Our goal is to find the answer choice that does NOT have to be an integer.
Since z is a factor of x and x is a factor of y, z divides into both x and y.
Since z is divides into both x and y, the answer choices with z in the denominator (A, C and D) are likely to yield integer values.
Try to show that B does not have to be an integer.
Let z=1, x=2, y=4.
B: (y+z)/x = (4+1)/2 = 5/2. Not an integer.
The correct answer is B.
Question 1
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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.
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For more information, please email me (Mitch Hunt) at [email protected].
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Note: To avoid confusion, I added some brackets to your answer choice.
Here's another approach:
x is a multiple of z
So, we can say that x = kz (for some integer k)
x is a factor of y
In other words, y is a multiple of x.
So, we can say that y = jx (for some integer j)
IMPORTANT: Since we already know that x = kz, let's replace x with kz to get: y = jkz
So, x = kz, y = jkz and z = z.
Let's plug in these values to see what we get:
A) (x+z)/z = (kz+z)/z = k+1 (= INTEGER)
B) (y+z)/x = (jkz+z)/kz = (jk+1)/k (not necessarily an integer)
C) (x+y)/z = (kz+jkz)/z = k+jk (= INTEGER)
D) (xy)/z = [(kz)(jkz)]/z = jk²z (= INTEGER)
E) (yz)/x = [(jkz)(z)]/kz = jz (= INTEGER)
Answer = B
Cheers,
Brent
Mitch already showed the approach of looking for values of x, y and z, such that we get a non-integer.If x, y, and z are positive integers such that x is a factor of y, and x is a multiple of z, which of the following is NOT necessarily an integer?
A) (x+z)/z
B) (y+z)/x
C) (x+y)/z
D) (xy)/z
E) (yz)/x
Here's another approach:
x is a multiple of z
So, we can say that x = kz (for some integer k)
x is a factor of y
In other words, y is a multiple of x.
So, we can say that y = jx (for some integer j)
IMPORTANT: Since we already know that x = kz, let's replace x with kz to get: y = jkz
So, x = kz, y = jkz and z = z.
Let's plug in these values to see what we get:
A) (x+z)/z = (kz+z)/z = k+1 (= INTEGER)
B) (y+z)/x = (jkz+z)/kz = (jk+1)/k (not necessarily an integer)
C) (x+y)/z = (kz+jkz)/z = k+jk (= INTEGER)
D) (xy)/z = [(kz)(jkz)]/z = jk²z (= INTEGER)
E) (yz)/x = [(jkz)(z)]/kz = jz (= INTEGER)
Answer = B
Cheers,
Brent
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Hi oquiella,
Both Mitch and Brent have provided solutions to this question, so I won't rehash any of that math here. Instead, I want to point out a design 'shortcut' in this question:
Notice how the prompt asks 'which of the following is NOT necessarily an integer?" - this wording implies that 4 of the answers will ALWAYS be integers, while one will not always be an integer. Once we find the one answer that isn't necessarily an integer, then we can stop working - that answer WILL be the correct answer.
GMAT assassins aren't born, they're made,
Rich
Both Mitch and Brent have provided solutions to this question, so I won't rehash any of that math here. Instead, I want to point out a design 'shortcut' in this question:
Notice how the prompt asks 'which of the following is NOT necessarily an integer?" - this wording implies that 4 of the answers will ALWAYS be integers, while one will not always be an integer. Once we find the one answer that isn't necessarily an integer, then we can stop working - that answer WILL be the correct answer.
GMAT assassins aren't born, they're made,
Rich
