[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
Tom painted 1/3 of a wall red, 1/5 of the wall blue and the
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- Max@Math Revolution
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We can PLUG IN THE ANSWERS, which represent the total area.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
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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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__.
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__.
- Max@Math Revolution
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=>
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
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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