bySayantani Barman Experta en el extranjero
Question: How many three-digit integers greater than 710 are there such that all their digits are different?
- 198
- 202
- 207
- 209
- 212
Answer:
Approach Solution 1:
First find how many integers between 200 and 999 are such that all their digits are different.
We have: (3 options for the first digit) * (9 options for the second digit) * (8 options for the third digit) = 216 numbers
Among these 216 numbers, 9 (701, 702, 703, 704, 705, 706, 708, 709, 710) are not bigger than 710. The answer to the question is therefore 216 – 9 = 207
Correct option: C
Approach Solution 2:
We have 3 options (7, 8, 9) for the first digit.
1) 188 = 64 ----- 7 is the first digit here
2) 198 = 72 ------ 8 is the first digit here
3) 198 = 72 ------- 9 is the first digit here
So total is 64+72+72 = 208.
However, in the first case we have to remove one number to account for 710. So answer is 207.
Correct option: C
“How many three-digit integers greater than 710 are there such that all their digits are different?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. 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.
Suggested GMAT Quant Questions:
- At a Dog Competition, a Dog is Awarded 10 Points if it Runs Through 4 Pipes, Makes 10 Jumps, and Walks on 2 Beams. GMAT Problem Solving
- The Population of the Bacteria Colony Doubles Every Day GMAT Problem Solving
- If tu=x tu=x and y=uxy=ux Where t, u, x, and y are Non-Zero Integers GMAT Problem Solving
- The farm has Chickens, Cows and Sheep. The Number of Chickens and Cows Combined is 3 Times the Number of Sheep. GMAT Problem Solving
- In how Many Different Ways Can a Group of 8 People be Divided into 4 Teams of 2 People Each? GMAT Problem Solving
- If m is Three Times n, and if 2n + 3 is 20% of 25, What is the value of m? GMAT Problem Solving
- If Ben Were to Lose the Championship, Mike would be the Winner GMAT Problem Solving
- A Train Travelling at a Certain Constant Speed takes 30 seconds GMAT Problem Solving
- After 6 Games, Team B Had an Average of 61.5 Points Per Game. GMAT Problem Solving
- If 12 Ounces of a Strong Vinegar Solution are Diluted with 50 Ounces of Water to Form a Three-Percent Vinegar Solution GMAT Problem Solving
- A Contractor Estimated that his 10-Man Crew Could Complete the Construction in 110 Days if There Was no Rain. GMAT Problem Solving
- A Conference Room is Equipped with a Total of 45 Metal or Wooden Chairs.GMAT Problem Solving
- How many litres of a 90% solution of concentrated acid needs to be mixed with a 75% solution GMAT problem solving
- Jug Contains Water And Orange Juice In The Ratio 5:7 . Another Jug Contains Water And Orange J GMAT problem solving
- The number of ways in which 8 different flowers can be seated to form a garland so that 4 particular flowers are never separated GMAT problem solving
- A train travels from Albany to Syracuse, a distance of 120 miles, at an average rate of 50 miles per hour GMAT problem solving
- The hexagon ABCDEF is regular. That means all its sides are the same length and all its interior angles are the same size. GMAT problem solving
- y varies directly as x and when x = 6, y = 24. What is the value of y, when x = 5? GMAT problem solving
- If k is an Integer and 2 < k < 7, for How Many Different Values of k is There a Triangle With Sides of Lengths 2, 7, and k? GMAT problem solving
- How many factors does 36^2 have? GMAT problem solving
- A number when divided successively by 4 and 5 leaves remainder 1 and 4 respectively GMAT problem solving
- Walking at 6/7 th of his usual speed, a man is 25 min too late GMAT problem solving
- An Inlet Pipe can Fill in an Empty Cistern in 30 minutes Whereas a leak in the Bottom of the Cistern can Empty a Filled Tank in 40 minutes GMAT problem solving
- A milkman cheats his customers by adding water to the milk he sells GMAT problem solving
- if 80 lamps can be lighted, 5 hours per day for 10 days for $21.25, then the number of lamps, GMAT problem solving
- Few of the corporate contributions to the earthquake relief fund, aside from Pterocom GMAT problem solving
- The product of the first 10 prime numbers is closest to which of the following? GMAT problem solving
- There is a 120 liter mixture of alcohol and water. The ratio of alcohol to water is 7 : 5 GMAT problem solving
- An equilateral triangle ABC is inscribed in square ADEF, forming three right triangles GMAT problem solving
- A Furniture Store Sells Only Two Models of Desks, Model A and Model B. The Selling Price of Model A is $120 GMAT problem solving
- A contractor combined x tons of a gravel mixture that contained 10 percent gravel G GMAT problem solving
- There are 100 Apples in a Bag of which 98% are Green and Rest are Red GMAT problem solving
- The Smallest of Six Consecutive Odd Integers Whose Average (arithmetic mean) is x + 2 GMAT Problem Solving
- Two Consultants, Mary and Jim, Can Type up a Report in 12.5 Hours and Edit it in 7.5 Hours. GMAT Problem Solving
- How Many Litres of a 90% Solution of Concentrated Acid Needs to be Mixed with a 75% Solution GMAT Problem Solving GMAT Problem Solving
- What is the Largest Power of 3 Contained in 200! GMAT Problem Solving
- What is the Value of x? 1) x^2 + x + 10 = 16 2) x = 4y^4+2y^2+2 GMAT Problem Solving
- A Jar Full of Whisky Contains 40% Alcohol GMAT Problem Solving
- X is Older Than Y, Z Is Younger Than W And V is Older Than Y. Is Z Younger Than X?
- A Flagstaff 17.5 m High Casts a Shadow of Length 40.25 m
- Frances Can Complete a Job in 12 hours, and Joan Can Complete the Same Job in 8 Hours GMAT Problem Solving
- Running at the Same Constant Rate, 6 Identical Machines can Produce a Total of 270 Bottles Per Minute. GMAT Problem Solving
- If abc ≠ 0 is (a/b)/c = a/(b/c) GMAT Problem Solving
- If 0 < a < b < c, Which of the Following Statements Must be True? GMAT Problem Solving
- Find The Value Of x
- Two Consultants, Mary and Jim, Can Type up a Report in 12.5 Hours and Edit it in 7.5 Hours GMAT Problem Solving
- 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 GMAT Problem Solving
- The square of 5√252 =? GMAT Problem Solving
Comments