Problem Solving

received a pm.

"galaxian" has nailed it; there's really not much more to say. nicely done.

jainrahul1985 wrote: ↑

Sun Jul 24, 2011 5:54 am

Amount indicated by resident | Number of Residents
300 | 10
100 | 20
50 | 30
10 | 20


The table shows the number of residents in a certain development who are willing to contribute to build a swimming pool, provided the required contribution does not exceed the amount indicated by the resident. The following three amounts are being considered as the required contribution. Which would ensure that more than half of the residents contribute to build the pool?

I) $33
II) $48
III)$55

(A) None
(B) I only
(C) II only
(D) I and II only
(E) I, II, and III

OA D

Before we try answering the question, let's first make sure we understand what the table is telling us.

The TOP row tells us that 10 residents are willing to pay up to $300 each.
The SECOND row tells us that 20 residents are willing to pay up to $100 each.
The THIRD row tells us that 30 residents are willing to pay up to $50 each.
The BOTTOM row tells us that 20 residents are willing to pay up to $10 each.
TOTAL number of residents = 80

Now let's examine the three statements...

Ⅰ. $33
10 residents are willing to pay $33 each.
20 residents are willing to pay $33 each.
30 residents are willing to pay $33 each.
10 + 20 + 30 = 60
So, 60 of the 80 residents are willing to pay $33 each.
In other words, more than half of the residents are willing to pay $33 each.

Ⅱ. $48
10 residents are willing to pay $48 each.
20 residents are willing to pay $48 each.
30 residents are willing to pay $48 each.
10 + 20 + 30 = 60
So, more than half of the residents are willing to pay $48 each.


Ⅲ. $55
10 residents are willing to pay $55 each.
20 residents are willing to pay $55 each.
10 + 20 = 30
So, 30 of the 80 residents are willing to pay $55 each.
In other words, LESS than half of the residents are willing to pay $55 each.

Answer: D

Cheers,
Brent

jainrahul1985 wrote: ↑

Sun Jul 24, 2011 5:54 am

Amount indicated by resident | Number of Residents
300 | 10
100 | 20
50 | 30
10 | 20


The table shows the number of residents in a certain development who are willing to contribute to build a swimming pool, provided the required contribution does not exceed the amount indicated by the resident. The following three amounts are being considered as the required contribution. Which would ensure that more than half of the residents contribute to build the pool?

I) $33
II) $48
III)$55

(A) None
(B) I only
(C) II only
(D) I and II only
(E) I, II, and III

OA D

The total number of residents is 10 + 20 + 30 + 20 = 80.

If the required contribution is $33, then 10 + 20 + 30 = 60 residents would contribute, which is more than half of the residents.

If the required contribution is $44, then again 10 + 20 + 30 = 60 residents would contribute, which is more than half of the residents.

If the required contribution is $55, then 10 + 20 = 30 residents would contribute, which is less than half the residents.

Answer: D