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{"id": "GMAT Club Math Book 2024 v8_q_19_1", "source_name": "GMAT Club Math Book 2024 v8", "source_file": "GMAT Club Math Book 2024 v8.pdf", "page": 19, "topic_guess": "general", "question_text": "Example #1 (easy)\nIf the remainder is 7 when positive integer n is divided by 18, what is the\nremainder when n is divided by 6?", "options": {"A": "0", "B": "1", "C": "2", "D": "3", "E": "4"}, "correct_answer": null, "solution_text": null}
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{"id": "GMAT Club Math Book 2024 v8_q_19_2", "source_name": "GMAT Club Math Book 2024 v8", "source_file": "GMAT Club Math Book 2024 v8.pdf", "page": 19, "topic_guess": "number_theory", "question_text": "Example #2 (easy)\nIf n is a prime number greater than 3, what is the remainder when n^2 is\ndivided by 12 ?", "options": {"A": "0", "B": "1", "C": "2", "D": "3", "E": "5"}, "correct_answer": null, "solution_text": null}
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{"id": "GMAT Club Math Book 2024 v8_q_20_3", "source_name": "GMAT Club Math Book 2024 v8", "source_file": "GMAT Club Math Book 2024 v8.pdf", "page": 20, "topic_guess": "general", "question_text": "Example #3 (easy)\nWhat is the tens digit of positive integer x ?\n(1) x divided by 100 has a remainder of 30.\n(2) x divided by 110 has a remainder of 30.\n(1) x divided by 100 has a remainder of 30. We have that : 30, 130, 230,\n... as you can see every such number has 3 as the tens digit. Sufficient.\n(2) x divided by 110 has a remainder of 30. We have that : 30, 140, 250,\n360, ... so, there are more than 1 value of the tens digit possible. Not sufficient.", "options": {}, "correct_answer": null, "solution_text": null}
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{"id": "GMAT Club Math Book 2024 v8_q_20_4", "source_name": "GMAT Club Math Book 2024 v8", "source_file": "GMAT Club Math Book 2024 v8.pdf", "page": 20, "topic_guess": "number_theory", "question_text": "Example #5 (medium)\nIf s and t are positive integers such that s/t = 64.12, which of the following\ncould be the remainder when s is divided by t ?", "options": {"A": "2", "B": "4", "C": "8", "D": "20", "E": "45"}, "correct_answer": null, "solution_text": null}
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{"id": "GMAT Club Math Book 2024 v8_q_21_5", "source_name": "GMAT Club Math Book 2024 v8", "source_file": "GMAT Club Math Book 2024 v8.pdf", "page": 21, "topic_guess": "general", "question_text": "Example #6 (medium)\nPositive integer n leaves a remainder of 4 after division by 6 and a remainder of\n3 after division by 5. If n is greater than 30, what is the remainder that n leaves\nafter division by 30?", "options": {"A": "3", "B": "12", "C": "18", "D": "22", "E": "28"}, "correct_answer": null, "solution_text": null}
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{"id": "GMAT Club Math Book 2024 v8_q_22_6", "source_name": "GMAT Club Math Book 2024 v8", "source_file": "GMAT Club Math Book 2024 v8.pdf", "page": 22, "topic_guess": "general", "question_text": "Example #8 (hard)\nWhen 51^25 is divided by 13, the remainder obtained is:", "options": {"A": "12", "B": "10", "C": "2", "D": "1", "E": "0"}, "correct_answer": null, "solution_text": null}
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{"id": "GMAT Club Math Book 2024 v8_q_22_7", "source_name": "GMAT Club Math Book 2024 v8", "source_file": "GMAT Club Math Book 2024 v8.pdf", "page": 22, "topic_guess": "general", "question_text": "Example #9 (hard)\nWhen positive integer x is divided by 5, the remainder is 3; and when x is\ndivided by 7, the remainder is 4. When positive integer y is divided by 5, the\nremainder is 3; and when y is divided by 7, the remainder is 4. If x > y, which of\nthe following must be a factor of x - y?", "options": {"A": "12", "B": "15", "C": "20", "D": "28", "E": "35"}, "correct_answer": null, "solution_text": null}
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{"id": "GMAT Club Math Book 2024 v8_q_23_8", "source_name": "GMAT Club Math Book 2024 v8", "source_file": "GMAT Club Math Book 2024 v8.pdf", "page": 23, "topic_guess": "number_theory", "question_text": "Example #10 (hard)\nIf p, x, and y are positive integers, y is odd, and p = x^2 + y^2, is x divisible by\n4?\n(1) When p is divided by 8, the remainder is 5\n(2) x – y = 3\n(1) When p is divided by 8, the remainder is 5. This implies that .\nSince given that , then -->\n.\nSo, . Now, if then\n and if then\n, so in any case\n --> --> in order to be multiple of 4 must be\nmultiple of 16 but as we see it's not, so is not multiple of 4. Sufficient.\n(2) x – y = 3 --> --> but not sufficient to say whether it's\nmultiple of 4.", "options": {}, "correct_answer": null, "solution_text": null}
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{"id": "GMAT Club Math Book 2024 v8_q_25_9", "source_name": "GMAT Club Math Book 2024 v8", "source_file": "GMAT Club Math Book 2024 v8.pdf", "page": 25, "topic_guess": "algebra", "question_text": "GMAT Club Math Book\nAlgebra\nhttps://gmatclub.com/forum/algebra-101576.html\n Algebra 101\nScope\nManipulation of various algebraic expressions\nEquations in 1 & more variables\nDealing with non-linear equations\nAlgebraic identities\nNotation & Assumptions\nIn this document, lower case roman alphabets will be used to denote variables such as a,b,c,x,y,z,w\nIn general it is assumed that the GMAT will only deal with real numbers ( ) or subsets of such as Integers ( ),\nrational numbers ( ) etc\nConcept of variables\nA variable is a place holder, which can be used in mathematical expressions. They are most often used for two\npurposes :\n(a) In Algebraic Equations : To represent unknown quantities in known relationships. For eg : \"Mary's age is 10\nmore than twice that of Jim's\", we can represent the unknown \"Mary's age\" by x and \"Jim's age\" by y and then\nthe known relationship is \n(b) In Algebraic Identities : These are generalized relationships such as , which says for any\nnumber, if you square it and take the root, you get the absolute value back. So the variable acts like a true\nplaceholder, which may be replaced by any number.\nBasic rules of manipulation", "options": {"A": "When switching terms from one side to the other in an algebraic expression + becomes - and vice versa.", "B": "When switching terms from one side to the other in an algebraic expression * becomes / and vice versa.", "C": "you can add/subtract/multiply/divide both sides by the same amount. Eg.", "D": "you can take to the exponent or bring from the exponent as long as the base is the same."}, "correct_answer": null, "solution_text": null}
