Problem Solving

LUANDATO wrote:A housing subdivision contains only two types of homes: ranch-style homes and townhomes. There are twice as many townhomes as ranch-style homes. There are 3 times as many townhomes with pools than without pools. What is the probability that a home selected at random from the subdivision will be a townhome with a pool?

(A) 1/6
(B) 1/5
(C) 1/4
(D) 1/3
(E) 1/2

The OA is E.

Can any expert explain this PS question please? Thanks.

Say the number of townhomes without pools = x, thus, the number of townhomes with pools = 3x;

Thus, the total number of townhomes = x + 3x = 4x

=> the number of ranch-style homes = 4x/2 = 2x

=> Total number of homes in the subdivision = 4x + 2x = 6x

The probability that a home selected at random from the subdivision will be a townhome with a pool

= (Number of townhomes with pools) / (Total number of homes in the subdivision) = 3x/6x = 1/2

The correct answer: E

Hope this helps!

-Jay

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BTGmoderatorLU wrote:A housing subdivision contains only two types of homes: ranch-style homes and townhomes. There are twice as many townhomes as ranch-style homes. There are 3 times as many townhomes with pools than without pools. What is the probability that a home selected at random from the subdivision will be a townhome with a pool?

(A) 1/6
(B) 1/5
(C) 1/4
(D) 1/3
(E) 1/2

The OA is E.

Can any expert explain this PS question please? Thanks.

If we let the total number of homes = 12, then 4 are ranch-style homes, and 8 are townhomes; 6 townhomes have pools, and 2 do not.

Thus, P(town home with a pool) = 6/12 = 1/2.

Answer: E

Hi All,

We're told that a housing subdivision contains only TWO types of homes: ranch-style homes and townhomes. There are TWICE as many townhomes as ranch-style homes. There are 3 times as many townhomes with pools as without pools. We're asked for the probability that a home selected at random from the subdivision will be a townhome WITH a pool. This question can be solved in a couple of different ways, including by TESTing VALUES.

Since there are twice as many townhomes as ranch-style homes, the number of townhomes MUST be a multiple of 2...
and since there are 3 times as many townhomes with pools as without pools, the number of townhomes MUST be a multiple of 4...

IF.....
there are 4 total townhomes (3 with pools and 1 without a pool)....
then there are 2 ranch-style homes
Total homes = 4+2 = 6

The probability of selecting a townhome with a pool is 3/6 = 1/2

Final Answer: E

GMAT assassins aren't born, they're made,
Rich