If two numbers, a and b, are to be chosen from a set of 4. .

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 am; Followed by:3 members

If two numbers, a and b, are to be chosen from a set of 4. .

by VJesus12 » Thu Nov 30, 2017 9:32 am

If two numbers, a and b, are to be chosen from a set of 4 consecutive integers starting with 1 and a set of three consecutive even integers starting with 4, respectively, what is the probability that b/a will not be an integer?

(A) 1/6
(B) 1/4
(C) 1/3
(D) 1/2
(E) 2/3

The OA is B. Experts, can you show me why is B the correct answer? Thanks.

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Source: Beat The GMAT — Problem Solving | Thu Nov 30, 2017 9:32 am

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by [email protected] » Thu Nov 30, 2017 10:57 am

Hi VJesus12,

We're told that A is a number from the set {1, 2, 3, 4} and B is a number from the set {4, 6, 8}. We're asked for the probability that B/A will NOT be an integer.

Since there are 4 numbers in A and 3 numbers in B, there are (4)(3) = 12 possible outcomes. The outcomes that will NOT end in an integer are:

8/3
6/4
4/3

Thus, 3 out of the 12 options will NOT end in an integer. 3/12 = 1/4

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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by Scott@TargetTestPrep » Sat Oct 12, 2019 3:53 pm

VJesus12 wrote:If two numbers, a and b, are to be chosen from a set of 4 consecutive integers starting with 1 and a set of three consecutive even integers starting with 4, respectively, what is the probability that b/a will not be an integer?

(A) 1/6
(B) 1/4
(C) 1/3
(D) 1/2
(E) 2/3

The OA is B. Experts, can you show me why is B the correct answer? Thanks.

We see that a is chosen from the set {1, 2, 3, 4} and b is chosen from the set {4, 6, 8}. Since there are 4 numbers in the first set and 3 numbers in the second set, the total number of ordered pairs (a, b) is 4 x 3 = 12. Of these ordered pairs (a, b), we have (1, 4), (1, 6), (1, 8), (2, 4), (2, 6), (2, 8), (3, 6), (4, 4), and (4, 8) that produce an integer when b is divided by a. integer. In other words, the probability that b/a is an integer is 9/12 = 3/4, and thus the probability that b/a is not an integer is 1 - 3/4 = 1/4.

Answer: B

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