Magoosh
In 2004, 2,400 condos sold, 15% of the total housing units sold that year. How many units sold in 2004 were not condos?
A. 16,000
B. 13,600
C. 12,400
D. 11, 200
E. 8,600
OA is B.
In 2004, 2,400 condos sold, 15% of the total housing units
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We can solve the question with equivalent ratiosAAPL wrote:Magoosh
In 2004, 2,400 condos sold, 15% of the total housing units sold that year. How many units sold in 2004 were not condos?
A. 16,000
B. 13,600
C. 12,400
D. 11, 200
E. 8,600
OA is B.
If 15% of the units sold WERE condos, then 85% of the units sold new NOT condos.
So we want to determine the number of sold units that represent 85% of all units sold
We'll use the ratio: (number of units sold)/(percent of units sold)
Let x = the number of NON-CONDO units sold that represent 85% of all units sold
We get: (2400)/(15) = (x)/(85)
Cross multiply to get: (15)(x) = (2400)(85)
Divide both sides by 15 to get: x = (2400)(85)/(15)
Evaluate: 13,600
Answer: B
Cheers,
Brent
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We can also solve this with a little number senseAAPL wrote:Magoosh
In 2004, 2,400 condos sold, 15% of the total housing units sold that year. How many units sold in 2004 were not condos?
A. 16,000
B. 13,600
C. 12,400
D. 11, 200
E. 8,600
OA is B.
If 15% of the units sold WERE condos, then 85% of the units sold new NOT condos.
GIVEN: 2,400 represents 15% of the total housing units sold that year
So, 4,800 must represent 30% of the total housing units sold that year
And 9,600 must represent 60% of the total housing units sold that year
And 14,400 must represent 90% of the total housing units sold that year
Oops, we went too far. We need to subtract 5% worth of housing units to get down to the desired 85%
If 2,400 represents 15% of the total housing units sold that year. . .
Then 800 must represent 5% of the total housing units sold that year
So, 85% of the housing units sold = 14,400 - 800 = 13,600
Answer: B
Cheers,
Brent
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Of the units sold, non-condos constitute 85% = 85/100 = 17/20.AAPL wrote:Magoosh
In 2004, 2,400 condos sold, 15% of the total housing units sold that year. How many units sold in 2004 were not condos?
A. 16,000
B. 13,600
C. 12,400
D. 11, 200
E. 8,600
Implication:
Of every 20 units sold, 17 are non-condos, with the result that the number of non-condos must be a multiple of 17.
A. 16000
B. 13600
C. 12400
D. 11200
E. 8600
Only the portion in green is a multiple of 17:
136/17 = 8.
The correct answer is B.
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Let´s use the "backbone" of our method: connect DATA to FOCUS as soon and as clearly as possible:AAPL wrote:Magoosh
In 2004, 2,400 condos sold, 15% of the total housing units sold that year. How many units sold in 2004 were not condos?
A. 16,000
B. 13,600
C. 12,400
D. 11, 200
E. 8,600
\[{\text{DATA}}:\,\,\,\,\,2,400\,\,{\text{condos}}\,\,\,\mathop = \limits^{\left( * \right)} \,\,\,\frac{{15}}{{100}}\,\,\left( {{\text{total}}} \right)\]
\[{\text{FOCUS}}:\,\,\,? = \frac{{85}}{{100}}\left( {{\text{total}}} \right)\]
\[? = \boxed{\frac{{85}}{{15}}} \cdot \underbrace {\frac{{15}}{{100}}\,\,\left( {{\text{total}}} \right)}_{\left( * \right)\,\,\,2400}\,\, = \,\,\,\frac{{17}}{3}\left( {2400} \right) = \underleftrightarrow {100 \cdot \left( {\frac{{17 \cdot 24}}{3}} \right)}\,\, = \,\,13600\]
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
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We can create the following equation in which n = the total number of housing units sold in 2004:AAPL wrote:Magoosh
In 2004, 2,400 condos sold, 15% of the total housing units sold that year. How many units sold in 2004 were not condos?
A. 16,000
B. 13,600
C. 12,400
D. 11, 200
E. 8,600
2,400 = 0.15n
2,400/0.15 = n
16,000 = n
Thus, the number of housing units sold that were not condos was 16,000 - 2,400 = 13,600.
Alternate Solution:
We can set up a ratio: if 15% is 2,400, then 85% is x, as follows:
0.15/2400 = 0.85/x
0.15x = 2400 * 0.85
x = (2400 * 0.85)/0.15
x = 13,600
Answer: B
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