Bonnie Can Paint a Stolen Car in x hours, and Clyde Can Paint GMAT Data Sufficiency

bySayantani Barman Experta en el extranjero

Question: Bonnie can paint a stolen car in x hours, and Clyde can paint the same car in y hours. They start working simultaneously and independently at their respective constant rate at 9:45 am. If both x and y are odd integers, is x = y?

\(x^2+y^2<12\)
Bonnie and Clyde complete the painting of the car at 10:30 am

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.

Solution and Explanation

Approach Solution (1):

Given:

Bonnie takes x hours to do a job
Clyde takes y hours to do the same job
Both start independent at the same time- 9:45 am
x and y are odd integer

To find: x = y?

S1: \(x^2+y^2<12\)

Since we already know that x and y are odd integers, there’s not much left to check for in the above condition and since adding two squares will very soon pass such a small number as 12, we can do the manual work here- x = 1; y = 1: Yes ( both equal and sum of squares less than 12)
x = 1; y = 3: No (both unequal and still the sum of squares less than 12)
Hence not sufficient

S2: Bonnie and Clyde complete the painting of the car at 10: 30 am.
Quite straightforward

Basically, they started at the same time they took was same- x = y
Hence sufficient

Correct Option: B

Approach Solution (2):

Given that both completed the work in \(\frac{3}{4}\)hours, we can write it as

\(\frac{1}{x}+\frac{1}{y}=\frac{1}{\frac{3}{4}}....(A)\)

Let’s assume x = y …(B)

Using (A) and (B), we get \(x=\frac{3}{2}\)

However, from the question stem, x is an odd integer
Therefore, our assumption x = y is incorrect

Correct Option: B

Approach Solution (3):

Bonnie and Clyde, when working together, complete the painting of the car in \(\frac{xy}{x+y}\)hours (sum of the rates equal to the combined rate or reciprocal of total time: \(\frac{1}{x}+\frac{1}{y}=\frac{1}{T}\). From that we can get that \(T=\frac{xy}{x+y}\)).

Now, if x = y, then the total time would be: \(\frac{x^2}{2x}=\frac{x}{2}\), since x is odd, then this time would be \(\frac{odd}{2}\): 0.5 hours, 1.5 hours, 2.5 hours, …

(1)\(x^2+y^2<12\). It is possible that x and y are odd and equal to each other if x = y = 1, but it’s also possible that x = 1 and y = 3

Not sufficient

(2) Bonnie and Clyde complete the painting of the car at 10:30 am. They complete the job in \(\frac{3}{4}\)of an hour (45 minutes), since it’s not \(\frac{odd}{2}\) then x and y are not equal

Sufficient

Correct Option: B

“Bonnie can paint a stolen car in x hours, and Clyde can paint the same car in y hours. They start working simultaneously and independently at their respective constant rate at 9:45 am. If both x and y are odd integers, is x = y?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

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Bonnie Can Paint a Stolen Car in x hours, and Clyde Can Paint GMAT Data Sufficiency

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