If n > 0 , Which of the Following Must be True? GMAT Problem Solving

Question: If n > 0, which of the following must be true?

1. \(n^2>1\)
2. \(n-n^2<0\)
3. \(2n-1>1\)

1. I only
2. II only
3. III only
4. I and II only
5. None

Correct Answer: E

Approach Solution (1):

(1) True for all values of n except 1
When n = 1; \(n^2>1\)

(2) True for all values of n except 1
When n = 1; \(n-n^2<0\)

(3) True for all values of n

Correct Answer: E

Approach Solution (2):

Note: n is positive but we don’t know whether it is an integer or fraction.

(1)\(n^2>1\). Not necessarily, let x be \(\frac{1}{2}\)

(2)\(n-n^2<0\). Let x be \(\frac{1}{2}\). False

(3) 2n – 1 > 0. Let be \(\frac{1}{2}\). 2 * \(\frac{1}{2}\)- 1 = 0. False

Thus, none of these options are correct. This question is designed to test fractional case.

Correct Answer: E

“If n > 0, which of the following must be true?”- 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.

Suggested GMAT Problem Solving Samples

• A Driver Completed the First 20 Miles of a 40-Mile Trip at an Average Speed of 50 Miles Per Hour GMAT Problem Solving
• The sum of three numbers is 98. If the ratio between first and second be 2:3 and between second and third be 5:8 GMAT Problem Solving
• How Many Three-Letter Words Can be Constructed Using All the 26 Letters of the English Alphabet GMAT Problem Solving
• How Many Litres of Pure Alcohol Must be Added to a 100-litre Solution That is 20 Percent Alcohol GMAT Problem Solving
• For Any Four Digit Number, abcd, *abcd*= (3^a)(5^b)(7^c)(11^d) GMAT Problem Solving
• How Many Five Digit Numbers Can be Formed Using Digits 0, 1, 2, 3, 4, 5, Which Are Divisible By 3 GMAT Problem Solving
• An “Armstrong Number” is an n-Digit Number That is Equal to the Sum of the nth Powers GMAT Problem Solving
• A train crosses a bridge of length 500 m in 40 seconds and a lamp post on the bridge in 15 seconds GMAT Problem Solving
• A Train can Travel 50% Faster than a Car GMAT Problem Solving
• A rectangle is inscribed in a hexagon that has all sides of equal length and all angles of equal measure GMAT Problem Solving
• A Positive Integer Is Divisible by 9 If And Only If The Sum of Its Digits is Divisible By 9 GMAT Problem Solving
• The two lines are tangent to the circle GMAT Problem Solving
• In a Certain Population, There are 3 Times as Many People Aged Twenty-One or Under GMAT Problem Solving
• In How Many Different Ways can 3 Identical Green Shirts and 3 Identical Red Shirts be Distributed Among 6 Children GMAT Problem Solving
• The Interior of a Rectangular Carton is Designed by a Certain Manufacturer GMAT Problem Solving
• How Many Factors of 80 are Greater Than\(\sqrt80\)? GMAT Problem Solving
• If ‘A’ Can Complete a Task in 3 Hours and ‘B’ Can Complete the Same Task in 6 Hours GMAT Problem Solving
• Is Zero Even Integer or Odd Integer? GMAT Problem Solving
• If 20 Men or 24 Women or 40 Boys can do a Job in 12 Days GMAT Problem Solving
• If 10 millimeters equal 1 centimeter, how many square centimeters does 1 square millimeter equal? GMAT Problem Solving
• How many Terminating Zeroes does 200 Have GMAT Problem Solving
• Properties of Circle GMAT Problem Solving
• If 10, 12 and ‘x’ are Sides of an Acute Angled Triangle, How Many Integer Values of ‘x’ are Possible? GMAT Problem Solving
• For How Many Values of k is 12^12 the Least Common Multiple GMAT Problem Solving
• Bag A Contains Red, White and Blue Marbles such that GMAT Problem Solving
• Assume that all 7-Digit Numbers That do not Begin with 0 or 1 are Valid Phone Numbers. GMAT Problem Solving
• A Car Travels from Mayville to Rome at an Average Speed of 30 miles per hour GMAT Problem Solving
• A Certain Sum of Money is Divided Among A, B and C such that A Gets One GMAT Problem Solving
• The Ratio of Boys to Girls in Class A is 1 to 4, and that in Class B is 2 to 5 GMAT Problem Solving
• The Maximum Mark in an Examination is 100 and the Minimum is 0 GMAT Problem Solving
• A Rectangular Box has Dimensions 12*10*8 Inches GMAT Problem Solving
• If A Equals the Sum of the Even Integers from 2 to 20, Inclusive GMAT Problem Solving
• A Store Currently Charges The Same Price for Each Towel That It Sells. GMAT Problem Solving
• What is the Value of [ √ 7 + √ 29 − √ 7 − √ 29 ] 2 GMAT Problem Solving
• What is The Area of a Triangle with the Following Vertices GMAT Problem Solving
• The Product of the Five Smallest Two-Digit Prime Numbers GMAT Problem Solving
• The Square of 5^√2 =? GMAT Problem Solving
• Two Adjacent Angles of a Parallelogram are in the Ratio of 1:3 GMAT Problem Solving
• Which of The Following is a Perfect Cube? GMAT Problem Solving
• If a Right Angled Isosceles Triangle Has an Area of 2x^2 + 2x + ½. GMAT Problem Solving
• A number N^2 has 35 factors. How many factors can N have? GMAT Problem Solving
• If the Total Surface Area of a Cube is 24, What is the Volume of the Cube? GMAT Problem Solving
• There are 5,280 Feet in 1 Mile and 12 Inches in One Foot GMAT Problem Solving
• An Isosceles Right Triangle has an Area of 50. What is the Length of the Hypotenuse? GMAT Problem Solving
• A is Thrice as Good a Workman as B and Takes 10 days Less to do a Piece of Work GMAT Problem Solving
• 999,999^2−1 equals? GMAT Problem Solving
• Which of the following represents the largest 4 digit number GMAT Problem Solving
• The Lengths of the Sides of an Obtuse-Angled Triangle are x, y, and z, Where x, y and z are Integers GMAT Problem Solving
• If the expression sqrt2+2+2+2+ ... extends to an infinite number of roots GMAT Problem Solving
• How Many Different Lines Are Determined by 4 Distinct Points in a Plane If No 3 GMAT Problem Solving