24. Isosceles triangle: ratio of sides
25. 30:60:90 triangle ratio of sides
26. Diagonal of a square
27. Diagonal of a cube
28. Common Pythagorean triplets
29. For an unbiased die, the no. of possible outcomes.
30. For an unbiased coin toss, the number of possible outcomes.
31. Vertex of a parabola
32. Slope of a horizontal line
33. Slope of a vertical line
34. slopes of perpendicular lines
35. For a circle, circumference/diameter
36. Divisibility by 4
37. Divisibility by 6
38. Divisibility by 8
39. Divisibility by 9.
40. Integer + Integer
41. Integer x Integer
42. To find all the prime factors of a number
43. If you add or subtract multiples of N
44. If N is a divisor of x and of y then
45. Odd +/- Odd
46. Odd +/- Even
47. Odd x Odd
48. Odd x Even
49. Even x Even
50. As the exponent increases, the value of the expression decreases when...
51. Negative exponent
52. When something with an exponent is raised to another power,
53. - x squared
54. (-x) squared
55. All sets of consecutive integers
56. All sets of consecutive multiples.
57. All evenly spaced sets are fully defined if the following parameters are known:
58. For all evenly spaced sets
59. For consecutive integers, the number of terms in the set is equal to
60. For consecutive multiples, the formula for the number of elements in the set is equal to
61. On ANY number line, numbers get bigger
62. The distance between the tick marks on a number line is given by
63. For a number line, 4 tick marks correspond to
64. When questions provide incomplete information about the relative positions of points on a line segment,
65. To construct number lines efficiently and accurately, while remembering to keep track of different possible scenarios
66. ** The ratio of men to women in a room is 3:4 may be written as
67. Car A and Car B are driving directly towards each other.
68. Car A is chasing Car B and catching up.
69. Car A is chasing car B and falling behind.
70. Left.......and met/ arrived
Sue left her office at the same time as Tara left hers. They met sometime later.
71. A runs a race 30 secs faster than B
72. Sue and Tara left at the same time, but Sue arrived home about 1 hour before Tara did.
73. Sue left the office 1 hour after Tara, but they met on the road.
74. The Kiss: Car A and Car B start driving toward each other at the same time. Eventually they meet each other.
75. The QUARREL: Car A and Car B start driving away from each other at the same time...
76. The CHASE: Car A is chasing car B. How long does it take for A to catch up to Car B?
Please note that the cars start at the same time.
77. The ROUND TRIP: Jan drives home to work in the morning, then takes the same route in the evening.
78. The FOLLOWING FOOTSTEPS: Jan drives home to the store along the same route as bill.
79. The HYPOTHETICAL: Jan drove home from work. If she had driven home along the same route 10 miles per hour faster......
80. If an object moves the same distance twice, but at different rates, then the average rate
81. POPULATION PROBLEMS: Some population typically increases by a common factor every time period.
82. For SD problems
83. If you see a problem focusing on CHANGES in the SD ( i.e. when a set is transformed)
85. Adding a constant to each data point in a set i.e. increase by 7 ....
86. Increase each data point by a factor of 7 i.e. each data point is multiplied by 7....
87. A set is divided into 4 quartiles
88. For a normal distribution (Gaussian distribution)..
89. Fundamental Counting Principle
90. The number of ways of putting n distinct objects in order, if there are no restrictions is
If a GRE problem requires you to choose from two or more sets of items from separate pools..
93. To determine the probability that event X and event Y will both occur..
94. To determine the probability that event X or event Y will occur...
95. If on a GRE problem, "success" contains multiple possibilities - especially if the wording contains phrases such as "at least" or "at most"..
96. Be aware of both explicit constraints (restrictions actually stated in the text) and hidden constraints (restrictions implied by real-world aspects of a problem).
97. In most cases, you can maximize or minimize quantities (or optimize schedules, etc.) by
98. For overlapping sets, remember that..
99. For Quantitative comparison questions, to try to prove D..
100. For Quantitative comparisons, Use the Invisible Inequality...
101. Use Quantitiy B as a Benchmark..
102. Try to prove D when..
103. If a quadratic appears in one or both quantities:
104. If a Quadratic appears in the common information:
105. If a Quantitative comparison question with a strange symbol formula contains numbers...
106. If a Quantitative Comparison question with a strange symbol does not contain numbers...
107. It is impossible for an absolute value
108. If you need to maximize an absolute value
109. Sometimes, inequalities are used to..
110. When simplifying complex fractions, look to:
111. When fractions contain exponents and you have to plug in numbers for the exponents...
112. When dealing with percents, always pay attention to
113. The following 3-step process for tackling Geometry QC questions will be emphasized:
114. When Quantity B is a number:
For Geometry QC questions, keywords such as area, perimeter and circumference are good indications that..
115. When quantity B is a number for a geometry QC:
Many geometry QC's will provide enough information to reach a definite conclusion. To solve for the value that you NEED TO KNOW:
116. For Geometry QC questions, remember
117. For geometry QC problems
On questions for which both quantities contain UNKNOWN VALUES...
