If a and b are Positive Integers and (2a)^b= 2^3, What is the Value GMAT Problem Solving

Question: If a and b are positive integers and (2a)^b= 2^3, what is the value of 2^a∗2^b?

A) 6
B) 8
C) 16
D) 32
E) 64

“If a and b are positive integers and (2a)^b= 2^3, what is the value”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation:
Approach Solution 1:
(2^a)^b= 2^3
2^ab= 2^3
ab=3

ab must be (1)(3) or (3)(1)

2^a*2^b= 2^a+b
2^1+3= 2^4= 16

Correct Answer: C

Approach Solution 2:
(2^a)^b = 2^3
=>2^ab = 2^3
ab = 3
If a = 1 then b = 3 or if a=3 then b=1

2^a*2^b = 2^(a+b)
= 2^4 = 16

Correct Answer: C

Approach Solution 3:
Given:
(2^a)^b= 2^3

Apply the Power of a Power rule to get:

2^ab= 2^3

From this we can conclude that: ab=3

Since a and b are positive integers, we can be certain that one of the values (a or b) is 1, and the other value is 3
This means the SUM of a and b is 4 (1 + 3 = 4)
We want to find the value of 2^a∗2^b

Apply the Product rule to get: 2^a+b
Since we now know the SUM of a and b is 4, we can write:
2^a+b= 2^4= 16

Correct Answer: C

Suggested GMAT Problem Solving Questions

• A Truck Travelling At 70 Kilometres Per Hour Uses 30% More Diesel To GMAT Problem Solving
• If The Area Of A Rectangle Is Equal To The Area Of A Square, Then The GMAT Problem Solving
• The rectangles shown above are similar and the ratio of the area of GMAT Problem Solving
• A School has Set Different Minimum Qualifying Marks in an Exam GMAT Problem Solving
• The Temperature of Delhi and Lucknow were in the Ratio 3:5 in July GMAT Problem Solving
• When a Certain Tree was First Planted, it was 4 feet Tall and the Height GMAT Problem Solving
• When a Number A is Divided by 6, the Remainder is 3 and When Another GMAT Problem Solving
• Which of the Following is the Correct Ordering of 2√13, 4√3, 5√2 and 3√6 ? GMAT Problem Solving
• If the mean of set S does not exceed mean of the subset of set S, which GMAT Problem Solving
• A Milkman Sells Milk after Adding Some Water in it GMAT Problem Solving
• It Was Observed by National Geographic that Equinox Happened GMAT Problem Solving
• Paracelsus University has Two Kinds of Professors, Academic Professors GMAT Problem Solving
• What is the Smallest Prime Factor of 5^8+10^6–50^3? GMAT Problem Solving
• In A Locality, There Are Ten Houses In A Row. On A Particular Night GMAT Problem Solving
• The “Connection” Between Any Two Positive Integers a And b GMAT Problem Solving
• Find the least positive integers which must be added to 15,463 so that the result GMAT Problem Solving
• Mayank Buys Some Candies for $15 a dozen and An Equal Number of Different GMAT Problem Solving
• If John Throws a Coin Until a Series of Three Consecutive Heads GMAT Problem Solving
• In the Diagram Above, ABCD is a Parallelogram and the Areas of Yellow GMAT Problem Solving
• On certain road 10% of the motorists exceed the posted speed limit GMAT Problem Solving