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Bunuel
In 1979 approximately 1/3 of the 37.3 million airline passengers traveling to or from the United States used Kennedy Airport. If the number of such passengers that used Miami Airport was 1/2 the number that used Kennedy Airport and 4 times the number that used Logan Airport, approximately how many millions of these passengers used Logan Airport that year?

(A) 18.6
(B) 9.3
(C) 6.2
(D) 3.1
(E) 1.6

This question illustrates the importance of ALWAYS checking the answer choices BEFORE getting bogged down with time-consuming calculations.
For more on this important strategy, you can watch the video below

Since the answer choices are VERY spread apart, we can be quite aggressive in our rounding and estimation.

In 1979 approximately 1/3 of the 37.3 million airline passengers traveling to or from the United States used Kennedy Airport.
Let's say that "In 1979 approximately 1/3 of the 36 million airline passengers traveling to or from the United States used Kennedy Airport. "
1/3 of 36 = 12
So, 12 million passengers used Kennedy Airport

The number of such passengers that used Miami Airport was 1/2 the number that used Kennedy Airport
12 million passengers used Kennedy Airport
1/2 of 12 million = 6 million
So, 6 million passengers used Miami Airport

The number of such passengers that used Miami Airport was 4 times the number that used Logan Airport
In other words, the number of such passengers that used Logan Airport was 1/4 the number that used Miami Airport
1/4 of 6 million = 1.5 million

So, 1.5 million passengers used Logan Airport

Check the answer choices . . . only answer choice E is close to 1.5

Answer: E

RELATED VIDEO FROM OUR COURSE

Hi Brent,

In general when we have statements like 'Miami Airport was 1/2 the number that used Kennedy Airport and 4 times the number that used Logan Airport', we interpret them as \(M = \frac{1}{2}K + 4L\)

Any specific reason for spliting into two equations here?

Warm Regards,
Pritishd
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Bunuel
In 1979 approximately 1/3 of the 37.3 million airline passengers traveling to or from the United States used Kennedy Airport. If the number of such passengers that used Miami Airport was 1/2 the number that used Kennedy Airport and 4 times the number that used Logan Airport, approximately how many millions of these passengers used Logan Airport that year?

(A) 18.6
(B) 9.3
(C) 6.2
(D) 3.1
(E) 1.6

Lets not do calculations rather look at the kind of formula that emerges finally- \frac{37.3}{4*3*2}
Since, 4*3*2 = 24, therefore the division would result in 1 < number < 2, hence answer E
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Pritishd


Hi Brent,

In general when we have statements like 'Miami Airport was 1/2 the number that used Kennedy Airport and 4 times the number that used Logan Airport', we interpret them as \(M = \frac{1}{2}K + 4L\)

Any specific reason for spliting into two equations here?

Warm Regards,
Pritishd

EDIT: Someone just pointed out that my earlier response was incorrect. I should have read it better.
Here's my new response to the above question:

I think you may have misinterpreted information in the question.

It tells us that: the number of such passengers that used Miami Airport was 1/2 the number that used Kennedy Airport and 4 times the number that used Logan Airport
In other words: M = 0.5K and M = 4L

I believe you are reading the information as: the number of such passengers that used Miami Airport was 1/2 the number that used Kennedy Airport PLUS 4 times the number that used Logan Airport
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Hi BrentGMATPrepNow, If I use M=1/2K+4L
M = 1/2 (12.4) + 4L
M = 6 + 4L or L = M-6/4
Not sure how to proceed from here in order to get 1/4 of 6 million = 1.5 million or have I missed something here? Thanks Brent.
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Hi BrentGMATPrepNow, If I use M=1/2K+4L
M = 1/2 (12.4) + 4L
M = 6 + 4L or L = M-6/4
Not sure how to proceed from here in order to get 1/4 of 6 million = 1.5 million or have I missed something here? Thanks Brent.

I think you may have misinterpreted information in the question.

