CMAT Maths Puzzle Numerical Ability Area and Volume

Out of a group of swans, 72 times the square root of the total number of swans are playing on the shore of the pond. The remaining two swans are inside the pond. Which of the following can be the total number of swans?
Option
(a) 12
(b) 10
(c) 14
(d) 16

Read Solution (Total 1)

Let the total no. of swans = x
No. of swans playing on the shore = 7/2 √x
Remaining swans = 2
A/Q x=7/2 √x+2
x-2 = 7/2 √x
2(x-2) = 7√x
4(x-2)² = 49x
4(x²-4x+4) = 49x
4x²-65+16 = 0
(x-16) (4x -1) = 0
x-16 = 0 or 4x-1 = 0
x = 16 or x = 1/4
Since, the no. of swans cannot be 1/4
∴ x = 16
The total no.of swans = 16
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CMAT Other Question

Between 1 to 1000, how many natural numbers are there which when divided by 3, 4 and 5 leave a remainder of 2, 3 and 4 respectively but when divided by 7 leave no remainder?
Option
(a) 1
(b) 2
(c) 3
(d) None of these Co-efficient of x in the equation x2 + px + q = 0 was wrongly written as 17 in place of 13 and the roots thus found were –2 and –15. The roots of the correct equation would be
Option
(a) 3, –10
(b) –3, –10
(c) –3, 10
(d) 3, 10