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{"id": "GMAT Club Math Book 2024 v8_q_31_10", "source_name": "GMAT Club Math Book 2024 v8", "source_file": "GMAT Club Math Book 2024 v8.pdf", "page": 31, "topic_guess": "fractions_decimals_percents", "question_text": "b) --> . --> . x e { , } and both solutions satisfy the\ncondition.\n(Optional) The following illustration may help you understand how to open modulus at different conditions.", "options": {}, "correct_answer": null, "solution_text": null}
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{"id": "GMAT Club Math Book 2024 v8_q_37_11", "source_name": "GMAT Club Math Book 2024 v8", "source_file": "GMAT Club Math Book 2024 v8.pdf", "page": 37, "topic_guess": "sequences_patterns", "question_text": "Example 4\nFor every integer k from 1 to 10, inclusive, the kth term of a certain sequence is given by\n(-1)^(k+1) *(1/2^k). If T is the sum of the first 10 terms in the sequence then T is\na)greater than 2\nb)between 1 and 2\nc)between 1/2 and 1\nd)between 1/4 and 1/2\ne)less than 1/4.\nSolution\nThe sequence given has first term 1/2 and each subsequent term can be obtained by\nmultiplying with -1/2. So it is a GP. We can use the GP summation formula\n1023/1024 is very close to 1, so this sum is very close to 1/3\nAnswer is d\nExample 5\nThe sum of the fourth and twelfth term of an arithmetic progression is 20. What is the\nsum of the first 15 terms of the arithmetic progression?", "options": {"A": "300", "B": "120", "C": "150", "D": "170", "E": "270"}, "correct_answer": null, "solution_text": null}
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{"id": "GMAT Club Math Book 2024 v8_q_61_12", "source_name": "GMAT Club Math Book 2024 v8", "source_file": "GMAT Club Math Book 2024 v8.pdf", "page": 61, "topic_guess": "word_problems", "question_text": "The ‘how much is left’ construction\nSometimes, the question will give you a total amount that is made up of a number of\nsmaller amounts of unspecified sizes. In this case, just assign a variable to the unknown\namounts and the remaining amount will be what is left after deducting this named amount\nfrom the total.\nConsider the following:\nA hundred-pound order of animal feed was filled by mixing products from Bins A, B and C,\nand that twice as much was added from Bin C as from Bin", "options": {"A": "Then the amount from Bin C was \"2a\", and the"}, "correct_answer": null, "solution_text": null}
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{"id": "GMAT Club Math Book 2024 v8_q_67_13", "source_name": "GMAT Club Math Book 2024 v8", "source_file": "GMAT Club Math Book 2024 v8.pdf", "page": 67, "topic_guess": "word_problems", "question_text": "calculate the rate at which B works: Rate at which B works = .\n‘B prints 5 pages a minute more than printer A’ This means that the difference between\nthe amount of work B and A complete in one minute corresponds to 5 pages. So, let us\ncalculate that difference. It will be \n‘How many pages does the task contain?’ If of the job consists of 5 pages, then the 1\njob will consist of pages.\nExample 4.\nMachine A and Machine B are used to manufacture 660 sprockets. It takes machine A ten\nhours longer to produce 660 sprockets than machine", "options": {"B": "Machine B produces 10% more", "A": "How many sprockets per hour does machine A"}, "correct_answer": null, "solution_text": null}
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{"id": "GMAT Club Math Book 2024 v8_q_81_14", "source_name": "GMAT Club Math Book 2024 v8", "source_file": "GMAT Club Math Book 2024 v8.pdf", "page": 81, "topic_guess": "general", "question_text": "Question:: how many students play exactly two of these sports?\nApply first formula:\n{Total}={Hockey}+{Cricket}+{Football}-{HC+CH+HF}+{All three}+{Neither}\n50=20+15+11-(7+4+5)+{All three}+18 --> {All three}=2;\nThose who play ONLY Hockey and Cricket are 7-2=5;\nThose who play ONLY Cricket and Football are 4-2=2;\nThose who play ONLY Hockey and Football are 5-2=3;\nHence, 5+2+3=10 students play exactly two of these sports.", "options": {}, "correct_answer": null, "solution_text": null}
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{"id": "GMAT Club Math Book 2024 v8_q_84_15", "source_name": "GMAT Club Math Book 2024 v8", "source_file": "GMAT Club Math Book 2024 v8.pdf", "page": 84, "topic_guess": "sets_probability_counting", "question_text": "There are 6 equally possible outcomes when we roll a die. The probability of getting any\nnumber out of 1-6 is .\nAll possibilities: {1,2,3,4,5,6}\nMarbles, Balls, Cards...\nLet's assume we have a jar with 10 green and 90 white marbles. If we randomly choose a\nmarble, what is the probability of getting a green marble?\nThe number of all marbles: N = 10 + 90 =100\nThe number of green marbles: n = 10\nProbability of getting a green marble: \nThere is one important concept in problems with marbles/cards/balls. When the first\nmarble is removed from a jar and not replaced, the probability for the second marble\ndiffers ( vs. ). Whereas in case of a coin or dice the probabilities are always the\nsame ( and ). Usually, a problem explicitly states: it is a problem \nwith replacement or\nwithout replacement.\nIndependent events\nTwo events are independent if occurrence of one event does not influence occurrence of\nother events. For n independent events the probability is the product of all probabilities of\nindependent events:\np = p1 * p2 * ... * pn-1 * pn\nor\nP(A and B) = P", "options": {"A": "* P", "B": "- A and B denote independent events"}, "correct_answer": null, "solution_text": null}
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{"id": "GMAT Club Math Book 2024 v8_q_85_16", "source_name": "GMAT Club Math Book 2024 v8", "source_file": "GMAT Club Math Book 2024 v8.pdf", "page": 85, "topic_guess": "number_theory", "question_text": "Example #3\nQ:There are two sets of integers: {1,3,6,7,8} and {3,5,2}. If Robert chooses randomly\none integer from the first set and one integer from the second set, what is the probability\nof getting two odd integers?", "options": {}, "correct_answer": null, "solution_text": null}
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{"id": "GMAT Club Math Book 2024 v8_q_99_17", "source_name": "GMAT Club Math Book 2024 v8", "source_file": "GMAT Club Math Book 2024 v8.pdf", "page": 99, "topic_guess": "statistics", "question_text": "Example #4\nQ: There is a set A of 19 integers with mean 4 and standard deviation of 3. Now we form\na new set B by adding 2 more elements to the set", "options": {"A": "What two elements will decrease the"}, "correct_answer": null, "solution_text": null}
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{"id": "book 2_q_18_1", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 18, "topic_guess": "general", "question_text": "Try-It #0-1\nA jar is filled with red, white, and blue tokens that are equivalent\nexcept for their color. The chance of randomly selecting a red\ntoken, replacing it, then randomly selecting a white token is the\nsame as the chance of randomly selecting a blue token. If the\nnumber of tokens of every color is a multiple of 3, what is the\nsmallest possible total number of tokens in the jar?\n 9", "options": {"A": "12", "B": "15", "C": "18"}, "correct_answer": null, "solution_text": null}
