GMAT prep exam questions fully solved & updated 2024

What are the first ten prime numbers? 2, 3,5, 7, 11, 13, 17, 19, 23, 29 Sum of two primes All prime numbers are odd, except the number 2. Thus, the sum of any two primes will be even unless one of those primes is the number 2 If a sum of primes is odd, one of those primes must be the number 2 Brainpower Read More Previous Play Next Rewind 10 seconds Move forward 10 seconds Unmute 0:01 / 0:15 Full screen Counting total factors If a number has prime factorization a^w x b^y x c^z (where a, b, and c are all prime), then the number has (w +1)(y + 1)(z + 1) different factors Perfect squares 1) All perfect squares have an odd number of total factors, which always sum up to an odd number 2) Prime factorization of a perfect square contains only even powers of primes Should vs. Must Must = binding obligation Should = moral obligation Relative pronoun rules That - if the clause is essential, it must begin with "that" rather than "which" Who/whom - must modify people Which - cannot modify people Whose - can modify people or things Which/whom - sometimes follow prepositions Where - can modify a noun place but cannot modify metaphorical place (condition, situation, circumstances, arrangement) When - modify a noun event or time; "in which" can also be used instead of when Words used for two things vs. three or more Use between only with two things or people. Use among when talking about three or more things or people Is it ok to insert a comma before because? Acceptable if "because" is a subordinating conjunction; in that case, it can be separated from a main clause by a comma. If there are two possible interpretations without including a comma, there needs to be a comma If "because" is imperative for the rest of the sentence, don't separate it with a comma Also, do not use "because" after "the reason". Use "the reason" plus "that" Incorrect: The reason he left is because he was frustrated Correct: The reason he left is that he was frustrated Like vs. As "Like" is used to compare nouns, pronouns, or noun phrases "As" can be used to compare two clauses Right: Like her brother, Ava aced the test Right: As her brother did, Ava aced the test Comparative and Superlative Do not compare an adverb that ends in -ly by changing the ending to -er Wrong: He runs quicker than Jacob. Right: He runs more quickly than Jacob. Some adverbs that do not end in -ly are made into comparatives by adding -er Right: He runs faster than Jacob. Do not use a comparative adjective unless you have a than in the sentence Wrong: With winter coming, I will have higher energy bills Right: I will have higher bills than last year Pronouns "This" and "These" are never used as standalone pronouns, nor are "that" and "those" Idioms for "ability..." and "capability..." Wrong: ability of doing... Right: ability to do... Right: capability of doing... Compound Subjects If two nouns disagree in number with an "or" conjunction, use the noun closest to the verb to determine agreement Right: Either the manager or the employees take a break Right: Either the employees or the manager takes a break Colon rules What comes before the colon must be able to stand alone as a sentence You can insert "namely" or "that is" after the colon, and the result would still be acceptable Right: I love listening to many kinds of music: namely, classical, rock, rap, and pop Whatever needs explanation should be placed as close to the colon as possible Worse: Three factors affect the rate of a reaction: concentration... Better: The rate of a reaction is affected by three factors: concentration... The clause after the colon must explain what precedes the colon What to consume during test During the break after IR, eat something with protein, fat, and complex carbs. During the break after Quant, drink glucose (coconut water) What property do all terminating decimals share? The simplified denominator of the decimal must contain only 2's and 5's as prime factors. For example, 7/250 is a terminating decimal 0.028, as 250 equals to 2 x 5^3. Fraction 3/30 is also a terminating decimal because 3/30 = 1/10 and denominator 10 = 2 x 5 "view X as Y" or "view X to be Y" ? view X as Y Ex: Many financial experts believe policy makers at the Federal Reserve, now viewing the economy as balanced between moderate growth and low inflation, are almost certain to leave interest rates unchanged. Is "media" singular or plural? Plural Equation for the sum of the degree measures of the n interior angles of a polygon 180(n - 2) Each of 90 students participated in at least one of three track tryouts: high jump, long jump, and 100-meter dash. If 20 students participated in the high jump, 40 