What number is 108 more than two-thirds of itself?
A. 72
B. 144
C. 162
D. 216
E. 324
E
OG What number is 108 more
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We can PLUG IN THE ANSWERS.AbeNeedsAnswers wrote:What number is 108 more than two-thirds of itself?
A. 72
B. 144
C. 162
D. 216
E. 324
When 108 is added to 2/3 of the correct answer choice, the resulting sum will be equal to the answer choice.
B: 144
(2/3)(144) = (2)(48) = 96.
96 + 108 = 204.
Here, the resulting sum is 60 greater than the answer choice.
Eliminate B.
D: 216
(2/3)(216) = (2)(72) = 144.
144 + 108 = 252.
Here, the resulting sum is 36 greater than the answer choice.
Eliminate D.
Notice the PATTERN implied by the portions in blue:
As the answer choice gets BIGGER, the resulting sum draws CLOSER to the answer choice.
Thus, for the resulting sum to be EQUAL to the answer choice, a value greater than D is needed,
The correct answer is E.
Algebraic solution:
Since adding 108 to 2/3 of the number must yield the number itself, we get:
108 + (2/3)x = x
108 = (1/3)x
324 = x.
The correct answer is E.
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Hi AbeNeedsAnswers,
This question can be solved rather easily by TESTing THE ANSWERS (the approach that Mitch used). It can also be solved algebraically.
We're asked to find a number that is 108 more than 2/3 of itself...
X = 108 + (2/3)(X)
Now we can combine like terms and simplify:
(1/3)X = 108
X = 324
Final Answer: E
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Rich
This question can be solved rather easily by TESTing THE ANSWERS (the approach that Mitch used). It can also be solved algebraically.
We're asked to find a number that is 108 more than 2/3 of itself...
X = 108 + (2/3)(X)
Now we can combine like terms and simplify:
(1/3)X = 108
X = 324
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
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We can let the number = n and create the following equation:AbeNeedsAnswers wrote:What number is 108 more than two-thirds of itself?
A. 72
B. 144
C. 162
D. 216
E. 324
108 + (2/3)n = n
Multiplying the entire equation by 3, we have:
324 + 2n = 3n
324 = n
Answer: E
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Let x = the numberAbeNeedsAnswers wrote:What number is 108 more than two-thirds of itself?
A. 72
B. 144
C. 162
D. 216
E. 324
E
We're told that the number is 108 more than two-thirds of itself.
In other words, x = (2/3)x + 108
Or we can write: x = (2x)/3 + 108
Eliminate the fraction by multiplying both sides by 3 to get: 3x = 2x + 324
Solve: x = 324
Answer: E
Cheers,
Brent