118. Both quantities unknown
For a Geometry QC question, if a diagram presents a common shape, such as a triangle or a quadrilateral..
For ANY word geometry question, the first step in establishing what you KNOW is the same
120. Word geometry QC
USING NUMBERS is a useful strategy when a Word geometry question..
A very popular theme related to Number properties is...
The most important dichotomy in QC's is
On questions that involve variables and exponents,
To compare the sums of sets of consecutive integers,
125. Whenever you see a word problem on Quantitative comparisons,
On a ratios problem..
In any question that involves two groups that have some kind of average value....
128. The Basic process of solving a Data Interpretation Question
129. The Basic process of solving a Data Interpretation Question
130. The Basic process of solving a Data Interpretation Question
131. The Basic process of solving a Data Interpretation Question
132. The Basic process of solving a Data Interpretation Question
133. The Basic process of solving a Data Interpretation Question
134. The Basic process of solving a Data Interpretation Question
135. Shortcut tips and strategies when attempting data interpretation graphs.
136. For multiple data interpretation graphs...
139. right circular cylinder
142. set of integers
143. lcm of two non-zero integers a and b
144. hcf of 2 non-zero integers a and b is
145. hcf of 2 non-zero integers a and b is
146. a prime number
147. composite number
a prime number
148. for odd order roots
149. for even order roots
150. Domain of x
151. The equation of a circle is given by
152. consider the absolute value function defined by h(x) = lxl
153. In general, for any function h(x) and any positive number c, the graph of h(x) + c is
154. In general, for any function h(x) and any positive number c, the graph of h(x) - c
155. In general, for any function h(x) and any positive number c, the graph of h(x+c)
156. In general, for any function h(x) and any positive number c, the graph of h(x-c)
157. In general, for any function h(x) and any positive number c, the graph of ch(x)
161. Measure of the arc of a circle
162. Isosceles triangle has at least
163. Effect of outliers on range,mean and median
164. Percentiles are mostly used for
165. Measures of position include
166. Measures of dispersion include
167. A measure of dispersion that is not affected by outliers is
168. Measures of central tendency
169. A measure of spread that depends on each number in the list
170. The std deviation is computed by
171. Sample standard deviation is calculated by
172. Standardization is
173. Arithmetic with remainders
174. Mathematical relationship between dividend, divisor, quotient and remainder.
175. For mensuration area problems, the only thing that matters is that
176. The Euclidean distance between two points of the plane with Cartesian coordinates (x1,y1) and (x2,y2) is
177. Total after Percentage change
181. 1/11 or 9/99
182. 3/11 or 27/99
183. Mean ( working definition)
184. 13 squared
185. 14 squared
186. 15 squared
187. 16 squared
188. 17 squared
189. 18 squared
190. 19 squared
200. area of a rhombus
201. For quantitative comparison questions containing a variable
202. For lines with negative slopes in the xy plane you see that for each line that does not pass through the origin
203. For a line that does not pass through the origin, if the x intercept is twice the y intercept you can conclude that
204. When dealing with QC questions that have variables and inequalities....
205. If ab > 0, then
206. When using inequalities (variables) with specified ranges, consider using
207. To solve for the values of a recursive sequence you need to be given...
208. When solving quadratic equations, if you have trouble determining the factors...
209. Rules of exponents when
210. x^a = x^b then
211. If the cube root of x is 9 the what is the value of x?
212. If confused about the negative sign on a number when solving equations or inequalities, it may help to
213. As positive proper fractions are multiplied...
214. A Proper Fraction
215. Remainder must always be less than
216. When you divide an integer by a positive number N, the possible remainders range from
217. If x/y has a remainder of 0 and z/y has a remainder of 3, then what is the remainder of xz/y?
218. 4/5 has a remainder of
219. Can 0 be categorized as odd or even?
220. If f and g are prime numbers, what is f + g?
221. The 10ths digit of the product of two even integers divided by 4
The 10ths digit of the product of an even and and odd integer divided by 4.
