Hi
Need assistance in figuring out why the answer to the DS question (below) is option (D) Each statement alone is sufficient
"The positive integers x, y & z are such that x is a factor of y & y is a factor of z.
Is z even?
1) xz is even
2) y is even
Thanks
Thanks
Factors
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Here's a more formal approach.The positive integers x, y, and z are such that x is a factor of y and y is a factor of z. Is z even?
(1) xz is even
(2) y is even.
Target question: Is z even?
Given: x is a factor of y, and y is a factor of z.
There's a nice rule that says, "If D is a factor (divisor) of N, then N = kD for some integer k"
So, if x is a factor of y, then y = kx for some integer k.
Also, if y is a factor of z, then z = jy for some integer j
Statement 1: xz is even
This sets up two possible cases (x is even or z is even). We'll examine both:
case a: x is even.
If x is even, then kx is even, which means y is even (since y=kx).
If y is even, then jy is even, which means z is even (since z=jy).
case b: z is even
Since both possible cases yield the same answer to the target question, statement 1 is SUFFICIENT
Statement 2: y is even
If y is even, then jy is even, which means z is even (since z=jy).
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer = D
Cheers,
Brent
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Let's reverse the language:The positive integers x, y and z are such that x is a factor of y and y is a factor of z. Is z even.
1) xz is even
2) y is even.
z is a multiple of y, and y is a multiple of x.
Thus, z is a multiple of x.
Statement 1: xz is even.
If x = even, then z must be even since it's a multiple of an even value.
If x = odd, then z must be even in order for xz to be even.
Since in either case z is even, sufficient.
Statement 2: y is even.
If z is a multiple of an even number, then z too must be even.
Sufficient.
The correct answer is D.
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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.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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