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{"id": "book 2_q_19_2", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 19, "topic_guess": "general", "question_text": "Try-It #0-3\nIn the diagram to the right, the value\nof x is closest to which of the\nfollowing? \n21", "options": {"A": "2", "D": "1"}, "correct_answer": null, "solution_text": null}
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{"id": "book 2_q_37_3", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 37, "topic_guess": "general", "question_text": "Try-It #0-1\nA jar is filled with red, white, and blue tokens that are equivalent\nexcept for their color. The chance of randomly selecting a red\ntoken, replacing it, then randomly selecting a white token is the\nsame as the chance of randomly selecting a blue token. If the\nnumber of tokens of every color is a multiple of 3, what is the\nsmallest possible total number of tokens in the jar? \n 9", "options": {"A": "12", "B": "15", "C": "18"}, "correct_answer": null, "solution_text": null}
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{"id": "book 2_q_40_4", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 40, "topic_guess": "fractions_decimals_percents", "question_text": "In the very first equation above, each fraction on the\nle is less than 1, so their product is even smaller.\nThe denominators of the three fractions are all the\nsame.\nSo the numerator of the product", "options": {"B": "are out now. The smallest possible total is", "A": "and"}, "correct_answer": null, "solution_text": null}
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{"id": "book 2_q_42_5", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 42, "topic_guess": "general", "question_text": "A jar is filled with red, white, and blue\ntokens …\nBU is alert—what about 0?\nTD: “What about 0? Hmm…the wording at the\nbeginning assumes that there actually are tokens\nof each color. So there can’t be 0 tokens of any\nkind.”", "options": {"A": ". Let’s keep going. Try", "B": ".”", "C": "15", "D": "18", "E": "21"}, "correct_answer": null, "solution_text": null}
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{"id": "book 2_q_43_6", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 43, "topic_guess": "general", "question_text": "Select a white: \n , which is not “select a\nblue”", "options": {"A": "9", "B": "12", "C": ". Try", "D": ".”", "E": "21"}, "correct_answer": null, "solution_text": null}
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{"id": "book 2_q_44_7", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 44, "topic_guess": "coordinate_geometry", "question_text": "Try-It #0-2\nArrow \n , which is a line segment exactly 5 units long with an\narrowhead at A, is constructed in the xy-plane. The x- and y-\ncoordinates of A and B are integers that satisfy the inequalities 0 ≤\nx ≤ 9 and 0 ≤ y ≤ 9. How many different arrows with these\nproperties can be constructed?", "options": {}, "correct_answer": null, "solution_text": null}
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{"id": "book 2_q_46_8", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 46, "topic_guess": "general", "question_text": "There are 10 identical columns: x = 0\nthrough x = 9. 5 × 10 = 50 possible positions\nfor the arrow pointing straight up.\n50 × 2 = 100 possible positions for the\narrow if it points straight up or to the right.\nTD: “Great. I’ve Solved one part. Other\npossibilities?”\nBU notices the square is the same vertically as\nhorizontally. Go right.\nTD: “I get the same result for arrows pointing\nright. 50 more positions. Is that it? Am I done?”\n50 × 4 = 200 possible positions\nBU wonders about “down” and “le .”\nTD: “These arrows can point straight down or\nstraight le , too. Those would have the same\nresult. So there are 50 positions in each of the\nfour directions. Calculate at this point and\nevaluate answers. Eliminate", "options": {"A": "and", "B": ".”", "C": ", but I'm not done.”"}, "correct_answer": null, "solution_text": null}
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{"id": "book 2_q_48_9", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 48, "topic_guess": "general", "question_text": "Try-It #0-3\nIn the diagram to the right, the value of x is closest to which of the\nfollowing?", "options": {}, "correct_answer": null, "solution_text": null}
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{"id": "book 2_q_50_10", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 50, "topic_guess": "general", "question_text": "BU has no idea how to take the square root of\nthis.\nTD: “Neither do I. Let’s try estimating. If x2 is\nabout 3.5, then the square root must be a bit\nless than 2 (since the square root of 4 is 2). 182 is\n324 and 192 is 361, so the answer is around 1.8\nor 1.9.”\nTD: “Answer", "options": {"A": "2", "D": "1"}, "correct_answer": null, "solution_text": null}
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{"id": "book 2_q_51_11", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 51, "topic_guess": "geometry", "question_text": "Alternatively, the question stem asks for an approximate answer, so you\ncan also try estimating from the start. Draw the triangle carefully and start\nwith the same perpendicular line as before. This line is a little shorter than\nthe side of length \n (which is about 1.4). Call the two shorter legs 1.2\nand calculate the hypotenuse. It equals 1.2 multiplied by 1.4, or\napproximately 1.7. (Bonus question: How can you estimate that math\nquickly? Answer below.)\nNow, examine the answer choices using 1.4 for \n and 1.7 for \n :\nThey’re all close, but you can pretty confidently eliminate answers", "options": {"A": "2", "B": "1.7", "C": "1.4", "D": "1"}, "correct_answer": null, "solution_text": null}
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{"id": "book 2_q_58_12", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 58, "topic_guess": "number_theory", "question_text": "Try-It #1-1\nx = 910 − 317 and \n is an integer. If n is a positive integer that has\nexactly two factors, how many different values for n are possible? \nGlance. This is a PS problem. The answers are numbers but in written form;\nthis format is reserved for problems that ask for the number of numbers or\nnumber of possibilities for something. The numbers are small.\nRead. Dive into the text. Here are some possible answers to the Pólya\nquestions:\nWhat\nexactly is\nthe\nproblem\nasking\nfor?\nThe number of possible values for n.\nThis means that n might have multiple possible values. In fact, it probably can\ntake on more than one value.\nI may not need these actual values. I just need to count them.\nWhat are\nthe\nquantities\nI care\nabout?\nI’m given x and n as variables. These are the quantities I care about.\nOne", "options": {"A": "Two", "B": "Three", "C": "Four", "D": "Five"}, "correct_answer": null, "solution_text": null}
