To find the fraction of people earning more than 40K

[gmattesttaker2]

Hello,

Can you please tell me if my solution is correct:

What fraction of the people who attended a conference had an income of more than
$40,000 a year?

(1) 20% of the people at the conference had an income which was more than or equal to
$40,000 a year.
(2) 5% of the people at the conference had an income of $40,000 a year.

OA: C


I was trying to solve this as follows:

Since the question is asking for a faction, let the total number of people at the conference be 100.

So we need to find the number of people who have an income of more than $40,000

1) 20 people have an income greater than or equal to 40K - in-suff.
2) 5 people have an income of 40K - in-suff.

1 and 2: 15 people have an income greater than 40K.

I was wondering if this solution is correct?

Thanks,
Sri

[Brent@GMATPrepNow]

Hello,

Can you please tell me if my solution is correct:

What fraction of the people who attended a conference had an income of more than $40,000 a year?

(1) 20% of the people at the conference had an income which was more than or equal to $40,000 a year.
(2) 5% of the people at the conference had an income of $40,000 a year.

OA: C


I was trying to solve this as follows:

Since the question is asking for a faction, let the total number of people at the conference be 100.

So we need to find the number of people who have an income of more than $40,000

1) 20 people have an income greater than or equal to 40K - in-suff.
2) 5 people have an income of 40K - in-suff.

1 and 2: 15 people have an income greater than 40K.

I was wondering if this solution is correct?

Thanks,
Sri

Your solution is perfect, Sri.
The important part here is to recognize that the question involves the fraction of attendees who earn MORE THAN $40,000.
Statement 1 tells us the percent who earn a salary that is either MORE THAN or EQUAL TO $40,000
Statement 2 tells us the percent who earn a salary that is EQUAL TO $40,000

So, as you pointed out, we need both statements (C)

Cheers,
Brent

[Matt@VeritasPrep]

That's a great approach!

Another way to set it up:

Suppose that there are x people making more than $40,000, y people making exactly $40,000, and z people making less than $40,000. We want x/(x+y+z), or the fraction of the total making MORE than $40,000.

S1 tells us that (x+y)/(x+y+z) = 1/5. Insufficient, because we can't eliminate y.
S2 tells us that y/(x+y+z) = 1/20. Insufficient, because we can't isolate x.

Together, however, we have

(x+y)/(x+y+z) - y/(x+y+z) = x/(x+y+z)

Or (1/5) - (1/20) = the fraction we want. Success!