Bacteria population

[LulaBrazilia]

Four hours from now, the population of a colony of bacteria will reach 1.28 x 10^6. If the population of the colony doubles every 4 hours, what was the population 12 hours ago?

A) 6.4 x 10^2

B) 8.0 x 10^4

C) 1.6 x 10^5

D) 3.2 x 10^5

E) 8.0 x 10^6

[Patrick_GMATFix]

This solution is taken from the GMATFix App. My signature below has more info.



-Patrick

[Brent@GMATPrepNow]

Four hours from now, the population of a colony of bacteria will reach 1.28 x 10^6. If the population of the colony doubles every 4 hours, what was the population 12 hours ago?

A) 6.4 x 10^2
B) 8.0 x 10^4
C) 1.6 x 10^5
D) 3.2 x 10^5
E) 8.0 x 10^6

Let's work backwards.

Population 4 hours in future: 1.28 x 10^6
Population now: 0.64 x 10^6 (half the population 4 hours in future)
Population 4 hours ago: 0.32 x 10^6 (half the current population)
Population 8 hours ago: 0.16 x 10^6 (half the population 4 hours ago)
Population 12 hours ago: 0.08 x 10^6 (half the population 8 hours ago)

Now check the answer choices. Looks like the answer is either B or E
Answer choice E definitely doesn't match, so the correct answer must be B

For any doubters out there, notice that 0.08 x 10^6 = (8.0) x (10^-2) x 10^6
= [spoiler]8.0 x 10^4 = B[/spoiler]

Cheers,
Brent

[theCodeToGMAT]

Now - 12 = (1.28 x 10^6)/16 == .08 x 10^6

Now - 8 = (1.28 x 10^6)/8

Now - 4 = (1.28 x 10^6)/4

Now = (1.28 x 10^6)/2

4hrs = 1.28 x 10^6

[spoiler]{B}[/spoiler]

[Jeff@TargetTestPrep]

Four hours from now, the population of a colony of bacteria will reach 1.28 x 10^6. If the population of the colony doubles every 4 hours, what was the population 12 hours ago?

A) 6.4 x 10^2

B) 8.0 x 10^4

C) 1.6 x 10^5

D) 3.2 x 10^5

E) 8.0 x 10^6

Since the population doubles every 4 hours and the population will be 1.28 x 10^6 four hours from now, the current population must be half of 1.28 x 10^6, or ½(1.28 x 10^6) = 0.64 x 10^6.

Thus:

4 hours ago, the population was half the current population: ½(0.64 x 10^6) = 0.32 x 10^6.

8 hours ago, the population was half the population 4 hours ago: ½(0.32 x 10^6) = 0.16 x 10^6.

Finally, 12 hours ago the population was half the population 8 hours ago: ½(0.16 x 10^6) = 0.08 x 10^6 = 8 x 10^-2 x 10^6 = 8 x 10^4.

Answer: B

[Brent@GMATPrepNow]

Four hours from now, the population of a colony of bacteria will reach 1.28 x 10^6. If the population of the colony doubles every 4 hours, what was the population 12 hours ago?

A) 6.4 x 10^2

B) 8.0 x 10^4

C) 1.6 x 10^5

D) 3.2 x 10^5

E) 8.0 x 10^6

Let's work backwards.

Population 4 hours in future: 1.28 x 10^6
Population now: 0.64 x 10^6 (half the population 4 hours in future)
Population 4 hours ago: 0.32 x 10^6 (half the current population)
Population 8 hours ago: 0.16 x 10^6 (half the population 4 hours ago)
Population 12 hours ago: 0.08 x 10^6 (half the population 8 hours ago)

Now check the answer choices.
Only answer choices B and E have the same format with 8 times some power of 10
Answer choice E definitely doesn't match, so the correct answer must be B

For any doubters out there, notice that:
0.08 x 10^6 = (8.0) x (10^-2) x 10^6
= 8.0 x 10^4

Answer: B

Cheers,
Brent