Tough and Tricky questions: Exponents.

A certain population of bacteria doubles every 10 minutes. If the number of bacteria in the population initially was 10^5, then what was the number in the population 1 hour later?

A) 2(10^5)
B) 6(10^5)
C) (2^6)(10^5)
D) (10^6)(10^5)
E) (10^5)^6

Kudos for a correct solution.

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I did this problem by noticing a pattern. Since the population doubles every 10 minutes, basically all we are doing is doubling our coefficient in front of 10^5. It starts out at (1)10^5 and after 10 minutes it is (2)10^5 and at 20 its (4)10^5. I noticed every 10 minutes we are increasing our power of 2.

An hour is 60 minutes, so the bacteria will double 6 times. This means that our coefficient will end up being 2^6. Looking at the answer choices, choice (C), (2^6)(10^5) is correct.

Present population: 10^5
60 mins will have 6 intervals of 10 mins --> so the population will get doubled 6 times in 1hr --> 2*2*2*2*2*2*10^5 -->2^6*10^5

Illustration:
Present - 10^5
after 10 mins - 2*10^5
after 20 mins - 2(2*10^5) = 2^2*10^5
after 30 mins - 2*(2(2*10^5)) = 2^3*10^5
.
.
.
after 60 mins - 2^6*10^5

Ans. C) (2^6)(10^5)
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Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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