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Tom painted 1/3 of a wall red, 1/5 of the wall blue and the

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by Max@Math Revolution » Sun Jul 14, 2019 11:14 pm

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Difficulty—

[GMAT math practice question]

Tom painted 1/3 of a wall red, 1/5 of the wall blue and the remaining 238 m^2 black. What is the area of the wall in m^2?

A. 490
B. 500
C. 510
D. 520
E. 530
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by GMATGuruNY » Mon Jul 15, 2019 5:04 am
Max@Math Revolution wrote:[GMAT math practice question]

Tom painted 1/3 of a wall red, 1/5 of the wall blue and the remaining 238 m^2 black. What is the area of the wall in m^2?

A. 490
B. 500
C. 510
D. 520
E. 530
We can PLUG IN THE ANSWERS, which represent the total area.
When the correct answer is plugged in, the area painted black = 238.

Since 1/3 of the wall is painted red, it is almost certain that correct answer is a multiple of 3.
For an integer to be a multiple of 3, its digit sum must be a multiple of 3.
Only C has a digit sum divisible by 3:
5+1+0 = 6

C: 510
Area painted red = (1/3)(510) = 170
Area painted blue = (1/5)(510) = 102
Area painted black = 510 - (170+102) = 510 - 272 = 238
Success!

The correct answer is C.
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by swerve » Tue Jul 16, 2019 9:47 am
Let the area of the entire wall be 15x units (15 is the LCM of the denominators, 3 and 5).

The area of the wall that is painted red \(= \frac{1}{3}\cdot 15x = 5x\).

The area of the wall that is painted blue \(= \frac{1}{5}\cdot 15x = 3x\).

The remaining part of the wall \(= 7x\). So, \(7x = 238\) square metres. Solving this, we get \(x = 34\).

So the area of the wall \(= 15 \cdot 34 = 510\) square meters.

The correct answer option is __C__.
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by Max@Math Revolution » Wed Jul 17, 2019 12:18 am
=>

Using the Ivy Approach, we assume 15w is the area of the wall. We have chosen 15 since it is the lcm of the denominators, 3 and 5. So, 15w/3 = 5w is the area painted red, and 15w/5 = 3w is the area painted blue.
The area painted black is given by the equation
15w-(15w·1/3)-(15w·1/5)=15w-5w-3w=7w=238.

Solving for w yields w=34. So, the area of the whole wall is 15w=15·34=510 m^2.

Therefore, C is the answer.
Answer: C
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