three tough DS questions

[EddieU]

Hope someone can help me with these questions:

Q1:
The circular base of an above-ground swimming pool lies in a level yard and just touches two straight sides of a fence at points A and B , as shown in the figure above. Point C is on the ground where the two sides of the fence meet. How far from the center of the pool's base is point A ?
(1) The base has area 250 square feet.
(2) The center of the base is 20 feet from point C .




Q2:
After winning 50 percent of the first 20 games it played, Team A won all of the remaining games it played. What was the total number of games that Team A won?
(1) Team A played 25 games altogether.
(2) Team A won 60 percent of all the games it played.

Comment: It's obvious why the first hint is sufficient, but how come the second is sufficient too?


Q3:
Is 5k less than 1,000?
(1) 5k+1 >3,000
(2) 5k−1 = 5k −500

Comment: again, the second hint that causes me a headache...

Correct answers Q1 A. Q2 D. Q3 B.

Thank you in advance for your supprt

[Anurag@Gurome]

Question Number 1:

The circular base of an above-ground swimming pool lies in a level yard and just touches two straight sides of a fence at points A and B , as shown in the figure above. Point C is on the ground where the two sides of the fence meet. How far from the center of the pool's base is point A ?
(1) The base has area 250 square feet.
(2) The center of the base is 20 feet from point C

Refer to the following figure,



We can see that the distance of the center of the pool's base, O and the point A is nothing but the radius of the circular base. Hence, we have to find find the radius of the base.

Statement 1: We know the area of the circular base.
Hence, we can determine the radius of the base.

Sufficient

Statement 2: OC = 20
This doesn't tell us anything about the radius.

Not sufficient

The correct answer is A.

[Anurag@Gurome]

Question Number 2:

After winning 50 percent of the first 20 games it played, Team A won all of the remaining games it played. What was the total number of games that Team A won?
(1) Team A played 25 games altogether.
(2) Team A won 60 percent of all the games it played.

Say, number of remaining games was n.
Hence, the team has won (50% of 20 + n) = (n + 10) games
Therefore, we need to find n.

Statement 1: (20 + n) = 25 --> n = 5

Sufficient

Statement 2: (n + 10) = 60% of (n + 20) = 0.6*(n + 20)
We can solve for n from this equation as follows,
--> (n + 10) = (0.6n + 12)
--> 0.4n = 2
--> n = 5

Sufficient

The correct answer is D.

[Anurag@Gurome]

Question Number 3:

Is 5k less than 1,000?
(1) 5k+1 >3,000
(2) 5k−1 = 5k −500

I think all the 5k's are actually 5^k.

Statement 1: 5^(k + 1) > 3000 --> (5^k)*5 > 3000 --> 5^k > 600
Now 5^k can be more than or less than 1000.

Not sufficient

Statement 2: 5^(k - 1) = 5^k - 500
--> 5^k/5 = 5^k - 500
--> 5^k = 5*5^k - 2500
--> 4*5^k = 2500
--> 5^k = 625 < 1000

Sufficient

The correct answer is B.

Note : We don't have to calculate the value of 5^k for statement 2. From the statement we can see that a definite value of 5^k can obtained. Hence, we can tell whether that value will be less than 1000 or not.

[Anurag@Gurome]

How did you get from

--> 5^k = 5*5^k - 2500
--> 4*5^k = 2500
--> 5^k = 625 < 1000

What is the operation to multiply by 4?

--> 5^k = 5*(5^k) - 2500
--> 5^k - 5*(5^k) = -2500
--> 5*(5^k) - 5^k = 2500
--> (5 - 1)*(5^k) = 2500
--> 4*(5^k) = 2500
--> 5^k = 625 < 1000

Hope it is clear now.