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# In the 5-digit integer 54xy2, x and y are single digits. What is the p

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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In the 5-digit integer 54xy2, x and y are single digits. What is the p [#permalink]

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15 Dec 2017, 07:29
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[GMAT math practice question]

In the 5-digit integer $$54xy2$$, x and y are single digits. What is the probability that $$54xy2$$ is divisible by 4?

A. $$\frac{1}{4}$$
B. $$\frac{1}{3}$$
C. $$\frac{1}{2}$$
D. $$\frac{2}{3}$$
E. $$\frac{3}{4}$$
[Reveal] Spoiler: OA

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Director
Joined: 07 Dec 2014
Posts: 885
Re: In the 5-digit integer 54xy2, x and y are single digits. What is the p [#permalink]

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15 Dec 2017, 10:14
MathRevolution wrote:
[GMAT math practice question]

In the 5-digit integer $$54xy2$$, x and y are single digits. What is the probability that $$54xy2$$ is divisible by 4?

A. $$\frac{1}{4}$$
B. $$\frac{1}{3}$$
C. $$\frac{1}{2}$$
D. $$\frac{2}{3}$$
E. $$\frac{3}{4}$$

any even digit in the tens place will work
any digit in the hundreds place will work
1/2*1=1/2
C
Manager
Joined: 07 Jul 2012
Posts: 230
Location: India
Concentration: Finance
Re: In the 5-digit integer 54xy2, x and y are single digits. What is the p [#permalink]

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15 Dec 2017, 22:20
A number is divisible by 4 if the last two digits form a number divisible by 4.
So 54xy2 is divisible by 4 when y= (1,3,5,7,9)= 5 possible cases

54xy2 is not divisible by 4 when y= (0,2,4,6,8)= 5 possible cases

Required probability= $$\frac{5}{10}$$= $$\frac{1}{2}$$

Answer: C.
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4710
GPA: 3.82
Re: In the 5-digit integer 54xy2, x and y are single digits. What is the p [#permalink]

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17 Dec 2017, 23:29
=>
The divisibility of $$54xy2$$ by $$4$$ depends on the last two digits only. So, $$54xy2$$ is divisible by $$4$$ exactly when $$10y + 2$$ is divisible by $$4$$.
Out of the possible values for $$10y + 2, 12, 32, 52, 72, 92$$ are divisible by $$4$$, but $$02, 22, 42, 62, 82$$ are not. Therefore, the required probability is $$\frac{1}{2}$$.

Therefore, the answer is C.

Answer : C
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Re: In the 5-digit integer 54xy2, x and y are single digits. What is the p   [#permalink] 17 Dec 2017, 23:29
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# In the 5-digit integer 54xy2, x and y are single digits. What is the p

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