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In 2004, 2,400 condos sold, 15% of the total housing units

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In 2004, 2,400 condos sold, 15% of the total housing units

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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.

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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

OA is B.
We can solve the question with equivalent ratios

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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Post
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

OA is B.
We can also solve this with a little number sense


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

_________________
Brent Hanneson – Creator of GMATPrepNow.com
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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
Of the units sold, non-condos constitute 85% = 85/100 = 17/20.
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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Post
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
Let´s use the "backbone" of our method: connect DATA to FOCUS as soon and as clearly as possible:
\[{\text{DATA}}:\,\,\,\,\,2,400\,\,{\text{condos}}\,\,\,\mathop = \limits^{\left( * \right)} \,\,\,\frac{{15}}{{100}}\,\,\left( {{\text{total}}} \right)\]
\[{\text{FOCUS}}:\,\,\,? = \frac{{85}}{{100}}\left( {{\text{total}}} \right)\]
\[? = \boxed{\frac{{85}}{{15}}} \cdot \underbrace {\frac{{15}}{{100}}\,\,\left( {{\text{total}}} \right)}_{\left( * \right)\,\,\,2400}\,\, = \,\,\,\frac{{17}}{3}\left( {2400} \right) = \underleftrightarrow {100 \cdot \left( {\frac{{17 \cdot 24}}{3}} \right)}\,\, = \,\,13600\]

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

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Post
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
We can create the following equation in which n = the total number of housing units sold in 2004:

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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Scott Woodbury-Stewart Founder and CEO

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