What is the sum of the first 50 common numbers between the series 15,19,23....... and 14,19,24.........?
A) 25550
B) 24540
C) 24450
D) 25450
E) 25540
The given series are increasing by 4 and 5 respectively..
so the LCM=20
Hence they will have common numbers every 20...so common numbers will be like 19, 39, 59...
The common numbers is also an arithmetic series starting with 19 and with a difference of 20 between consecutive numbers....
therefore a=19
d=20
n=50
sum of arithmatic series
s = n/2(a+(n-1)*d)
= 25(19+49*20)
= 25450
Showing posts with label PROGRESSION. Show all posts
Showing posts with label PROGRESSION. Show all posts
Wednesday, September 15, 2010
Wednesday, July 21, 2010
GMAT Question of the day
What is the sum of all the even numbers bigger than (-10) and smaller than 12?
(a) 2.
(b) 10.
(c) 0.
(d) 8.
(e) 4.
This is a series of numbers with a constant difference between them.
The first number is (-8) and the last is (10), there are 10 numbers in total.
Hence its in AP .
The formula for such a series is: ((-8 + 10) x 10)/2 = 10.
The best answer is B.
(a) 2.
(b) 10.
(c) 0.
(d) 8.
(e) 4.
This is a series of numbers with a constant difference between them.
The first number is (-8) and the last is (10), there are 10 numbers in total.
Hence its in AP .
The formula for such a series is: ((-8 + 10) x 10)/2 = 10.
The best answer is B.
Monday, March 9, 2009
PREP FOR GMAT : PROGRESSION
CAT , GMAT , GRE , MBA
These notes will be useful in solving some of the GMAT problems.
ARITHMETIC PROGRESSION
nth term of an Arithmetic progression = a + (n-1)d
Sum of n terms in an AP = s = n/2 [2a + (n-1)d]
where, a is the first term and d is the common differnce.
If a, b and c are any three consecutive terms in an AP, then 2b = a + c
GEOMETRIC PROGRESSION
nth term of a GP is = a[r^(n-1)]
sum of n terms of a GP:
s = a [(r^n - 1)/(r-1)] if r > 1
s = a [(1 - r^n)/(r-1)] if r < 1]
sum of an infinite number of terms of a GP is
s(approx.) = a/ (1-r) if r <1
If a, b and c are any three consequtive terms in a GP, then b^2 = ac
HARMONIC PROGRESSION
A series of non-zero numbers is said to be harmonic progression (abbreviated H.P.) if the series obtained by taking reciprocals of the corresponding terms of the given series is an arithmetic progression.
For example, the series 1 +1/4 +1/7 +1/10 +..... is an H.P. since the series obtained by taking reciprocals of its corresponding terms i.e. 1 +4 +7 +10 +... is an A.P.
A general H.P. is 1/a + 1/(a + d) + 1(a + 2d) + ...
nth term of an H.P. = 1/[a +(n -1)d]
Three numbers a, b, c are in H.P. only if 1/a, 1/b, 1/c are in A.P.
i.e. only if 1/a + 1/c = 2/b
i.e. only if b= 2ac/(a + c)
Thus the H.M. between a and b is H = 2ac/(a + c)
TIPS FOR SOLVING GMAT PROBLEMS:
If A, G, H are arithmetic, geometric and harmonic means between two distinct, positive real numbers a and b, THEN
1. G² = AH i.e. A, G, H are in G.P.
2. A, G, H are in descending order of magnitude i.e. A > G > H.
These notes will be useful in solving some of the GMAT problems.
ARITHMETIC PROGRESSION
nth term of an Arithmetic progression = a + (n-1)d
Sum of n terms in an AP = s = n/2 [2a + (n-1)d]
where, a is the first term and d is the common differnce.
If a, b and c are any three consecutive terms in an AP, then 2b = a + c
GEOMETRIC PROGRESSION
nth term of a GP is = a[r^(n-1)]
sum of n terms of a GP:
s = a [(r^n - 1)/(r-1)] if r > 1
s = a [(1 - r^n)/(r-1)] if r < 1]
sum of an infinite number of terms of a GP is
s(approx.) = a/ (1-r) if r <1
If a, b and c are any three consequtive terms in a GP, then b^2 = ac
HARMONIC PROGRESSION
A series of non-zero numbers is said to be harmonic progression (abbreviated H.P.) if the series obtained by taking reciprocals of the corresponding terms of the given series is an arithmetic progression.
For example, the series 1 +1/4 +1/7 +1/10 +..... is an H.P. since the series obtained by taking reciprocals of its corresponding terms i.e. 1 +4 +7 +10 +... is an A.P.
A general H.P. is 1/a + 1/(a + d) + 1(a + 2d) + ...
nth term of an H.P. = 1/[a +(n -1)d]
Three numbers a, b, c are in H.P. only if 1/a, 1/b, 1/c are in A.P.
i.e. only if 1/a + 1/c = 2/b
i.e. only if b= 2ac/(a + c)
Thus the H.M. between a and b is H = 2ac/(a + c)
TIPS FOR SOLVING GMAT PROBLEMS:
If A, G, H are arithmetic, geometric and harmonic means between two distinct, positive real numbers a and b, THEN
1. G² = AH i.e. A, G, H are in G.P.
2. A, G, H are in descending order of magnitude i.e. A > G > H.
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