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Stuart@KaplanGMAT
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I'd just pick numbers.
The fractions in the stem are 1/4, 1/5 and 1/8; the LCM is 40, which is usually the best number to pick. A quick glance at the choices shows that 40 is a great choice.
So: 40 apartments total
1/4 = 10 with terraces
1/8 = 5 with skylights,
including 1/5(10) = 2 with terraces and skylights.
We want the # with neither, so:
10-2 = 8 with JUST terraces + 5 with skylights = 13 with either a terrace or a skylight.
40-13 = 27 with neither.
So, 27/40 have neither: choose (b).
* * *
As an aside, this would also have been a great question for guessing.
Even if we add the 1/8 + 1/4, ignoring overlap, that's 3/8 with terrace/skylight, which means that over half have neither. Only choice (b) is more than 1/2!
The fractions in the stem are 1/4, 1/5 and 1/8; the LCM is 40, which is usually the best number to pick. A quick glance at the choices shows that 40 is a great choice.
So: 40 apartments total
1/4 = 10 with terraces
1/8 = 5 with skylights,
including 1/5(10) = 2 with terraces and skylights.
We want the # with neither, so:
10-2 = 8 with JUST terraces + 5 with skylights = 13 with either a terrace or a skylight.
40-13 = 27 with neither.
So, 27/40 have neither: choose (b).
* * *
As an aside, this would also have been a great question for guessing.
Even if we add the 1/8 + 1/4, ignoring overlap, that's 3/8 with terrace/skylight, which means that over half have neither. Only choice (b) is more than 1/2!
Last edited by Stuart@KaplanGMAT on Mon May 26, 2008 9:31 am, edited 1 time in total.
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Ans is 27/40
Assume that we have 200 apartments
We call T is set of apartments that have terrace
S is set of apartments that have skylight
The number of apartments that have terrace = 1/4 x 200 = 50
The number of apartments that have skylight = 1/8 x 200 = 25
The number of apartments that have both terrace and skylight = 1/5 x 50 = 10
The number of apartments that have neither terrace nor skylight = 200 - T U S = 200 - (T + S - T ∩ S) = 200 - (50 + 25 - 10) = 135
Result = 135/200 = 27/40
Assume that we have 200 apartments
We call T is set of apartments that have terrace
S is set of apartments that have skylight
The number of apartments that have terrace = 1/4 x 200 = 50
The number of apartments that have skylight = 1/8 x 200 = 25
The number of apartments that have both terrace and skylight = 1/5 x 50 = 10
The number of apartments that have neither terrace nor skylight = 200 - T U S = 200 - (T + S - T ∩ S) = 200 - (50 + 25 - 10) = 135
Result = 135/200 = 27/40
Bia
The key in this problem is to
(1) Pick a total number that is the LCM or multiple of LCM
(2) Figure out that 1/5th fraction is the intersection of T & S
The solution by bia cuts a lot of time as opposed to the MGMAT grid. B T W it was not a 2 min Q for me.
(1) Pick a total number that is the LCM or multiple of LCM
(2) Figure out that 1/5th fraction is the intersection of T & S
The solution by bia cuts a lot of time as opposed to the MGMAT grid. B T W it was not a 2 min Q for me.
Simpler you can cosider this a venn diagram problem, it didnt take me long this way. just followed the arithmetic
let the total no. of appartments be X
The number of apartments that have skylight = (1/8)X
The number of apartments that have terrace = (1/4)X
The number of apartments that have both terrace and skylight = (1/4)X * (1/5)X = (1/20)X
let The number of apartments that dont have bothth terrace and skylight = Y
X = (1/8)X + (1/4)X - (1/20)X + Y
X = (13/40)X + Y
or Y = (27/40)X
let the total no. of appartments be X
The number of apartments that have skylight = (1/8)X
The number of apartments that have terrace = (1/4)X
The number of apartments that have both terrace and skylight = (1/4)X * (1/5)X = (1/20)X
let The number of apartments that dont have bothth terrace and skylight = Y
X = (1/8)X + (1/4)X - (1/20)X + Y
X = (13/40)X + Y
or Y = (27/40)X
Aks
Am I right or is the wording on this question total horse sh%$? "INCLUDING"??? When I read that I was like what the heck??
In a certain apartment complex, 1/4 of the apartments have terraces. If 1/8 of the apartments have skylights, of which 1/5 of those have terraces. what fraction of the apartments have neither terraces nor skylights?
I should file a law suit against Princeton Review for such a terribly worded question. The same should go for ETS. The math portion of the Quant on the GMAT is not a math exam, it is an English exam. ETS contrived the exam this way because had it been a minimally worded exam, with just straight math proof/solving questions, Indian and Chinese students would continually crush US students in this exam and take all the admission. Subversive racism.
"INCLUDING"??"INCLUDING"?? Doesn't that mean "In addition" to the "1/8 of the apartments that have skylights"? So 1/8(# of Apartments)+1/5(# of Terraces). This F*ed up Yo, veiled racism. I am guesing question 31 of the GMAT requires the exam taker to hold his hand to the screen to determine if it is the appropriate right shade to receiving a high score?
In a certain apartment complex, 1/4 of the apartments have terraces. If 1/8 of the apartments have skylights, of which 1/5 of those have terraces. what fraction of the apartments have neither terraces nor skylights?
I should file a law suit against Princeton Review for such a terribly worded question. The same should go for ETS. The math portion of the Quant on the GMAT is not a math exam, it is an English exam. ETS contrived the exam this way because had it been a minimally worded exam, with just straight math proof/solving questions, Indian and Chinese students would continually crush US students in this exam and take all the admission. Subversive racism.
"INCLUDING"??"INCLUDING"?? Doesn't that mean "In addition" to the "1/8 of the apartments that have skylights"? So 1/8(# of Apartments)+1/5(# of Terraces). This F*ed up Yo, veiled racism. I am guesing question 31 of the GMAT requires the exam taker to hold his hand to the screen to determine if it is the appropriate right shade to receiving a high score?