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| 30 |
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{"id": "book 2_q_65_13", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 65, "topic_guess": "sequences_patterns", "question_text": "Try-It #1-2\n for all integer values of n greater than 1. If S1 = 1,\nwhat is the sum of the first 61 terms in the sequence?\nNobody is going to write out all 61 terms and then add them up in two minutes.\nThere must be a pattern. The recursive definition of Sn doesn’t yield any secrets\nupon first glance. So write out the early cases in the sequence, starting at n = 1\nand looking for a pattern:\n−48", "options": {"A": "−31", "B": "−29", "C": "1", "D": "30"}, "correct_answer": null, "solution_text": null}
|
| 31 |
+
{"id": "book 2_q_67_14", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 67, "topic_guess": "word_problems", "question_text": "Try-It #1-3\nTruck A is on a straight highway heading due south at the same time\nTruck B is on a different straight highway heading due east. At 1:00\np.m., Truck A is exactly 14 miles north of Truck B. If both trucks are\ntraveling at a constant speed of 30 miles per hour, at which of the\nfollowing times will they be exactly 10 miles apart?\n1:10 p.m.", "options": {"A": "1:12 p.m.", "B": "1:14 p.m.", "C": "1:15 p.m.", "D": "1:20 p.m."}, "correct_answer": null, "solution_text": null}
|
| 32 |
+
{"id": "book 2_q_70_15", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 70, "topic_guess": "number_theory", "question_text": "Try-It #1-4\nIf x and y are positive integers and \n is the square of an odd\ninteger, what is the smallest possible value of xy ?\nAs you read, jot down the given information.\nNote that you might not immediately write down the square of an odd integer\ninfo if you still have to puzzle out what it means:\nWhat does the square of an odd integer look like? List out a few examples, on\npaper or in your head:\n 1", "options": {"A": "8", "B": "10", "C": "15", "D": "28"}, "correct_answer": null, "solution_text": null}
|
| 33 |
+
{"id": "book 2_q_78_16", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 78, "topic_guess": "word_problems", "question_text": "4. A rectangular solid is changed such that the width and length are\neach increased by 1 inch and the height is decreased by 9 inches.\nDespite these changes, the new rectangular solid has the same\nvolume as the original rectangular solid. If the width and length of\nthe original rectangular solid are equal and the height of the new\nrectangular solid is 4 times the width of the original rectangular\nsolid, what is the volume of the rectangular solid?\n 18", "options": {"A": "50", "B": "100", "C": "200", "D": "400"}, "correct_answer": null, "solution_text": null}
|
| 34 |
+
{"id": "book 2_q_95_17", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 95, "topic_guess": "algebra", "question_text": "Andra, Elif, and Grady each invested in a certain stock. Andra\ninvested q dollars, which was 40% more than Elif invested. If Elif\ninvested 25% less than Grady invested, what was the total amount\ninvested by all three, in terms of q ?\nThis problem can be solved algebraically: write a couple of equations and\nsolve for all three variables, then add them up. A glance at the answers,\nthough, indicates that the algebra is likely to get messy. Instead, choose a real\nnumber and solve the problem arithmetically.\nIf you’ve made it to the GMAT Advanced Quant book, then you have likely\nused this strategy before (or at least learned about it). At times, you may have\nbeen frustrated because this technique didn’t actually seem easier than doing\nthe math algebraically. If so, here’s the missing piece: you need to learn how\nto choose smart numbers in the best possible way.\nMost of the time, you’re going to choose for the variable given (in this case, q).\nIn some cases, though, starting with the given variable doesn’t make your life\nany easier. The problem above actually has three unknowns: one for Andra,\none for Elif, and one for Grady. Take a look at the relationship between those\nunknowns before you decide which one is the best starting point.\n2q", "options": {}, "correct_answer": null, "solution_text": null}
|
| 35 |
+
{"id": "book 2_q_96_18", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 96, "topic_guess": "general", "question_text": "Andra invests 40% more than Elif. For just these two, it would be easier to pick\na number for Elif and then calculate Andra’s amount.\nElif invests 25% less than Grady. For these two, it is easier to start with Grady\nand then calculate Elif. As a result, start with Grady, then find Elif, then find\nAndra.\nIf Grady invests $100, then Elif invests 25% less, or $75. Andra invests 40%\nmore than Elif, or $75 + $30 = $105. Make sure to note on your scrap paper\nthat q = 105.\nCollectively, the three invest $100 + $75 + $105 = $280. Find the answer choice\nthat matches $280:\nThe correct answer is", "options": {"A": "Eliminate.", "B": "Eliminate.", "C": ". Eliminate.", "D": "Correct!"}, "correct_answer": null, "solution_text": null}
|
| 36 |
+
{"id": "book 2_q_98_19", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 98, "topic_guess": "number_theory", "question_text": "Try-It #2-2\nIf \n , which of these integers could be the value of z ?\nLook at all of those fractions! Solving for z algebraically in this problem would\nnot be easy. Instead, notice two important clues: the problem asks for the\nvalue of a single variable and the answer choices offer nice-and-easy integers.\nWork backwards! People o en start at the beginning, with choice", "options": {"A": "1", "B": "2", "D": "4", "C": "3"}, "correct_answer": null, "solution_text": null}
|
| 37 |
+
{"id": "book 2_q_99_20", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 99, "topic_guess": "algebra", "question_text": "Try-It #2-3\nA certain college party is attended by both male and female students.\nThe ratio of male-to-female students is 3 to 5. If 5 of the male\nstudents were to leave the party, the ratio would change to 1 to 2.\nHow many total students are at the party?\nOf course, you could set up equations for the unknowns in the problem and\nsolve them algebraically. However, the numbers in the answers are pretty\nstraightforward integers. Try Working Backwards.\nAgain, begin with answer", "options": {"B": "48", "D": "90", "A": "30", "C": "80"}, "correct_answer": null, "solution_text": null}
