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An apartment building has apartments numbered 2 through 85

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Carcass
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An apartment building has apartments numbered 2 through 85 [#permalink] New post   03 Oct 2018, 23:23
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An apartment building has apartments numbered 2 through 85, consecutively.

Quantity A
Quantity B
The probability that the apartment number of a randomly selected tenant contains a 4
\(\frac{3}{14}\)


A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
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D
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Re: An apartment building has apartments numbered 2 through 85 [#permalink] New post   18 Jan 2022, 05:34
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At this point I am wondering if this was a question by ETS, what skill would they be testing through this question?
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Re: An apartment building has apartments numbered 2 through 85 [#permalink] New post   04 Oct 2018, 01:33
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It's enticing to straightaway start counting the number of apartments with 4 in their number. However, the question asks for randomly selecting 'a tenant' not 'an apartment'. Since we don't know the number of tenants in each apartment, we can't tell which quantity is greater.

Hence D.
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Re: An apartment building has apartments numbered 2 through 85 [#permalink] New post   10 Oct 2018, 21:03
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Without doubt D
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Re: An apartment building has apartments numbered 2 through 85 [#permalink] New post   18 Jan 2022, 06:23
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See here more on probability https://gre.myprepclub.com/forum/gre-tips- ... 23084.html
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Re: An apartment building has apartments numbered 2 through 85 [#permalink] New post   18 Jan 2022, 07:25
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Carcass wrote:
An apartment building has apartments numbered 2 through 85, consecutively.

Quantity A
Quantity B
The probability that the apartment number of a randomly selected tenant contains a 4
\(\frac{3}{14}\)


Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.


Consider these two cases.....

Case i: Each apartment has one occupant, EXCEPT for apartment #4, which has 1 BILLION occupants.
In other words, 1,000,000,083 people live in the apartment, 1,000,000,000 of whom live in apartment #4.
So if we randomly select someone from the apartment, it's very very very very very likely that that person lives in apartment #4.
So, in this case P(apartment number of a randomly selected tenant contains a 4) = a number very close to 1.
In this case, QUANTITY A IS GREATER

Case ii: Each apartment has one occupant, EXCEPT for apartment #5, which has 1 BILLION occupants.
In other words, 1,000,000,083 people live in the apartment, 1,000,000,000 of whom live in apartment #5.
So if we randomly select someone from the apartment, it's very very very very very likely that that person lives in apartment #5.
So, in this case P(apartment number of a randomly selected tenant contains a 4) = a number very close to 0.
In this case, QUANTITY B IS GREATER

Answer: D
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Re: An apartment building has apartments numbered 2 through 85 [#permalink] New post   05 Aug 2022, 07:12
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such questions are discriminatory in nature.
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Re: An apartment building has apartments numbered 2 through 85 [#permalink] New post   01 Oct 2023, 21:39
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The answer is C

The total number of apartment numbers containing 4 is 18. Hence 18/(85-2+1)=18/84 = 3/14. Hence C.
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An apartment building has apartments numbered 2 through 85 [#permalink] New post   06 Dec 2024, 11:48
1
Carcass wrote:
An apartment building has apartments numbered 2 through 85, consecutively.

Quantity A
Quantity B
The probability that the apartment number of a randomly selected tenant contains a 4
\(\frac{3}{14}\)


A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.




This solution says the answer is C

Step 1: Total Apartments
The apartments are numbered 2 through 85, so the total number of apartments is:

85−2+1=84.
Step 2: Apartments Containing the Digit 4
We need to count how many apartment numbers contain the digit
4
4. These numbers can be in either the tens place or the units place.

Case 1: Apartments with 4 in the Tens Place
The apartments with

4 in the tens place are:

40,41,42,43,44,45,46,47,48,49
There are
10
10 such apartments.

Case 2: Apartments with 4 in the Units Place
The apartments with
4 in the units place are:

4,14,24,34,44,54,64,74,84
There are
9 such apartments.

Overlap: Apartment 44
Apartment
44
44 is counted in both cases, so we subtract it once to avoid double-counting:

10+9−1=18 apartments contain the digit 4
.
10+9−1=18 apartments contain the digit 4.
Step 3: Probability of Selecting an Apartment with the Digit 4
The probability is:

P(Apartment contains a 4)
=
Number of favorable outcomes
Total outcomes
=
18/84
=
3/14
.
P(Apartment contains a 4)=
Total outcomes
Number of favorable outcomes
​
=
84/18
​
=
14/3
​
.

​
.
The two quantities are equal.
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An apartment building has apartments numbered 2 through 85 [#permalink]
06 Dec 2024, 11:48
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