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?
- 9
- 16
- 25
- 36
- 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.
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