|
| 38 |
+
{"id": "book 2_q_100_21", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 100, "topic_guess": "fractions_decimals_percents", "question_text": "3. TEST CASES\nIn the original ratio, you can use an unknown multiplier to represent\nthe total number of students: 3x + 5x = 8x. If there are 30 students\ntotal, then the unknown multiplier is \n = 3.75, leaving you with a\nnon-integer number of students. This is impossible, so this answer\nmust be incorrect.", "options": {"B": "If there are 24 total students, then the unknown multiplier is 3: there", "A": "If there are 80 students total, then the unknown multiplier is 10, so"}, "correct_answer": null, "solution_text": null}
|
| 39 |
+
{"id": "book 2_q_101_22", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 101, "topic_guess": "strategy", "question_text": "Some problems allow you to choose real numbers to solve, but you can’t\nchoose just one set of numbers as you do when you choose smart numbers.\nRather, you have to test multiple scenarios to get yourself to the one correct", "options": {}, "correct_answer": null, "solution_text": null}
|
| 40 |
+
{"id": "book 2_q_102_23", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 102, "topic_guess": "general", "question_text": "n n3 − n\nCase 1 1 0\nTry your next case, ignoring answers", "options": {"B": "Yes, 0 is a multiple of 6. (0 is a multiple of any number.)", "D": "Yes, 0 does not have more than two prime factors.", "C": "Yes, 6 does not have more than two distinct prime factors. (The prime", "A": "Yes, 6 is a multiple of 6."}, "correct_answer": null, "solution_text": null}
|
| 41 |
+
{"id": "book 2_q_103_24", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 103, "topic_guess": "general", "question_text": "n n3 − n\nCase 3 5 120\nThe correct answer is", "options": {"C": "No, 120 does have more than two distinct prime factors. (The prime", "B": "and", "D": ".", "A": "."}, "correct_answer": null, "solution_text": null}
|
| 42 |
+
{"id": "book 2_q_105_25", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 105, "topic_guess": "fractions_decimals_percents", "question_text": "Try-It #2-5\nThe percent change from 29 to 43 is approximately what percent of\nthe percent change from 43 to 57 ?\nIn this case, the question stem straight up tells you that you can estimate. Any\ntime you see the word approximately (or a synonym), definitely do not try to\nsolve for the exact", "options": {}, "correct_answer": null, "solution_text": null}
|
| 43 |
+
{"id": "book 2_q_107_26", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 107, "topic_guess": "fractions_decimals_percents", "question_text": "Try-It #2-6\n is equivalent to which of the following?\nAt first glance, it appears that precise long division is necessary. The answer\nchoices are very close together, making estimation difficult. However, with\nsome manipulation and factoring, the solution is much more straightforward.\nThe key to factoring this fraction is to move the decimals of both the\nnumerator and denominator three places to the right so that you’re dealing\nwith integers. Then you might notice that 3,507 is divisible by 7 (3,500 and 7\nare both divisible by 7, providing a clue that you may be able to factor out 7).\nMoreover, 10,020 is divisible by 10 and by 2 (10,020 ends in a 0, and 1,002 is\neven):\nThe correct answer is", "options": {"A": "0.3505", "B": "0.3509", "C": "0.351", "D": "0.3527"}, "correct_answer": null, "solution_text": null}
|
| 44 |
+
{"id": "book 2_q_108_27", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 108, "topic_guess": "general", "question_text": "Alternatively, you might observe that 10.02 is very slightly larger than 10.\nTherefore, the correct answer will be slightly smaller than\n Guess between choices", "options": {"A": "and", "B": "."}, "correct_answer": null, "solution_text": null}
|
| 45 |
+
{"id": "book 2_q_108_28", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 108, "topic_guess": "general", "question_text": "Try-It #2-7\nWhat is the value of \nSince 102 is extremely small compared to 105, and the choices are somewhat\nspread out, estimate:\nNotice that by ignoring the 102 term, you made the denominator slightly\nlarger than it originally was. Therefore, 0.81918 is slightly smaller than the\ncorrect answer, 0.82. The correct answer is", "options": {"D": "0.81", "A": "8.02", "B": "0.89", "C": "0.82"}, "correct_answer": null, "solution_text": null}
|
| 46 |
+
{"id": "book 2_q_109_29", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 109, "topic_guess": "algebra", "question_text": "Try-It #2-8\nA shoe cobbler charges n dollars to repair a single pair of loafers.\nTomorrow, he intends to earn $240 repairing loafers. If he were to\nreduce his fee per pair by $20, he would have to repair an additional\npair of the loafers to earn the same amount of revenue. How many\npairs of loafers does he intend to repair tomorrow?\nThe problem may not seem too bad . . . until you try to set it up algebraically.\nAssign x to represent the number of pairs of loafers the cobbler intends to\nrepair tomorrow. Using the equation for revenue gives you the following:\nFurthermore, reducing his fee by $20 would result in the need to repair an\nadditional pair of shoes for the same amount of revenue gives you the\nfollowing:\n1", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": null, "solution_text": null}
|
| 47 |
+
{"id": "book 2_q_113_30", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 113, "topic_guess": "fractions_decimals_percents", "question_text": "Try-It #2-9\nAt a certain high school, the junior class is twice the size of the\nsenior class. If \n of the seniors and \n of the juniors study\nJapanese, what fraction of the students in both classes do not study\nJapanese?\nNote that two pairs of answers each add up to 1: \n , and\n. Answer", "options": {}, "correct_answer": null, "solution_text": null}
|
| 48 |
+
{"id": "book 2_q_115_31", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 115, "topic_guess": "word_problems", "question_text": "This strategy can sometimes be used in combination with an answer pairs\nstrategy, as pairs of answers are o en composed of a high and a low value.\nIn the previous problem, for example, \n of the seniors and \n of the\njuniors study Japanese. Therefore, somewhere between \n and \n of the\nstudents overall, or less than half, must study Japanese. This implies that\nthe fraction of students who do not study Japanese must be more than\nhalf. You could eliminate answer choices", "options": {"A": ",", "B": ", and", "C": "because each of"}, "correct_answer": null, "solution_text": null}
|
| 49 |
+
