Quant - 2 Flashcards
Arithmetic Sequence
əˈrɪθmətɪk
دنباله حسابی
An arithmetic sequence is a sequence in which the difference between every pair of consecutive terms is the same.
Example: 5, 10, 15, 20
20 = 5 + ( 4 - 1 ) x 5
20 = 20
Sum of the terms of an Arithmetic Sequence
Geometric Sequence
A geometric sequence (or geometric progression) is one in which the ratio between every pair of consecutive terms is the same.
Example: 5, 10, 20, 40
40 = 5 x 2( 4 - 1 )
40 = 40
The general sum of a n term GP with common ratio r is given by:
b1 x [ (1-rn ) ÷ (1-r) ]
Perpendicular bisector
عمود منصف
Steepness of a line
The larger the absolute value of the slope of a line, the steeper the line.
Let (x,y) be a point on the xy-plane.
The reflection of (x,y) over:
the line y = x
the point (y,x).
Let (x,y) be a point on the xy-plane.
The reflection of (x,y) over:
the line y = -x
the point (-y,-x).
Let (x,y) be a point on the xy-plane.
The reflection of (x,y) over:
the line y = b
the point (x,2b - y).
Let (x,y) be a point on the xy-plane.
The reflection of (x,y) over:
the line x = a
the point (2a - x,y).
Let (x,y) be a point on the xy-plane.
The reflection of (x,y) over:
the origin
the point (-y , -x).
What is the quadratic formula?
The formula of standard deviation:
when two sets have the same number of elements:
range ∝ sd
Surface area of Sphere:
4πr2
Sum of the first n integers
[1 , 2, 3, 4, 5, 6]
n = 6
1 + 2 + 3 + 4 + 5 + 6 = 21
Sum of the first n even integers
S = n x (n + 1)
n: number of terms
[2 , 4, 6, 8, 10]
n = 5
2 + 4 + 6 + 8 + 10 = 25
Sum of the first n odd integers
S = n2
n: number of terms
[1, 3, 5, 7]
n = 4
1 + 3 + 5 + 7 = 16
How many factors does exist in square of any prime number?
3
52 : [1 , 5 , 25]
Factor the given quadratic.
7 x2 + x - 66 = 0
Factoring the above quadratic may seem a bit daunting; however, we will use the same quadratics rules we normally follow when factoring a quadratic, with one small wrinkle.
Since we have a coefficient greater than 1 in front of x2, we can find 2 numbers that multiply to -66 and also two numbers that sum to 1 WHEN ONE OF THOSE NUMBERS IS MULTIPLIED BY 7.
We know this because the 7x2 term will break down to x and 7x.
he factors of -66 are:
-66 and 1 or -1 and 66
-33 and 2 or -2 and 33
-22 and 3 or -3 and 22
-11 and 6 or -6 and 11
Since the product of -3 and 7 is -21 and since the sum of -21 and 22 is 1, we can use the terms -3 and 22 for our factored quadratics.
So, we have:
Since the product of -3 and 7 is -21 and since the sum of -21 and 22 is 1, we can use the terms -3 and 22 for our factored quadratics.
So, we have:
7 x2 + x − 66 = 0 ⇒ (7x + 22) (x − 3) = 0
⇒ x = -22 or x = 3
Dividend, divisor, quotient, and remainder are related via the formula …
The product of n consecutive integers will always be devisible by …
Data sufficiency
If point A, which is located at (x, 6), is on a circle in the xy-plane, what is the value of x?
1) The center of the circle is at the origin.
2) The circle has an area of 100π.
E!
A train traveled from Town X to Town Y, covering twice as much distance in the second part of the trip as in the first part. If the average speed of the train during the second part of the trip was twice its average speed during the first part, which of the following is equal to the ratio of the train’s average speed for the entire journey to the train’s average speed during the second half of the trip.
- 1/2
- 1/4
- 1/3
- 2/3
- 3/4
Data sufficiency
5, 9, 11, 11, 13, 17, 17, x, y
What is the median of the list above?
1. x < 11
2. y = 11
We need to determine the value of the median.
Since there is an odd number of terms in this list, we know that the median is the middle number of the list when the terms are written in numerical order.
Statement One Alone:
⇒ x < 11
Statement one may appear to provide insufficient information. However, we can evaluate two scenarios and determine an interval for the possible values of the median.
The maximum possible value of the median can be determined if we assume the greatest possible values for the unknown terms in the list.
- In this case, x is a number slightly less than 11, and y is a number greater than 17.
The numbers in ascending order are {5, 9, x, 11, 11, 13, 17, 17, y}, and the median is 11.
The minimum possible value of the median can be determined if we assume the smallest possible values for the unknown terms in the list.
- In this case, both x and y are numbers much less than 5, and their order doesn’t matter.
The numbers in ascending order are {x, y, 5, 9, 11, 11, 13, 17, 17}, and the median is 11.
Since the maximum and minimum possible values of the median are both equal to 11, the median must be 11.
Statement one alone is sufficient.
Eliminate answer choices B, C, and E.
Statement Two Alone:
⇒ y = 11
We can use the same approach as we used for the analysis of statement one.
The maximum possible value of the median can be determined if we assume the greatest possible value for x.
- In this case, x is a number greater than 17.
The numbers in ascending order are {5, 9, 11, 11, 11, 13, 17, 17, x}, and the median is 11.
The minimum possible value of the median can be determined if we assume the smallest possible value for x.
- In this case, x is a number less than 5.
The numbers in ascending order are {x, 5, 9, 11, 11, 11, 13, 17, 17}, and the median is 11.
Since the maximum and minimum possible values of the median are both equal to 11, the median must be 11.
Statement two alone is sufficient.