It tells us that: the number of such passengers that used Miami Airport was 1/2 the number that used Kennedy Airport and 4 times the number that used Logan Airport
In other words: M = 0.5K and M = 4L

I believe you are reading the information as: the number of such passengers that used Miami Airport was 1/2 the number that used Kennedy Airport PLUS 4 times the number that used Logan Airport
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Pritishd


Hi Brent,

In general when we have statements like 'Miami Airport was 1/2 the number that used Kennedy Airport and 4 times the number that used Logan Airport', we interpret them as \(M = \frac{1}{2}K + 4L\)

Any specific reason for spliting into two equations here?

Warm Regards,
Pritishd

I broke it into steps to make sure I didn't lose anyone.
That said, I broke that step into pieces (as you probably did).
When you read "Miami Airport was 1/2 the number that used Kennedy Airport," you got \(M = \frac{1}{2}K\)
When you continued reading "....and 4 times the number that used Logan Airport" you got \(M = \frac{1}{2}K + 4L\)

Same idea. Different execution.

Cheers,
Brent

Thanks Brent BrentGMATPrepNow . so M = 0.5K and M = 4L is not equal to \(M = \frac{1}{2}K + 4L\) ?
I followed calculation from this post therefore got stuck in M = 1/2 (12.4) + 4L
M = 6 + 4L or L = M-6/4 ?

So this is not correct then?
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Thanks Brent BrentGMATPrepNow . so M = 0.5K and M = 4L is not equal to \(M = \frac{1}{2}K + 4L\) ?
I followed calculation from this post therefore got stuck in M = 1/2 (12.4) + 4L
M = 6 + 4L or L = M-6/4 ?

So this is not correct then?

Sorry, Kimberly77.
One of my earlier responses to a student's question was incorrect. Please see above.

The answer to your question is no, the pair of equations \(M = 0.5K\) and \(M = 4L\) cannot be combined to get \(M = \frac{1}{2}K + 4L\)

Consider these values: M = 20, K = 40 and L = 5
Notice that these values satisfy the equations \(M = 0.5K\) and \(M = 4L\)

If we plug the same values into the equation \(M = \frac{1}{2}K + 4L\), we get: \(20 = (\frac{1}{2})40 + 4(5)\)
Simplify to get: \(20 = 20 + 20\), which is not true.
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Thanks Brent BrentGMATPrepNow . so M = 0.5K and M = 4L is not equal to \(M = \frac{1}{2}K + 4L\) ?
I followed calculation from this post therefore got stuck in M = 1/2 (12.4) + 4L
M = 6 + 4L or L = M-6/4 ?

So this is not correct then?

Sorry, Kimberly77.
One of my earlier responses to a student's question was incorrect. Please see above.

The answer to your question is no, the pair of equations \(M = 0.5K\) and \(M = 4L\) cannot be combined to get \(M = \frac{1}{2}K + 4L\)

Consider these values: M = 20, K = 40 and L = 5
Notice that these values satisfy the equations \(M = 0.5K\) and \(M = 4L\)

If we plug the same values into the equation \(M = \frac{1}{2}K + 4L\), we get: \(20 = (\frac{1}{2})40 + 4(5)\)
Simplify to get: \(20 = 20 + 20\), which is not true.

Brilliant thanks BrentGMATPrepNow. Crystal clear now.
So "and" & "Plus" do not mean the same thing in Maths generally?
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Brilliant thanks BrentGMATPrepNow. Crystal clear now.
So "and" & "Plus" do not mean the same thing in Maths generally?

Tricky question!
It really depends on the context.
If I say I have 3 cats and 5 dogs, and then the total number of pets I have = 3 + 5
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Kimberly77


Brilliant thanks BrentGMATPrepNow. Crystal clear now.
So "and" & "Plus" do not mean the same thing in Maths generally?

Tricky question!
It really depends on the context.
If I say I have 3 cats and 5 dogs, and then the total number of pets I have = 3 + 5


Noted thanks BrentGMATPrepNow :please: :)
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