{"id": "book 2_q_115_32", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 115, "topic_guess": "statistics", "question_text": "Try-It #2-10\nThe eSoroban device is available in two colors, orange and green.\nIn 2013, 60% of the eSoroban devices sold were purchased by\nwomen, \n of whom purchased the orange device. If an equal\nnumber of orange and green eSoroban devices were sold in 2013,\nwhat fraction of men who purchased an eSoroban in\n2013 purchased the green device?", "options": {}, "correct_answer": null, "solution_text": null}
|
| 50 |
+
{"id": "book 2_q_117_33", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 117, "topic_guess": "general", "question_text": "Try-It #2-11\nIf x □ y is defined to equal \n for all x and y, then (−1 □ 2) □ 3 is\nequivalent to which of the following?", "options": {"C": "−"}, "correct_answer": null, "solution_text": null}
|
| 51 |
+
{"id": "book 2_q_119_34", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 119, "topic_guess": "geometry", "question_text": "Try-It #2-12\nIn the diagram to the right, equilateral\ntriangle ADE is drawn inside square\nBCDE. A circle is then inscribed inside\ntriangle ADE. What is the ratio of the area\nof the circle to the area of the square?\nIf a Problem Solving question does not say that the diagram is not drawn to\nscale, then the diagram is drawn to scale. The circle is about \n the height\nof the square and about \n the width. Therefore, the area of the circle\nshould be approximately \n of the area of the square. Eliminate any answer\nchoices that are far away from that estimate:\nOk\nOn the high side\nToo high", "options": {}, "correct_answer": null, "solution_text": null}
|
| 52 |
+
{"id": "book 2_q_122_36", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 122, "topic_guess": "general", "question_text": "2. If x < 10, y < 8, and y < x, what must be true?\nxy < 80I.\nII.\nx 2 + y 2 > 1III.\nNone", "options": {"A": "II only", "B": "III only", "C": "I and II only", "D": "II and III only"}, "correct_answer": null, "solution_text": null}
|
| 53 |
+
{"id": "book 2_q_124_37", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 124, "topic_guess": "general", "question_text": "7. In a certain clothing store, the most expensive pair of socks sells for\n$1 less than twice the price of the cheapest pair of socks. A\ncustomer notices that for exactly $18, she can buy three fewer pairs\nof the most expensive socks than the cheapest socks. What could\nbe the number of pairs of the cheapest socks she could have\npurchased?\n 3", "options": {"A": "5", "B": "6", "C": "12", "D": "36"}, "correct_answer": null, "solution_text": null}
|
| 54 |
+
{"id": "book 2_q_126_38", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 126, "topic_guess": "general", "question_text": "Without solving problems 13–16, which answers could you confidently\neliminate and why?\nNone", "options": {"A": "II only", "B": "III only", "C": "I and II only", "D": "II and III only"}, "correct_answer": null, "solution_text": null}
|
| 55 |
+
{"id": "book 2_q_126_39", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 126, "topic_guess": "number_theory", "question_text": "12. The integer k is positive but less than 400. If 21k is a multiple of 180,\nhow many unique prime factors does k have?\nOne", "options": {"A": "Two", "B": "Three", "C": "Four", "D": "Five"}, "correct_answer": null, "solution_text": null}
|
| 56 |
+
{"id": "book 2_q_127_40", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 127, "topic_guess": "fractions_decimals_percents", "question_text": "15. In the 7-inch square to the right, another\nsquare is inscribed. What fraction of the\nlarger square is shaded?", "options": {}, "correct_answer": null, "solution_text": null}
|
| 57 |
+
{"id": "book 2_q_130_41", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 130, "topic_guess": "general", "question_text": "does not have to be true. Eliminate answers", "options": {"B": "and", "E": ".", "C": "and", "A": "."}, "correct_answer": null, "solution_text": null}
|
| 58 |
+
{"id": "book 2_q_133_43", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 133, "topic_guess": "general", "question_text": "# Cheap Pairs\n(c)\n$c Pairs\n # e Pairs (c −\n3)\n$e Pairs\n Match?\n$e = 2($c) − 1?", "options": {"B": "is incorrect. Note that you don’t actually have to figure out", "A": "and", "C": "are also probably not correct answers. Try answer", "D": "makes the final equation work, so it is the correct"}, "correct_answer": null, "solution_text": null}
|
| 59 |
+
{"id": "book 2_q_135_44", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 135, "topic_guess": "general", "question_text": ", or \n . Therefore, x = −1.\nTesting choices is fast, too. In this case,", "options": {"B": "and", "D": "are both fractions,", "A": ",", "C": ", and", "E": "instead."}, "correct_answer": null, "solution_text": null}
|
| 60 |
+
{"id": "book 2_q_136_45", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 136, "topic_guess": "general", "question_text": "does not have to be true. Eliminate answer", "options": {"D": ".", "A": "and", "C": ".", "E": "and choose correct answer", "B": "."}, "correct_answer": null, "solution_text": null}
|
| 61 |
+
{"id": "book 2_q_218_48", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 218, "topic_guess": "algebra", "question_text": "This tactic may seem identical to the previous one, but it is not. Notice in\nthis example that statement (1) does not determine whether y is positive or\nnegative, and statement (2) does not even include z. Therefore, neither\nstatement is a subset of the other.\nThat said, the fact that y is negative does not change anything in statement\n(1), because regardless of the value of y, z will remain the same if you swap\ny and −y. If y = 4, then you’d get 4x + (−4)x = z. If y = −4, then you’d get (−4)x +\n4x = z. Those equations are the same! The sign of y doesn’t matter because\ny and −y are symmetric. So knowing the sign of y adds no information to\nstatement (1).\nNote that in this example,", "options": {"A": ",", "B": ",", "D": ", and", "E": "are all still possible answers,", "C": "can be eliminated."}, "correct_answer": null, "solution_text": null}
|
| 62 |
+
{"id": "book 2_q_219_50", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 219, "topic_guess": "general", "question_text": "Try-It #4-13\nIf \n and ab ≠ 0, what is the value of K ?\nYou can prove that the two statements combined are sufficient without\nactually doing any math. If you wanted to, you could plug the value of a\nfrom statement (1) into statement (2) to solve for the value of b. Then, you\ncould plug those values into the question to solve for K.\nImmediately be skeptical. Answer", "options": {"C": "should seem too easy. A er all, you", "A": ",", "B": ", and", "D": ". In some problems, the individual statements may"}, "correct_answer": null, "solution_text": null}
|
| 63 |
+