students in long-jump, and 60 students in 100-meter dash, and if 5 students participated in all three tryouts, how many students participated in only two of these tryouts? Let x be the number who participated in exactly 1 of the tryouts, y be 2 of tryouts, z be 3 of tryouts. Then x + y + z = 90 and x + 2y + 3z = 120. It is given that z = 5, so x + y = 85 and x + 2y = 105. Thus, y = 20 Equation for the sum of the first n terms in an arithmetic sequence (n/2)(A1 + An) A train traveled from Station A to B at ave speed of 80 km/hr and from Station B to C at ave speed 60 km/hr. If the train didn't stop at Station B, what was the average speed at which the train traveled from Station A to C? 1) The distance that the train traveled from A to B was 4 times the distance from B to C 2) The amount of time it took the train to travel from A to B was 3 times the amount of time that it took the train to travel from B to C Time = Dist / Speed d1/80 is the amt. of time it took to travel from A to B, and d2/60 is the amt. of time it took to travel from B to C. We want to find average speed from A to C, given by Total Dist / Total Time = (d1 + d2) / ( (d1/80) + (d2/60) ) 1) gives d1 = 4d2, which plugged into the above yields an answer 2) gives d1/80 = 3(d2/60), or d1 = 4d2, same as above Each statement alone is sufficient A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 75 kilometers per hour. At what speed, in kilometers per hour, is the car traveling? Traveling at 75 km/hr, the car takes 1/75 hr to travel 1 km. In seconds, this equals 3600/75 = 48 seconds. So this car takes 50 seconds to travel 1 km. In hours, this equals 50/3600 = 1/72 hr. Thus, the speed of the car is 72 km/hr Is x > 10^10? 1) x > 2^34 2) x = 2^35 Take square roots of both. 2^17 = 2^10 x 2^7 = 1024 x 128 > 10^5 = 100,000 Therefore each statement alone is sufficient. What is 2^9? 2^8? List first ten roots of 2. 2^9 = 512. 2^8 = 256. 2, 4, 8, 16, 32, x^6 = 64, x^7 = 128, 256, x^8 = x^9 = 512, x^10 = 1024 List all prime numbers from 1 to 100 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, (101) Procedure for finding the standard deviation of a set 1) Find the difference between each term in the set and the mean of the set 2) Average the squared differences 3) Take the square root of that average A list contains n distinct integers. Are all n integers consecutive? 1) The average of the list with the lowest number removed is 1 more than the average of the list with the highest number removed 2) The positive difference between any two numbers in the list is always less than n Each statement alone is sufficient If two inscribed angles in a circle have the same intercepted arc, are the angles equal? Yes T/F: A right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle True. The reverse is also true...if the diameter of the circle is also the triangle's hypotenuse, then that triangle is a right triangle If x is a positive number, is x an even integer? 1) 3x is an even integer 2) 5x is an even integer 1 and 2 alone are not sufficient, x could be 2/3 or 2, 2/5 or 2. (1) + (2) We have that 3x = even and 5x = even. Subtract 5x - 3x = even - even --> 2x = even --> x = even/2 = integer. We have that 3x = even integer, thus x must be an even integer. Sufficient together If Y1/X1 = Y2/X2 then what is true about the line containing points (X1, Y1) and (X2, Y2)? The line passes through the origin If a line contains points (m, n) and (-m, -n), what is true about the line? The line passes through the origin Area of a triangle given the coordinates of the three vertices of the triangle 1/2 [ X1(Y2 - Y3) + X2(Y3 - Y1) + X3(Y1 - Y2) ] Absolute value Leila is playing a carnival game in which she is given 4 chances to throw a ball through a hoop. If her chance of success on each throw is 1/5, what is the chance that she will succeed on at least 3 of the throws? P = P(exactly 3) + P(exactly 4) = 4C3 x (1/5)^3 x (4/5)^1 + (1/5)^4 = 17 x (1/5)^4 Pascal has 96 miles remaining to complete his cycling trip. If he reduced his current speed by 4 miles per hour, the remainder of the trip would take him 16 hours longer than it would if he increased his speed by 50%. What is his current speed? A) 6, B) 8, C) 10, D) 12, E) 16 Calculating difference in time 96/(x-4) - 96/(3x/2) = 16 6/(x-4) - 4/x = 1 Plug in answer choices to find that x = 8 If x and y are positive integers, which of the following CANNOT be the greatest common divisor of 35x and 20y? A) 5 B) 5(x-y) C) 20x D) 20y E) 35x When finding greatest common divisor, look for a choice that CANNOT be a divisor, which means the quotient should not be an integer. A) 35x/5 = 7, 20y/5 = 4 B) x = 2, y = 1, 5(2-1) = 10 C) 35x/20x = 7/4 --> not an integer C