Question: What is the greatest positive integer n such that 2^n is a factor of 12^10?
A) 10
B) 12
C) 16
D) 20
E) 60
Correct Answer: D
Solution and Explanation:
Approach Solution 1:
It has asked to find out the greatest positive integer n such that 2^n is a factor of 12 ^ 10.
Exponent rules and the proper way to "rewrite" a number raised to a power are key to answering this query.
12 = (2)(2)(3)
12^2 = (2^2)(2^2)(3^2) = (2^4)(3^2)
12^3 = (2^3)(2^3)(3^3) = (2^6)(3^3)
You should be able to rewrite 12 ^ 10 once you recognize this pattern.
12^10 = (2^10)(2^10)(3^10) = (2^20)(3^10)
Therefore, 20 is the biggest "power of 2," which is a factor of 12 ^ 10.
D is the correct answer.
Approach Solution 2:
It has asked to find out the greatest positive integer n such that 2^n is a factor of 12 ^ 10.
We have to factorize the number into prime numbers to find the answer.
12^10=(2^2∗3)^10=2^20∗3^10
The greatest value of n such that 2^n is a factor of 12^10 is 20.
These are the more common and slightly more complicated factorial questions. What is the biggest positive number n, for instance, such that 2^n is a factor of 12!
D is the correct answer.
“What is greatest positive integer n such that 2^n is a factor of 12^10?" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.
To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses.
Suggested GMAT Problem Solving Samples
- The income of a broker remains unchanged though the rate of commission is increased GMAT Problem Solving
- Curly Brackets {} Around the Last Digits of a Decimal Fraction Signify GMAT Problem Solving
- For the infinite sequence a1, a2, a3, ... an, an+1, an=3(an−1) for all GMAT Problem Solving
- The quantities S and T are positive and are related by the equation GMAT Problem Solving
- A child paints the six faces of a cube with six different GMAT Problem Solving
- In an opera theater. there are 300 seats available GMAT Problem Solving
- At the Rate of m Meters Per s Seconds, How Many Meters Does a Cyclist GMAT Problem Solving
- NASA Received Three Messages in a Strange Language From a Distant Planet GMAT Problem Solving
- Two Cyclists Start From the Same Place to Ride in the Same Direction GMAT Problem Solving
- A Sphere is Inscribed in a Cube with an Edge of 10. What is GMAT Problem Solving
- Mike, Tom, and Walt are working as sales agents for an insurance company GMAT Problem Solving
- A Commonwealth condominium complex has k apartments, n of which are rented at s dollars a month, providing total monthly revenue of p dollars GMAT Problem Solving
- The Figure Below Shows a Square Inscribed in a Circle with the Radius of√6. What is the Area of the Shaded Region? GMAT Problem Solving
- What is the value of k if the sum of consecutive odd integers from 1 to k equals 441? GMAT Problem Solving
- A circle with a radius R is inscribed into a square with a side K GMAT Problem Solving
- Machine A can do a certain job in 12 days working 2 full shifts while Machine B can do the same job in 15 days working 2 full shifts GMAT Problem Solving
- The square of \(5^\sqrt2)\ =? GMAT Problem Solving
- The population of the bacteria colony doubles every day. If it was started 9 days ago with 2 bacteria and each bacteria lives for 12 days, how large is the colony today? GMAT Problem Solving
- If t/u= x/y and t/y=u/x where t, u, x, and y are non-zero integers, which of the following is true? GMAT Problem Solving
- A farm has chickens, cows and sheep GMAT Problem Solving
- 1/2 + 1/3 + 1/4 + 1/5 + 1/6 GMAT Problem Solving
- A Regular Pentagon is Inscribed in a Circle. If A and B are GMAT Problem Solving
- A Certain Culture of Bacteria Quadruples Every Hour GMAT Problem Solving
- If 2^x + 2^y = x^2 + y^2, Where x and y are Nonnegative GMAT Problem Solving
- If 3 < x < 100, for how many values of x is x/3 the square GMAT Problem Solving
- Hot Competition 3 Sep/8AM: In A Triangle ABC, Shown Above, Three Lines GMAT Problem Solving
- A Thief Steals a Car at 2.30 p.m. and Drives it at 60 km/h. The Theft GMAT Problem Solving
- If |x + 1 | > 2x - 1, Which Of The Following Represents The Correct Range GMAT Problem Solving
- Which Of The Following Is A True Statement? GMAT Problem Solving
- A machine puts c caps on bottles in m minutes. How many hours will it GMAT Problem Solving
- Find the greatest number that will divide 43, 91 and 183 GMAT Problem Solving
- Of the 150 Houses in a Certain Development GMAT Problem Solving
- A man can hit a target once in 4 shots. If he fires 4 shots in succession GMAT Problem Solving
- If 75 Percent of a Class Answered the First Question on a Certain Test Correctly GMAT Problem Solving
- A Clock Strikes 4 taking 9 seconds GMAT Problem Solving
- What is the Largest Power of 3 Contained in 200! GMAT Problem Solving
- Find The Value Of x GMAT Problem Solving
- 4 Out Of 15 Apples Are Rotten. They Are Taken Out One By One At Random GMAT Problem Solving
- Last Year 26 Members of a Certain Club Traveled to England, 26 Members Traveled to France, and 32 Members Traveled to Italy GMAT Problem Solving
- Running at the Same Constant Rate, 6 Identical Machines can Produce a Total of 270 Bottles Per Minute GMAT Problem Solving
- Of The 800 Employees Of Company X, 70 Percent Have Been With The Company GMAT Problem Solving
- To 100 Litres Of Milk, 10 Litres Of Water Is Added And Then 20 Litres GMAT Problem Solving
- Walking at 3/4 of his normal speed, Mike is 16 minutes late GMAT Problem Solving
- There are 12 yes or no questions. How many ways can these be answered? GMAT Problem Solving
- There are 7 Red and 5 Blue Marbles in a Jar GMAT Problem Solving
- A Basket Contains 3 White and 5 Blue Balls GMAT Problem Solving
- Working together, John and Jack can type 20 pages in one hour GMAT Problem Solving
- Is x^2 *x^5*z>0? GMAT Problem Solving
- If 2^98=256L+N, where L and N are integers and 0≤N≤4, what is the value of N? GMAT Problem Solving
- After 6 games, Team B had an average of 61.5 points per game GMAT Problem Solving
*The article might have information for the previous academic years, please refer the official website of the exam.