222. When is |x-4| equal to 4-x?
223. The average of any set of consecutive integers with an EVEN number of items is
224. If a>b and ab<0 then,
225. Another way to think of |x - 3.5| is
226. Is 6/5n greater or less than n?
227. To simplify complex fractions
228. To switch from an improper fraction to a mixed number
229. To compare fractions and to estimate computations involving fractions
230. When dealing with percents, always pay attention to the size of the original value.
232. If two numbers have a finite sum (396 + 404 = 800 and 398 + 402 = 800)
233. In geometry, for a finite perimeter, the area of a shape is maximized by
234. Third Side Rule
235. Knowing the signs of what you are multiplying or dividing is enough
236. When adding or subtracting, to know the sign of the answer, you need to know
237. For a rectangle (e.g. TV) with a fixed perimeter or even diagonal (both the perimeter and the diagonal depend on width and height)
238. For the Third Side Rule: If the two sides of a triangle are x and y, then the possible values of the third side must lie between
239. For a triangle with 2 GIVEN sides, the area is maximized if
240. For mensuration problems please remember to
241. 21 squared
242. 22 ^ 2
243. 23 ^ 2
244. 24 ^ 2
245. 25 squared
246. For an isosceles right triangle or a 30-60-90 triangle, if you are given the area, then
247. For a circles problem, if asked to calculate the length of a sector, then
248. For circles, arcs may be defined or labeled unusually as
249. When doing calculations on paper
250. When adding or subtracting (especially for simultaneous and other linear equations) make sure that
251. Multiplying the numerator of a positive, proper fraction by a number greater than 1
252. Divisibility by 7
253. Equation for a parabola
254. The "vertex" form of a (regular, vertical) parabola with its vertex at (h, k) is:
255. The "vertex" form of a (sideways, horizontal) parabola with its vertex at (h, k) is:
256. State the vertex and focus of the parabola having the equation (y – 3)^2 = 8(x – 5).
257. State the vertex and directrix of the parabola having the equation (x + 3)^2 = –20(y – 1).
258. Every terminating decimal shares this characteristic
259. If both the numerator and denominator of a fraction are irrational numbers
260. To find the units digit of a product or a sum of integers
261. Which integer values of b would give the number 2002/10^-b a value between 1 and 100?
262. Distance between 2 points (x1,y1) and (x2,y2) on a coordinate system is given by the formula
263. x intercept of a line is obtained when
264. y intercept of a line is obtained when
265. When comparing fractions a shortcut used is cross-multiplication
266. For geometry problems that use the same figure but varying values...
267. (1/2) ^ - 1/2
268. (- 1/2) ^ - 1/2
269. 3 ^ 5.5
270. A great way to solve successive percent problems is to
271. The fastest way to success with percent problems WITH UNSPECIFIED AMOUNTS is to
272. Probability of an event happening
273. For probability tree diagrams
274. For probability tree diagrams
275. 45% of the children in a school have a dog, 30% have a cat, and 18% have a dog and a cat.
What percent of those who have a dog also have a cat?
276. probability questions, with Replacement:
277. For probability questions, without Replacement:
(e.g. marbles in a bag)
278. To determine whether events are dependent or independent
279. The probability of event B given event A equals
280. Probability of event A and event B equals
281. For permutations use
n ^ r
282. For permutations without repetition use
283. Combinations without Repetition
284. Combinations with Repetition
285. For combinatorics with repetition you may verify your answer using
286. If seven people board an airport shuttle with only three available seats, how many different seating arrangements are possible? (Assume that three of the seven will actually take the seats.)
287. If three of seven standby passengers are selected for a flight, how many different combinations of standby passengers can be selected?
288. For permutations with repetition, to reduce the number of available choices
289. For Venn diagrams, if a value is neither given nor able to be calculated, then
290. % Profit/Loss
291. When applying the rules of direct and inverse proportion to fractions
292. relative speed and similar rate problems
293. Yana and Gupta travel for the same amount of time till the time they meet between x and y.
So, the distance covered by them will be
294. 3/4 of a man's usual speed means
295. For a boat traveling in a stream
296. If both 112 and 33 are factors of the number a * 43 * 62 * 1311, then what is the smallest possible value of 'a'?
297. Find the largest five digit number that is exactly divisible by 7, 10, 15, 21 and 28.
298. Greatest common divisor
299. Test of Divisibility by 11
300. If a number 'n' can be expressed as ap * bq, where a and b are prime factors of n, the number of factors of n
301. How many numbers are exactly divisible by 49 between 1 and 5000?
302. For the Pythagorean theorem, remember that
303. Least common multiple of 2 numbers a and b is
304. For percentage problems with unknown values
305. Rs.432 is divided amongst three workers A, B and C such that 8 times A’s share is equal to 12 times B’s share which is equal to 6 times C’s share. How much did A get?
306. When computing the result of successive percent changes and individual percent changes
307. The final value of principal P plus interest at a rate of r, compounded annually for t years is given by
308. Squaring on the online calculator
309. 1 - 0.01
310. 1 - 0.02
311. 1 - 0.03
312. 1 - 0.04
313. 1 - 0.05
314. a/9, ab/99, abc/999 .....
315. If asked to convert a recurring number into a fraction
316. root 3
317. root 2
318. When asked to compare slopes think
319. For negative slopes, a steeper slope means
320. When a quadrilateral is inscribed inside a circle
321. circumference of a circle equals
322. Variables versus smart numbers
323. When an integer is raised to an integer power, it falls into one of 4 possible cases
324. When 2 even numbers are multiplied the product is always
325. Are fractions odd or even numbers?
334. If you are given a set of numbers, of which one is a variable, and you need to calculate the median or change in the median, then
335. After reading the question it may help to scan the answer choices prior to calculation
338. n is an integer and |2n+7| is less than or equal to 10, may also be written as
339. When looking for representative cases for say x^2 - ax + b = 0
340. If a is not the square of an integer, its square root
341. 1/2 (y - 1) = |x - 4| may also be written as
342. Any number (+ve) divided by a proper fraction becomes
343. Any number (+ve) multiplied by a proper fraction becomes
344. GDP/GDP per capita
345. Debt as a percentage of GDP
346. Debt per capita