At a garden site, 16 Mango trees,24 banyan trees and 28 Guava trees are to be planted in certain no of rows in such a way that each row has equal no of trees of the same species. what is the minimum number of rows that are required for this purpose
4 mango trees in 4 rows
4 banyan trees in 6 rows
4 guava trees in 7 rows
Total = 4+6+7=17
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The arithmetic mean of three numbers is 55. if the largest number is 2.5 times the smallest number and the remaining number is twice the smallest number, what is te largest of the three numbers.
A number when divided by D leaves a remainder of 8 and when divided by 3D leaves a remainder of 21. What is the remainder left, when twice the number is divided by 3D?
Let's number is N
so N = DX + 8 -------(1)
N = 3DY + 21 ---------(2)
From Eq. 1 & 2
=> D(X-3Y) = 13
"13" is prime number, and its factors will be 1 and 13 only
=> X-3Y must be 1
Let X = 4 and Y = 1, D=13
So, N = 60
Remainder Left = 2N / 3D
= 120 / 39 = 3
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The shopkeeper charged 12 rupees for a bunch of chocolate. but i bargained to shopkeeper and got two extra ones, and that made them cost one rupee for dozen less then first asking price. How many chocolates I received in 12 rupees ?
n chocolates = Rs 12
Price per dozen = 144/n
I got n+2 in rs 12 = > Price per dozen = 144/n+2
144/n+2 = 144/n - 1
=> n = 16
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The sum of the four consecutive two digit odd numbers, when divided by 10, becomes a perfect square. Which of the following can be one of these four numbers?
Let the numbers are 2a +1, 2a + 3, 2a + 5, 2a + 7 and their sum = 8a + 16
Given that if this sum is divided by 10, results in a perfect square.
So, (8a+16)/10 = k^2.
=> a = (10k^2?16) /8
=> a=[ 5(k^2)/4 ]?2
As k^2 is a perfect square and has to be divided by 4, only even numbers should be considered for k.
For k = 2, we get, a = 3, but 2a + 1 is not a two digit number.
For k = 4, a = 18 for which the given condition is satisfying.
So the numbers are 37, 39, 41, 43.
For k = 6, a = 43. The number are 87, 89, 91, 93.
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What is the greatest power of 143 which can divide exactly 125!
In this problem, ABS(x) provides absolute value of x, without regard to its sign. For example ABS(3) = ABS(-3) = 3
The graphs of y = – ABS(x – a) + b and y = – ABS(x – c) + d intersect at points (2,5) and (8, 3).
Find a + c
Both curves intersect at (2, 5)
So 5 = – |2 – a| + b ? 5 + |2 – a| – b = 0 - - - (1)
5 = – |2 – c| + d ? 5 + |2 – c| – d = 0 - - - (2)
Also,
3 = – |8 – a| + b ? 3 + |8 – a| – b = 0 - - - (4)
3 = – |8 – c| + d ? 3 + |8 – c| – d = 0- - - (4)
Equating 1 and 3, 5 + |2 – a| = 3 + |8 – a| ? 2 + |2 – a| = |8– a|
So a = 4
Similarly if we equate 2 and 4, we get c = 4
a + c = 8
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For a scholarship, n out of 2n + 1 students are to be selected. If the number of different ways in which at least one student can be selected is 63, then the maximum number of students to be selected are :
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