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For 6-digit integer 46x,y12, when x and y are drawn at random from {3,

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Bunuel
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For 6-digit integer 46x,y12, when x and y are drawn at random from {3, [#permalink] New post   05 Jul 2023, 03:45
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For 6-digit integer 46x,y12, when x and y are drawn at random from {3,5,8}, what is the probability that the integer drawn is divisible by 8?

A. 1/6
B. 1/3
C. 1/2
D. 2/3
E. 5/6
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Re: For 6-digit integer 46x,y12, when x and y are drawn at random from {3, [#permalink] New post   05 Jul 2023, 04:07
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Bunuel wrote:
For 6-digit integer 46x,y12, when x and y are drawn at random from {3,5,8}, what is the probability that the integer drawn is divisible by 8?

A. 1/6
B. 1/3
C. 1/2
D. 2/3
E. 5/6


Divisibility test of 8: Last 3 digits of the number must be Divisible by 8


i.e. for 46xy12 to be divisible by 8, y12 must be divisible by 8
for y12 to be divisible by 8, y must be either 3 or 5 because 312 and 512 are divisible by 8

i.e. y can be chosen in two ways and x can be anything i.e. it may be chosen in 3 ways

so Favorable outcomes = 3*2 = 6
Total outcomes = 3*3 (as each x and y may be chosen in 3 ways)

Probability = 6/9 = 2/3

Answer: Option D

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For 6-digit integer 46x,y12, when x and y are drawn at random from {3, [#permalink] New post   05 Jul 2023, 05:22
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GMATinsight wrote:
Bunuel wrote:
For 6-digit integer 46x,y12, when x and y are drawn at random from {3,5,8}, what is the probability that the integer drawn is divisible by 8?

A. 1/6
B. 1/3
C. 1/2
D. 2/3
E. 5/6


Divisibility test of 8: Last 3 digits of the number must be Divisible by 8


i.e. for 46xy12 to be divisible by 8, y12 must be divisible by 8
for y12 to be divisible by 8, y must be either 3 or 5 because 312 and 512 are divisible by 8

i.e. y can be chosen in two ways and x can be anything i.e. it may be chosen in 3 ways

so Favorable outcomes = 3*2 = 6
Total outcomes = 3*3 (as each x and y may be chosen in 3 ways)

Probability = 6/9 = 2/3

Answer: Option D

CLICK HERE For Accessing Complete set of Video on Probability and SUBSCRIBE the channel


1st Video solutions based Modular On-Demand QUANT Course: All Concepts | 2000+Qns | 20+ Tests |
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Is the question stem asking for the entire integer to be divisible by 8 (probably yes!) or x, y to be divisible by 8?

Considering scenario 1: I’ll only be concerned about the value of y. Since 312 and 512 are both divisible by 8, the probability of the “final” integer to be divisible by 8 is 1/3 + 1/3 = 2/3. (Picking up 3,5 from 3,5,8)

Appreciate any comments. Thanks!

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For 6-digit integer 46x,y12, when x and y are drawn at random from {3, [#permalink]
05 Jul 2023, 05:22
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