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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
Set A consists of all the integers between 10 and 21, inclusive. Set B
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02 Aug 2021, 01:18
02 Aug 2021, 01:18
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Set A consists of all the integers between 10 and 21, inclusive. Set B consists of all the integers between 10 and 50, inclusive. If x is a number chosen randomly from Set A, y is a number chosen randomly from Set B, and y has no factor z such that 1 < z < y, what is the probability that the product xy is divisible by 3?
A. 1/4
B. 1/3
C. 1/2
D. 2/3
E. 3/4
A. 1/4
B. 1/3
C. 1/2
D. 2/3
E. 3/4
Retired Moderator
Joined: 19 Nov 2020
Posts: 326
Given Kudos: 64
GRE 1: Q160 V152
Re: Set A consists of all the integers between 10 and 21, inclusive. Set B
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05 Aug 2021, 08:38
05 Aug 2021, 08:38
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under one minute, "y has no factor z such that 1 < z < y" implies that y is prime, and we check sets A and B for the integers, multiples of 3 (sum of digits must be divisible by 3). Consequently multiples of 3 in Set A= {12, 15, 18, 21} and in set B= {none}. Primes in set B= {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47}. Hence, the number of total outcomes= (21-10+1)*11 and the number of favorable outcomes is 4*11. Probability is (4*11) / (12*11)=1/3. Answer is B
GeminiHeat wrote:
Set A consists of all the integers between 10 and 21, inclusive. Set B consists of all the integers between 10 and 50, inclusive. If x is a number chosen randomly from Set A, y is a number chosen randomly from Set B, and y has no factor z such that 1 < z < y, what is the probability that the product xy is divisible by 3?
A. 1/4
B. 1/3
C. 1/2
D. 2/3
E. 3/4
A. 1/4
B. 1/3
C. 1/2
D. 2/3
E. 3/4
gmatclubot
Re: Set A consists of all the integers between 10 and 21, inclusive. Set B [#permalink]
05 Aug 2021, 08:38
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