knight247 wrote:If x is a randomly chosen integer between 1 and 20, inclusive, and y is a randomly chosen integer between 21 and 40, inclusive, what is the probability that xy is a multiple of 4?
A. 1/4
B. 1/3
C. 3/8
D. 7/16
E. ½
OA is E. Fairly simple to solve using the complementary method. Would like some help with the direct method. No Complementary Please.
Case 1: even*even = multiple of 4.
1/2 the numbers in each range are even.
P(x is even AND y is even) = 1/2 * 1/2 = 1/4.
Case 2: multiple of 4 * odd = multiple of 4.
Since every other even number is a multiple of 4, and 1/2 the numbers in each range are even, 1/4 of the numbers in each range are multiples of 4.
1/2 the numbers in each range are odd.
Thus:
P(x is a multiple of 4 AND y is odd) = 1/4 * 1/2 = 1/8.
P(x is odd AND y is a multiple of 4) = 1/2 * 1/4 = 1/8.
Since getting the first result (1/4) OR the second result (1/8) OR the third result (1/8) is a good outcome, we add the fractions.
1/4 + 1/8 + 1/8 = 1/2.
The correct answer is
E.
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
