 2: If x=6 and y=2, then z = 5(6) + 6(2) = 42.
z=42 and 18 are both divisible by 3 and 6.
In each case, z and 18 have a common factor greater than 1.
One more to be safe:
Case 3: If x=9 and y=5, then z = 5(9) + 6(5) = 75.
z=75 and 18 both divisible by 3.
In every case, z and 18 have a common factor greater than 1.
Thus, the correct answer choice must include statement III.
Eliminate A.
The correct answer is
D.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
