Number System/Averages Flashcards
Least prime no
2
Prime nos between 1-100?
4422322321
Sum of prime no less than 100
1060
π is rational irrational?
Value?
Irrational
22/7
Sum of first n natural nos?
n(n+1) /2
Sum of first n odd nos?
n^2
Sum of first n even nos?
n(n+1)
Sum of squares of first n nos?
n(n+1) (2n+1) /6
Sum of cubes of first n nos?
{n(n+1) /2}^2
Divisibility rule of 7?
Remove last digit
Double it
Subtract from leftover no
Result divisible by 7
Sequence of operation?
VODMAS
(a+b) ^2 + (a-b) ^2
(a+b) ^2 - (a-b) ^2
2(a^2+b^2)
4 ab
HCF and LCM given and one number given find other no?
HCF * LCM = one no. * other no.
A number when divided by 120 gives 17 as remainder on dividing the same number by 15 what would be the remainder?
120/15 = 0 remainder 17/15 = 2 remainder
Ans: 2
GCD of 1/2, 2/3, 3/4, 4/5
GCD : Greatest common divisor
LCM of 2,3,4,5 then reciprocal
Ans: 60
The least number which when divided by 5,6,4 and 3 leaves a remainder 1 but when divided by 7 leaves no remainder.
LCM of 5,6,4,3 = 60
60+1
But not divisible by 7
Multiples check!
602 + 1 = 121
603 + 1 = 181
60*5 + 1 = 301
Ans: 301
Five bells begin to toll together and toll respectively at intervals of 6, 5, 7, 10 and 12 seconds. How many times will they toll together in one hour excluding the one at the start ? A. 7 times B. 8 times C. 9 times D. 11 times
To toll together we need to take the LCM of each seconds of bell.
L.C.M. of 6, 5, 7, 10 and 12 = 420.
420/60 = 7 minutes
So, the bells will toll together after every 7 minutes.
Therefore, in 1-hour (or 60 minutes), the bells will toll together 8 times (7 x 8 = 56), excluding the one at the start.
m/s to km/hr
Km/hr to m/s
18/5
5/18
A is thrice as efficient as B then ratio of work done by A to B is?
3:1
Average of 1st 23 multiples of 3?
23+1/2 = 12th place is in mid
So avg : 3*12 = 36
Average of 1st n natural nos?
n+1/2
Average of odd numbers between 2 numbers?
Avg = total number of odd numbers
Total no of odd numbers = n+1/2
Avg of first n even nos?
n+1
A B
20 30
(Avg) (Avg)
Total
Avg?
3 2 (ration of number)203 + 302/3+2
Ans: 24
Arithmetic Mean
- a, b
- a, b, c
a+b/2
a+b+c/3
Geometric Mean
- a, b
- a, b, c
√ab
Or
(ab)^1/2
(abc) ^1/3
Harmonic mean?
- a, b
- a, b, c
- 2 2ab
________ = _______
1/a + 1/b a+b
- 3 3abc
________ = ____________
1/a + 1/b + 1/c ab+bc+ac
The average of 5 consecutive odd no is 25, find the largest no?
29
When the difference between two consecutive numbers is same then average is the middle value.
Difference between all the odd numbers are to show the average is 25 that is it is the middle value so the previous two and the after two values can be found out.
Average age of ABCD 5 years ago was 45 years so their average age in the current year would be.
45+5 = 50
A motorist travels to a place 150 km away at an average speed of 50 km per hour and returns at 30 km/h is average speed for the whole journey in kilometre per hour is?
Use harmonic mean to directly find the answer.
Or
150/50 = t1= 3 150/30 = t2 = 5
8 min total
Distance total = 300
Avg speed = 300/8 = 37.5 kn/hr
