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What is the ratio of houses with smoke alarms to houses without smoke

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New post 30 Sep 2019, 20:32
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EMPOWERgmat DS Series:
Block 1, Question 5

What is the ratio of houses with smoke alarms to houses without smoke alarms on Gleaner Street?

1) On Gleaner Street, 7/18 of the houses do not have smoke alarms.
2) There are 90 houses on Gleaner Street.


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New post 30 Sep 2019, 20:52
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EMPOWERgmatRichC wrote:
EMPOWERgmat DS Series:
Block 1, Question 5

What is the ratio of houses with smoke alarms to houses without smoke alarms on Gleaner Street?

1) On Gleaner Street, 7/18 of the houses do not have smoke alarms.
2) There are 90 houses on Gleaner Street.


48 Hour Window To Win An $85 EMPOWERgmat Tuition Credit (1 Month Free!)
Share your explanation! The GMAT Club member with the most verified Kudos in total on the 5 question DS Block 1 question pack will win an $85 EMPOWERgmat tuition credit, which will entitle the winner to a full month of complete access to the EMPOWERgmat system. Even if you're not sure about your answer or your rationale, share your explanation to help boost your learning and earn a chance to win.

To be eligible, your explanation must be submitted within the 48 hour window after this post was created and should explain your reasoning why the answer you chose is correct

The OA and official explanation will be held until the 48 hour window has lapsed.


(1) On Gleaner Street, 7/18 of the houses do not have smoke alarms.
--> 7/18th do not have smoke alarms
--> Houses with smoke alarms = 1 - 7/18 = 11/18
So, Required ratio = (11/18)/(7/18) = 11:7 --> Sufficient

(2) There are 90 houses on Gleaner Street.
Nothing can be said about the ratio of houses with & without smoke alarm --> Insufficient

IMO Option A
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Re: What is the ratio of houses with smoke alarms to houses without smoke  [#permalink]

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New post 30 Sep 2019, 21:17
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EMPOWERgmatRichC wrote:
EMPOWERgmat DS Series:
Block 1, Question 5

What is the ratio of houses with smoke alarms to houses without smoke alarms on Gleaner Street?

1) On Gleaner Street, 7/18 of the houses do not have smoke alarms.
2) There are 90 houses on Gleaner Street.




We require ratio of number of houses with smoke alarm to houses with no smoke alarm

(1) Number of houses with No smoke alarm is 7/18 of total number of houses, then Number of houses with smoke alarm must be 1-(7/18) ie. 11/18 of total number. From this required ratio can be calculated. Sufficient

BCE eliminated.

(2) With total number of houses, it is not possible to find the ratio of number of houses with alarm to houses with no alarm. Insufficient

A is correct.
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Re: What is the ratio of houses with smoke alarms to houses without smoke  [#permalink]

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New post 01 Oct 2019, 21:30
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Ratio of number of houses with smoke alarm to houses with no smoke alarm

(1) Number of houses with no smoke alarm = 7/18 of total number of houses,
Number of houses with smoke alarm = 1-(7/18) ie. 11/18 of total number of houses .
From this required ratio can be calculated. Sufficient

BCE eliminated.

(2) With just total number of houses, it is not possible to find the ratio of number of houses with alarm to houses with no alarm. Insufficient

A is correct.
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What is the ratio of houses with smoke alarms to houses without smoke  [#permalink]

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New post 03 Oct 2019, 11:28
OFFICIAL EXPLANATION

Hi All,

We're asked for the ratio of houses with smoke alarms to houses without smoke alarms on Gleaner Street. This is a value question; since it asks us for a RATIO, there are a couple of different ways that we can answer it (we either need the exact number of each type of house OR some other way to define the relationship between those two numbers).

1) On Gleaner Street, 7/18 of the houses do not have smoke alarms.

With the information in Fact 1, we know that the total number of houses is some multiple of 18 AND that the number without smoke alarms would be an equivalent multiple of 7. This creates a pattern....

IF... there were 18 houses, 7 would NOT have a smoke alarm and the remaining 11 would... so the answer to the question would be 11:7
IF... there were 36 houses, 14 would NOT have a smoke alarm and the remaining 22 would... so the answer to the question would be 22:14 = 11:7
IF... there were 54 houses, 21 would NOT have a smoke alarm and the remaining 33 would... so the answer to the question would be 33:21 = 11:7
Etc.
The answer to the question is ALWAYS 11:7
Fact 1 is SUFFICIENT

2) There are 90 houses on Gleaner Street.

Fact 2 gives us the total number of houses, but tells us NOTHING about the number that have (or do not have) a smoke alarm.
Fact 2 is INSUFFICIENT

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What is the ratio of houses with smoke alarms to houses without smoke   [#permalink] 03 Oct 2019, 11:28
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