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The formula to find number of diagonals (D) given total number of vertices or sides (N) is
N * (N – 3)
D = ———–
2
Using the formula, we get
1325 * 2 = N * (N – 3)
N2 – 3N – 2650 = 0
Solving the quadratic equation, we get N = 53 or -50
It is obvious that answer is 53 as number of vertices can not be negative.
Alternatively, you can derive the formula as triange has 0 diagonals, quadrangel has 2, pentagon has 5, hexagon has 9 and so on……
Hence the series is 0, 0, 0, 2, 5, 9, 14, …….. (as diagram with 1,2 or 3 vertices will have 0 diagonals).
Using the series one can arrive to the formula given above.
75/8 days
Let the person ate x banana on first day, so below is the equation for five days
X+x+6+x+12+x+18+x+24=100
So, he ate 8 banana first day
(x+2)+(x)+(x-2)
X+2+x+x-2=18
3x=18
X=6
The 3digit number is 864
as i assume the time taken to complete the job is not to be
changed while increasing the employees as it does not
clearly states so……….
30 men wrk for 9 hrs
therefore for the work to be done if no of workers is
increases the no of hrs / day to work should decrease so
here s a inverse relation
solving further we get
30 = K /9 ==> K= 270
now
40 = 270/y ==> y= 6.75
therefore ans is d)none
7 1/2
Let\: the\: total\: price \: be\: Rs. X\: then,
B= 2x/7 & A= \left ( x-2 \right )/7
So, A:B = 5x/7 : 2x/7 = 5 : 2
Let \: B’s \: capital\; be\: Rs.Y\: then\: \left ( 16000\ast 8 \right )/4y= 5/2
=> (16000\ast 8\ast 2)/(4\ast 5) = y
=> y = Rs. 12800
divide 100 by 7, and you get 14.28. (Obviously you aren’t talking about decimals here) and so 14 numbers can be divisible by 7 up to 100.
The answer is 14.
CITOXE
Given:
In a group of 15 students,
7 have studied Latin,
8 have studied Greek,
3 have not studied either.
To find:
The number of students who studied both Latin and Greek.
Solution:
In a group of 15 students, have studied Latin, 8 have studied Greek, 3 have not studied either.
Therefore,
n(A∪B) = 15 – 3
n(A∪B) = 12
7 have studied Latin,
n(A) = 7
8 have studied Greek,
n(B) = 8
n(A∩B) is the number of students who studied both Latin and Greek.
n(A∩B) = n(A) + n(B) – n(A∪B)
n(A∩B) = 7 + 8 – 12
n(A∩B) = 15 – 12
n(A∩B) = 3
The number of students who studied both Latin and Greek is 3
Final answer:
3 of them studied both Latin and Greek.
Thus, the correct answer .3
Cousin
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