{"id": "book 2_q_223_51", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 223, "topic_guess": "general", "question_text": "Try-It #4-15\nIs xy < 1 ?\nStatement (1) might imply that \n , but only if x is positive. If it is\nnegative, you would need to flip the sign: \n . You need to know the\nsign of x—information that is provided in statement (2). The correct answer\nis", "options": {"C": ".", "A": "or", "B": "trap, in that you might fail"}, "correct_answer": null, "solution_text": null}
|
| 64 |
+
{"id": "book 2_q_228_52", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 228, "topic_guess": "general", "question_text": "2.\nSpot One Statement Inside the Other (High): If a narrow statement is\ncompletely contained within a broader statement, then eliminate", "options": {"C": "and “broader statement only” (either", "A": "or", "B": ")."}, "correct_answer": null, "solution_text": null}
|
| 65 |
+
{"id": "book 2_q_246_53", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 246, "topic_guess": "statistics", "question_text": "9.\nFor x = 7, 8, or 9, set A contains two integers that are within the range 1\nto 100: x and x2. In all three cases, x3 and x4 are outside of the range.\nAlso, set B contains four integers that are within the range, but one of\nthem, x itself, is also contained in set A. So in every case in which x is\nbetween 5 and 10, there are exactly five distinct integers in the range\nthat are contained in one or both sets.\nThe correct answer is", "options": {"C": "."}, "correct_answer": null, "solution_text": null}
|
| 66 |
+
{"id": "book 2_q_284_54", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 284, "topic_guess": "sequences_patterns", "question_text": "6. In sequence A, A1 = 1, A2 = 100, and the value of An is strictly\nbetween the values of An – 1 and An – 2 for all n ≥ 3. Which of the\nfollowing must be true? \nA100 < A200 < A300 < A400", "options": {"A": "A100 < A300 < A400 < A200", "B": "A200 < A400 < A300 < A100", "C": "A400 < A200 < A300 < A100", "D": "A400 < A300 < A200 < A100"}, "correct_answer": null, "solution_text": null}
|
| 67 |
+
{"id": "book 2_q_286_55", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 286, "topic_guess": "general", "question_text": "The sum of the first 10 terms of S is\nBetween −1 and", "options": {"A": "Between ", "B": "Between 0 and", "C": "Between ", "D": "Greater than 1"}, "correct_answer": null, "solution_text": null}
|
| 68 |
+
{"id": "book 2_q_313_56", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 313, "topic_guess": "algebra", "question_text": "In contrast, when you subtract these two templates, the end terms cancel,\nleaving the middle term:\n Factored\n Distributed\nSquare of a Sum (a + b)2 = a2 + 2ab + b2\n+ Square of a Difference (a − b)2 = a2 − 2ab + b2\n \nSubtraction: (a + b)2 − (a − b)2 = 0 + 4ab + 0\nThis is handy for simplification. Also, whenever you see the sum of two\nsquares (a2 + b2), which is not itself a Quadratic Template, remember that it\ncan be derived from this sum of two templates.\nTry It #6-5\nWhat is the sum of 9,9992 and 10,0012?\n99,980,001", "options": {"A": "199,999,998", "B": "200,000,002", "C": "399,999,996", "D": "400,000,004"}, "correct_answer": null, "solution_text": null}
|
| 69 |
+
{"id": "book 2_q_336_57", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 336, "topic_guess": "fractions_decimals_percents", "question_text": "Try-It #7-1\nA rectangular wooden dowel measures 4 inches by 1 inch by 1 inch.\nIf the dowel is painted on all surfaces and then cut into \n-inch\ncubes, what fraction of the resulting cube faces are painted?\nIf you draw a picture, this problem becomes a matter of counting:", "options": {}, "correct_answer": null, "solution_text": null}
|
| 70 |
+
{"id": "book 2_q_358_59", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 358, "topic_guess": "statistics", "question_text": "The monthly sales (in thousands of $) at a certain restaurant for the past two\nyears are given in the chart above. If the standard deviation of the monthly\nsales is greater this year than last year, which of the following are possible\nvalues for x and y ?\nExcept for x and y, the two lists of monthly sales numbers are identical, so focus\nexclusively on those terms that changed: 9.5 and 12.5 from last year were replaced by x\nand y this year. If this year’s standard deviation is greater, then this year’s numbers\nmust be more spread out from the mean than last year’s. The numbers are close\nenough together to indicate that the average should be somewhere around 11.\nVisually, here are the interesting terms from last year:\nThis problem does not require actual computation of the standard deviation using the\nnew x and y values. The math would be too complex to complete in two minutes.\nInstead, determine visually which x and y values increase the standard deviation: the\npair of x and y values that are farther from the mean than are 9.5 and 12.5 will increase\nthe standard deviation.\n9 and 12.5", "options": {"A": "10 and 11", "B": "10 and 12.5", "C": "11 and 11", "D": "11 and 12.5"}, "correct_answer": null, "solution_text": null}
|
| 71 |
+
{"id": "book 2_q_359_60", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 359, "topic_guess": "statistics", "question_text": "Try-It #7-11\nA list of 12 test scores has an average (arithmetic mean) of 500 and a standard\ndeviation of 50. Which of the following lists of additional test scores, when\ncombined with the original list of 12 test scores, must result in a combined list\nwith a standard deviation less than 50 ?\n6 test scores with average of 450 and standard deviation of 50", "options": {"A": "6 test scores with average of 500 and standard deviation of 25", "B": "6 test scores with average of 550 and standard deviation of 25", "C": "12 test scores with average of 450 and standard deviation of 25", "D": "2 test scores with average of 550 and standard deviation of 50"}, "correct_answer": null, "solution_text": null}
|
| 72 |
+
{"id": "book 2_q_360_61", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 360, "topic_guess": "statistics", "question_text": "It is not generally true that all of the terms in a list are within 1 standard deviation of the\nmean. However, standard deviation is a measure of the spread of the terms of a list, so\nyou could represent the original list of scores this way:\nThe oval spans ±1 standard deviation from the mean, where many of the scores will\nlikely be. This simplification is acceptable as long as you represent all of the other lists\nthe same way so that you can compare the relative effects of the new test scores\nsystematically.\nFor each of the answer choices, overlay the representative ovals for the new data on top\nof the oval for the original data:", "options": {}, "correct_answer": null, "solution_text": null}
|
| 73 |
+
