At a Dog Competition, a Dog is Awarded 10 Points if it Runs Through 4 Pipes, Makes 10 Jumps, and Walks on 2 Beams.

Question: At a dog competition, a dog is awarded 10 points if it runs through 4 pipes, makes 10 jumps, and walks on 2 beams. If Roofy gets 9 points after missing a pipe and Ralph gets 7 points after missing a pipe and a beam, how many points does Butch get if he misses 4 jumps but goes through the rest of the exercises perfectly?

1. 8.2
2. 8.4
3. 8.8
4. 9.0
5. 9.2

“At a dog competition, a dog is awarded 10 points if it runs through 4 pipes, makes 10 jumps, and walks on 2 beams. If Roofy gets 9 points after missing a pipe and Ralph gets 7 points after missing a pipe and a beam, how many points does Butch get if he misses 4 jumps but goes through the rest of the exercises perfectly?”– is a topic of the  GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.0

Answer
Approach Solution 1

Firstly, create the three equations from the data given in the question:

Equation (1): 4P + 10J + 2B = 10
Equation (2): 3P + 10J + 2B = 9
Equation (3): 3P + 10J + 1B = 7
Subtracting equation (2) from equation (1) and equation (3) from equation (1), we will get:

3P + 10J + 2B – (4P + 10J + 2B) = 9 – 10
- P = -1 
P = 1

And
3P + 10J + 1B – (4P + 10J + 2B) = 7 – 10
- P – 1B = -3
- 1 – 1B = -3
- B = -2
B = 2

Therefore, J = 0.2
Butch will get 10 – (0.2 * 4) = 9.2 points

Correct option: E

Approach Solution 2

One pipe missed lead to 9 points
So, 4 pipes are worth 4 points in total
2 beams are worth 4 points as well in total, since missing one beam lead to loss of 2 points.
That’s 8 points so far.
2 points remaining
Consequently, 10 jumps = 2 points
So this means 10 J = 2

J = \(\frac{2}{10}=\frac{1}{5}\)

This is the value of each jump.
Butch only misses 4 jumps, but does the rest of the exercise perfectly.

So, his 8 points are secure. From the 4 jumps he’s missed, his loss in points will be: 4 * \(\frac{1}{5}\) = \(\frac{4}{5}\)

0.80
So, 10 – 0.80 = 9.20 

Correct option: E

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