Question: Out of a group of swans, seven times half of the square root of the number of swans were seen going away from a bank of a river and only one pair remained in the water. How many swans were there in the group?

1. 9
2. 16
3. 25
4. 36
5. 49

Correct Answer: B
Solution and Explanation:
Approach Solution:1
Let x be the total number of swans
x = (7/2) √x + 2
x-2 = (7/2) √x
2*(x-2) = 7*√x

Squaring Both sides:
4*(x-2)^2 = 49*x
4*(x^2-4x+4) = 49*x
4x^2-65x+16 = 0
(x-16) (4x -1) = 0
x-16 = 0 or 4x-1 = 0
x = 16 or x = ¼
x = 16

Approach Solution: 2
Let the total number of swans be x.

Approach Solution: 2
Let the total number of swans be x.
Number of swans going away from the bank = 7*½ ×√x
Number of swans remained in the water = x - 7/2 ×√x

=> 2 = x - 7/2 × √x (since one pair = 2 remained in the water)
=> 7/2 × √ x= x-2

Squaring both sides of the equation, we get :

49/4 * x= (x-2)²
=> 49 x= 4( x² - 4x +4)
=> 49x= 4x²-16x+16
=> 0=4x²- 16x-49x+16
=> 0= 4x²- 65x+16
=> 4x²-(64+1)x+16=0
=> 4x²-64x-x+16=0
=> 4x(x-16)-1(x-16)=0
=> (4x-1)(x-16)=0
=> (4x-1)=0 or (x-16)=0
=> x= ¼ or x= 16

As the number of swans cannot be a fraction. So, it has to be 16.

“Out of a group of swans, seven times half of the square root of the”- 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. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

Suggested GMAT Problem Solving Samples

• I Travel The First Part Of My Journey At 40 Miles Per Hour GMAT Problem Solving
• Profit Earned By Selling An Article At 1060 Is 20 % More Than The Loss GMAT Problem Solving
• A Perfect Square is a Number that Becomes an Integer when Square GMAT Problem Solving
• If x + y = 2 and x^2 + y^2 = 2, What is the Value of xy? GMAT Problem Solving
• If y= 4 + (x - 3)^2, Then y is Lowest When x = GMAT Problem Solving
• What is the Value of w in Terms of x and y GMAT Problem Solving
• A New Flag is to be Designed with Six Vertical Stripes Using Some GMAT Problem Solving
• If x^2 + 1/x^2 = 4, What is the Value of x^4 + 1/x^4 GMAT Problem Solving
• A Dog Breeder Currently has 9 Breeding Dogs. 6 of the Dogs have Exactly GMAT Problem Solving
• The Interior Angles Of A Convex Polygon Are In Arithmetic Progression GMAT Problem Solving
• (x^2 + 2x - 8)/(x^2 - 6x + 8) = ? GMAT Problem Solving
• Which Of The Following Is Equal To The Average (Arithmetic Mean) GMAT Problem Solving
• A Trader Has 400 kg Of Rice, A Part Of Which He Sells At 36% GMAT Problem Solving
• A Number, x is Chosen at Random from the Set of Positive Integers Less GMAT Problem Solving
• Which of the Following Could be the Area of an Isosceles Triangle GMAT Problem Solving
• After M Students Took a Test, There was a Total of 64% GMAT Problem Solving
• Perimeter of a Triangle with Integer Sides is Equal to 15 GMAT Problem Solving
• PQRS is a Quadrilateral Whose Diagonals are Perpendicular to Each Other GMAT Problem Solving
• Which of the following is closest to (10.001)^2 ? GMAT Problem Solving
• A Train of Length L is Traveling at a Constant Velocity and Passes a Pole GMAT Problem Solving
• In United States Currency, a Nickel is Worth 5 Cents GMAT Problem Solving
• After 200 Grams of Water were Added to the 24%- Solution of Alcohol GMAT Problem Solving
• Which of The Following Numbers is A Perfect Square? GMAT Problem Solving
• What is 1/(1*2) + 1/(2*3) + 1/(3*4) + 1/(4*5) + 1/(5*6) + 1/(6*7) GMAT Problem Solving
• What is the Remainder When\( 2^{99}\) is Divided by 99? GMAT Problem Solving
• The First Five Numbers in a Regular Sequence are 4, 10, 22, 46, and 94 GMAT Problem Solving
• A Bar is Creating a New Signature Drink. There are Five possible Alcohol GMAT Problem Solving
• A Can Complete a Certain Job in 12 Days. B is 60% More Efficient than GMAT Problem Solving
• An Alloy of Gold,Silver and Bronze Contain 90% Bronze, 7% Gold and GMAT Problem Solving
• When Positive Integer n is Divided by 5, the Remainder is 1 GMAT Problem Solving
• A is Thrice as Efficient as B and Hence Takes 12 Days Less to Complete GMAT Problem Solving
• A Tank is Filled by Three Pipes with Uniform Flow. The First Two Pipes GMAT Problem Solving
• Each Person in a Group of 110 Investors Has Investments in Either GMAT Problem Solving
• Jim Travels the First 3 Hours of His Journey at 60 mph Speed GMAT Problem Solving
• A Committee Of 7 Members Is To Be Formed To Put Up The Christmas GMAT Problem Solving
• In A Class Of 60 Students, 23 Play Hockey, 15 Play Basketball GMAT Problem Solving
• The Area Of An Equilateral Triangle With Side Length X Is The Same GMAT Problem Solving
• Which Of The Following Has A Decimal Equivalent That Is A GMAT Problem Solving
• A Number when Divided by a Divisor Leaves a Remainder of 24 GMAT Problem Solving
• How many Integers Less than 1000 have no Factors (other than 1) GMAT Problem Solving
• How Many Prime Numbers are there Between 50 and 70? GMAT Problem Solving
• If a Circle Passes through Points (1, 2) (2, 5), and (5, 4) GMAT Problem Solving
• If the Perimeter of Square Region S and the Perimeter of Rectangular GMAT Problem Solving
• If x^9= 9^9^9, What is the Value of x? GMAT Problem Solving
• In a Competition, a School Awarded Medals in Different Categories GMAT Problem Solving
• In How Many Ways can 5 Apples (Identical) be Distributed Among 4 Children? GMAT Problem Solving
• What is Greatest Positive Integer n such that 2^n is a Factor of 12^10? GMAT Problem Solving
• All The Five Digit Numbers In Which Each Successive Digit Exceeds Its GMAT Problem Solving
• A Box Contains Two White Balls, Three Black Balls And Four Red Balls GMAT Problem Solving
• Consider An Obtuse-Angled Triangles With Sides 8 Cm, 15 Cm GMAT Problem Solving