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# DS-1

Does x/y > 1 mean x>y? You can only infer x>y or x<y if you know the polarity of x and y. If you dont know the polarity, you can only conclude |x| > |y|
The cube of a positive number is positive. What about the cube of a negative number? Negative
In quadratic equation ax^2 + bx + c = 0, if one root is known how can you calculate the other? Assuming (x-m)(x-n) are the factors, then c is the product of -m and -n. Thus knowing either of them, the other can be calculated
If a number is divisible by 6, then is it divisible by 3? Yes. It is divisible by both 2 and 3, and all factors of 6.
If y^2 < 64, then what is the interval of y? -8<y<8
The product of 2 or more odd integers is? Always odd
What strategy to use when you have to test out multiple values in a DS problem? Build a table. It might take an extra 10 seconds, but save you an error
What is the exterior angle theorem? Exterior angle of a traingle is equal to the sum of opposite interior angles of the traingle. The exterior angle is formed by extending a side of the triangle
NC(N-1) = NC1 = ? Value = 1 (Combinations)
What technique to use when you see fractions or equations in the choices? Plugging numbers technique
How many 0's in 60! ? 10 = 2*5. There are as many 0's as the lesser of the powers of 2 & 5 in the prime factorization of 60!. There are fewer 5 in 60!; in all 14 (12 from 5 to 60 and 2 more from 25 and 50). Thus 14 zeros in 60!
If 13th root(x)<0, then is x<0? Yes. Odd roots, as well as oddexponents, preserve the sign of the number inside
Can you take the root of a negative number? No. The number within root has to be positive
When you squarean equation containing a variable, you may create extraneoussolutions. Potential answers need to be plugged back in tothe original equation before squaring and verified.
How to solve geometric sequence problems? Generally, in an exponential sequence, if you know the factor that eachterm is being multiplied by, 23 in this case, and if you know just oneterm, it is sufficient to solve for any other term in the sequence.
What is “Deluxe” Pythagorean Theorem? Use the “Deluxe” Pythagorean Theorem tofind the interior diagonal of a rectangular prism (a box): d² =x² + y² + z².
How can you use Pythgorean triplet 3-4-5 to form other triplets? By multiplying by the same number. For example, 27-36-45 is a triplet
The product of the slopes of perpendicular lines is? -1
In a circle, what is the relation between central angle (angle at center) and inscribed angle (angle at any point of the major arc with the same end points as central angle)? The inscribed angle is half of the central angle
Area of parallelogram = ? Base * Height
What is the units digits of numbers ending in 9? If the number is raised to odd exponent (1,3 etc), the units digit is 9. If exponent is even, units digit is 1.
If a number X is divisible by 12 and 9, is it divisible by 36? Yes. 36=2*2*3*3. So any number divisible by 36 should have at least two 2's and two 3's. 12=2*2*3 and 9=3*3. So any number divisible by 12&9 has at least two 2's and three 3's. Thus it becomes divisble by 36
The square of an integer must also be an integer? Yes
Square = N1 * N2. If N1 is a square of an integer, is N2 also square of an integer? Yes. Try 64 = 4*16, 36 = 4*9, 100 = 4*25
How should you view linear and quadratic equations in DS problems? Linear equation (such as y=x-2) is a line; it has infinite points - thus not sufficient. Quadratic equation (such as y=x^2-2) is a parabola with infinite points; not sufficient. Together, can you find a unique point?
How should you view even and odd numbers in DS problems? Even = 2n and Odd = 2m+1 for some different integers n and m
How are similar triangles related? Similar triangles are proportional in all respects including areas. Sides of the two triangles are in same proportion.
What is the formula when two percentages are successively applied to a number? Say, x is the first %change on and y is the second %change on a number n, then the final % change is given by Final %change = X + Y + (X*Y) / 100
In a trapezium, the diagonal cuts the area into two equal parts. T/F? True. The formula for the area of a trapezium is actually derived by summing the areas of the two triangles formed by the diagonal.
Whenever the question is about 'product' of postive integers and divisors need to be found, what is your strategy? Prime factorize
Can you use simultaneous operations on inequalities? Yes. x<8/9 and y<1/8 can be added up to get x+y<73/72. Both must be < or > for the operation to be possible
When testing for values in DS problems that involve roots & exponents, what value should you not forget to test? 1/4 since special exponent rules apply between 0 and 1
For any set of consecutive integers with an odd number of terms, the sum of the integers is always a multiple of the number of terms. For example, the sum of 1, 2, and 3 (three consecutives -- an odd number) is 6, which is a multiple of 3. For any set of consecutive integers with an even number of terms, the sum of the integers is never a multiple of the number of terms. For example, the sum of 1, 2, 3, and 4 (four consecutives -- an even number) is 10, which is not a multiple of 4
In a right angled triangle, what the product of the smaller sides equal to? It is equal to product of hypotenuse and altitude from right angle's vertex to the hypotenuse
When two cars are moving towards each other, how much distance do they cover before they meet? Combined they would have covered distance equal to the initial distance of separation. And the time both have traveled is the same (t). This principle can be applied even if the track is a circle.
If x and y are non-zero integers, what does x = -3y tell you? That x and y have opposite signs. Therefore |x|=3|y|
The units digit of any integer exponent of seven can be predicted since the units digit of base 7 values follows a patterned sequence of? 7^1 = 7, 7^2 = 9, 7^3 = 3, 7^4 = 1 and then the cycle repeats
What is 10P3? It is 10!/(10-3)! and not 10!/3!
Created by: deepak.bhavi