If n = (33)^43 + (43)^33 What is the Unit Digit of n? GMAT Problem Solving

Question: If n = (33)^43 + (43)^33 what is the unit digit of n?

1. 0
2. 2
3. 4
4. 6
5. 8

Correct Answer: A

Solution and Explanation:
Approach Solution 1:
This problem has only 1 approach to solve

First of all, the unit digit of (33)^43 is the same as that of 3^43 and the unit digit of (43)^33 is the same as that of 3^33. So, we need to find the unit digit of 3^43 + 3^33.

Next, the units digit of 3 in positive integer power repeats in blocks of four {3, 9, 7, 1}:

3^1=3 (the units digit is 3)

3^2=9 (the units digit is 9)

3^3=27 (the units digit is 7)

3^4=81 (the units digit is 1)

3^5=243 (the unit digit is 3 again!)

Thus, it can be stated that,

The unit digit of 3^43 is the same as the unit digit of 3^3, so 7 (43 divided by the cyclicity of 4 gives the remainder of 3).

The unit digit of 3^33 is the same as the unit digit of 3^1, so 3 (33 divided by the cyclicity of 4 gives the remainder of 1).

Therefore the unit digit of (33)^43 + (43)^33 is 7 + 3 = 0.

“If n = (33)^43 + (43)^33 what is the unit digit of n?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide 2018".To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

Suggested GMAT Problem Solving Questions

• In a Shooting Competition, Probability of A Hitting Target is 2/5, by B is 2/3 and C is 3/5 GMAT Problem Solving
• The Sides of a Quadrilateral Taken in Order are 16,16,14 and 10 GMAT Problem Solving
• If 80 Lamps Can Be Lighted, 5 Hours Per Day For 10 Days GMAT Problem Solving
• If denotes the area of a circle with diameter d, then which of the following is equal to <4>*<6> GMAT Problem Solving
• At exactly what time past 7:00 will the minute and hour hands of an accurate working clock be precisely perpendicular to each other for the first time? GMAT Problem Solving
• There is a 120 Liter Mixture of Alcohol and Water GMAT Problem Solving
• When X Is Divided By 13, The Answer Is Y With a Remainder of 3. GMAT Problem Solving
• If a/b = 2/3 Which of the Following is Not True? GMAT Problem Solving
• 1/3 of the Cookies in a Jar are Chocolate Chip, 2/3 of the Remaining Cookies are Peanut Butter GMAT Problem Solving
• The Kinetic Energy K, in Joules, Provided by the Mass of a Particle m GMAT Problem Solving
• A Recent Survey Showed That 50 Percent of People Polled Believe that Elected Officials Should Resign GMAT Problem Solving
• The Perimeter of a Square is Equal to the Perimeter of a Rectangle Whose Length And Width are 6m and 4m Respectively GMAT Problem Solving
• The Closing Price of Stock X Changed on Each Trading Day Last Month GMAT Problem Solving
• An Exam Consists of 8 True/False Questions GMAT Problem Solving
• From her Collection of 9 Different Hats Ellen Wants to Wear one Different Hat GMAT Problem Solving
• Company C Sells a Line of 25 Products with an Average Retail Price of $1,200 GMAT Problem Solving
• A Man has 1044 Candles. After Burning, He can Make a New Candle GMAT Problem Solving
• An Equilateral Triangle ABC is Inscribed in Square ADEF GMAT Problem Solving
• A Popular Website Requires Users to Create a Password Consisting of Digits Only GMAT Problem Solving
• A Furniture Store Sells Only Two Models of Desks, Model A and Model B GMAT Problem Solving
• In a Drawer, There are 4 White Socks, 3 Blue Socks, and 5 Grey Socks GMAT Problem Solving
• There are 100 Apples in a Bag of which 98% are Green and Rest are Red GMAT Problem Solving
• A palindrome is a number that reads the same forward and backward GMAT Problem Solving
• Three Cars Leave From A To B In Equal Time Intervals GMAT Problem Solving
• A Tank, Which Usually Takes 5 Hours to be Filled, Takes 6 Hours to Fill Because of a Leak GMAT Problem Solving
• There are 6 Tasks and 6 Persons. Task 1 Cannot be Assigned Either to Person 1 or to Person 2; Task 2 Must be Assigned to either Person 3 or Person 4 GMAT Problem Solving
• A Manufacturing Company is Testing out a New Design for One of its Most Popular Products GMAT Problem Solving
• A Contract is to be Completed in 46 days and 117 Men Were set to Work, each Working 8 hours a Day GMAT Problem Solving
• An Inlet Pipe can Fill in an Empty Cistern in 30 minutes GMAT Problem Solving
• Iqbal Dealt Some Cards to Mushtaq and himself from a Full Pack of Playing Cards GMAT Problem Solving
• A Zookeeper Counted the Heads of the Animals in a Zoo and Found it to be 80 GMAT Problem Solving
• In a Class of 120 Students Numbered 1 to 120, All Even Numbered Students Opt for Physics GMAT Problem Solving
• A Shop Stores x kg of Rice. The First Customer Buys half this Amount Plus half a kg of Rice GMAT Problem Solving
• Machine A Produces bolts at a Uniform Rate of 120 Every 40 seconds GMAT Problem Solving
• If a(a + 2) = 24 and b(b + 2) = 24, Where a ≠ b, Then a + b = GMAT Problem Solving
• How Many 4 Digit Numbers can be Formed Using the Digits 1, 2, 5, 6, 8 and 9 Without Repetition, So that 2 and 5 Never Come Together ? GMAT Problem Solving
• If The Average (arithmetic mean) of The Four Numbers 3, 15, 32, and (N + 1) is 18, then N = GMAT Problem Solving
• Out of 7 Consonants and 4 Vowels, How Many Words of 3 Consonants and 2 Vowels Can be Formed? GMAT Problem Solving
• 4 Bells Toll Together at 9:00 A.M. They Toll After 7, 8, 11 and 12 Seconds GMAT Problem Solving
• 12 Marbles are Selected at Random from a Large Collection of White, Red, Green and Yellow Marbles 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