{"id": "book 2_q_364_62", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 364, "topic_guess": "statistics", "question_text": "In a certain lottery drawing, five balls are selected from a tumbler in which\neach ball is printed with a different two-digit positive integer. If the average\n(arithmetic mean) of the five numbers drawn is 56 and the median is 60, what\nis the greatest value that the lowest number selected could be?\nThe goal is to maximize the value of the lowest-numbered ball. All balls contain a two-\ndigit positive integer, and none of the balls have the same number. The problem\nprovides enough information to calculate the sum and to lay out a visual listing of the\nnumbers:\nIn order to maximize the value of the first (lowest) number in the set, what do you need\nto do to the other numbers?\nYou’d want to minimize them. Select the smallest numbers that you can for the\nremaining slots:\nIn some problems, you might actually make different slots equal to each other (e.g., the\nthree largest numbers could be 60, 60, and 60). This problem, though, specifies that the\n43", "options": {"A": "48", "B": "51", "C": "53", "D": "56"}, "correct_answer": null, "solution_text": null}
|
| 74 |
+
{"id": "book 2_q_365_63", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 365, "topic_guess": "statistics", "question_text": "Try-It #7-14\nThe average (arithmetic mean) of six numbers is 18 and the median of the six\nnumbers is 16. What is the minimum possible value for the greatest number in\nthe list?\n19", "options": {"A": "20", "B": "21", "C": "22", "D": "23"}, "correct_answer": null, "solution_text": null}
|
| 75 |
+
{"id": "book 2_q_367_64", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 367, "topic_guess": "statistics", "question_text": "Try-It #7-15\nJake 51\nKeri 63\nLuke 15\nMia 38\nNora 22\nThe table above shows the number of points held by five players of a certain\ngame. If an integer number of Keri’s points were taken from her and given to\nLuke, and the median score of the five players increased, how many points\nwere transferred from Keri to Luke?\nThe key to this problem is that by taking enough points from Keri and giving them to\nLuke, the median of the list can change.\n23", "options": {"A": "24", "B": "25", "C": "26", "D": "27"}, "correct_answer": null, "solution_text": null}
|
| 76 |
+
{"id": "book 2_q_372_65", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 372, "topic_guess": "word_problems", "question_text": "Anton and Lena start at the same point on a circular track,\nmeasuring 10 meters in diameter, and begin walking\ncounterclockwise at the same time, with Anton walking more\nquickly than Lena. When Anton has traveled exactly halfway around\nthe track, they both stop walking. They then observe that the\ndistance between them along a straight line measures exactly \n meters, as shown above. What fraction of the track has Lena\ncovered?", "options": {}, "correct_answer": null, "solution_text": null}
|
| 77 |
+
{"id": "book 2_q_373_66", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 373, "topic_guess": "coordinate_geometry", "question_text": "10. \nA square is drawn in the coordinate plane with its vertices at the\npoints (–2, –2), (–2, 6), (6, 6), and (6, –2), and a non-vertical line is\ndrawn that passes through the point (0, 4). The portion of the\ncoordinate plane that lies within the square, but above the line, is\nthen shaded as shown above. If A is the area of the shaded region in\nsquare units, which of the following specifies all the possible values\nof A ?\n8 ≤ A ≤ 16", "options": {"A": "8 ≤ A < 48", "B": "16 ≤ A< 48", "C": "8 < A ≤ 32", "D": "16 < A ≤ 32"}, "correct_answer": null, "solution_text": null}
|
| 78 |
+
{"id": "book 2_q_376_67", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 376, "topic_guess": "general", "question_text": "There is a repeating cycle of four numbers. Starting at 5 on the number line,\nthe ant moves le 1, then right 6, then le 2, then right 7, which takes it to 15\non the number line. That is, the ant walks a total of 1 + 6 + 2 + 7 = 16 units to\nmove from 5 to 15. Then it walks another 16 units to move from 15 to 25, from\n25 to 35, and from 35 to 45. In total, the ant walks 4(16) = 64 units to move\nfrom 5 to 45.\nTo get from 45 to 50, the ant first walks one unit le to 44, then six units right\nto 50. In total, the ant walks 64 + 1 + 6 = 71 units to move from 5 to 50.\nFinally, add the five units it walks from the beginning: 71 + 5 = 76. \nIt is also possible to estimate the", "options": {}, "correct_answer": null, "solution_text": null}
|
| 79 |
+
{"id": "book 2_q_394_70", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 394, "topic_guess": "general", "question_text": "Where to Start\nSTARTING AT THE BEGINNING\nAs you contemplate the logical order of steps, you might feel less confident\nwith the second stage than with the first. If so, go ahead and start at the\nbeginning. Just articulate very clearly, “What intermediate result will I get\nonce I’m finished with the first part of the problem?”\nBegin by defining set", "options": {"A": "Set A consists of four consecutive integers, such as"}, "correct_answer": null, "solution_text": null}
|
| 80 |
+
{"id": "book 2_q_395_71", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 395, "topic_guess": "statistics", "question_text": "Set A Scenarios Set B Range\n1, 2,\n3, 4\nAll values increased by 10% 1.1, 2.2, 3.3,\n4.4\n4.4—1.1 =\n3.3\n1, 2,\n3, 4\nSmallest value increased by 10%, other values\ndecreased by 10%\n1.1, 1.8, 2.7,\n3.6\n3.6—1.1 =\n2.7\nSince different ranges are possible, the statement is insufficient. Eliminate\nanswers", "options": {"A": "and", "D": ". "}, "correct_answer": null, "solution_text": null}
|
| 81 |
+
{"id": "book 2_q_396_72", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 396, "topic_guess": "general", "question_text": "Now, put the two statements together. One option is to try a few different\ncases, making sure to increase the smallest integer in set A and decrease\nthe greatest integer in set", "options": {"A": "One of the two cases used for statement (1)", "B": "If two of the"}, "correct_answer": null, "solution_text": null}
|
| 82 |
+
{"id": "book 2_q_406_73", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 406, "topic_guess": "number_theory", "question_text": "5. If x and y are positive integers greater than 1 such that x − y and \nare both even integers, which of the following numbers must be\nnon-prime integers?\nxI.\nx + yII.\nIII.\nI only", "options": {"A": "II only", "B": "III only", "C": "I and II only", "D": "I, II, and III"}, "correct_answer": null, "solution_text": null}
|
| 83 |
+
{"id": "book 2_q_424_74", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 424, "topic_guess": "general", "question_text": "2. A batch of widgets costs p + 15 dollars for a company to produce\nand each batch sells for p(9 − p) dollars. For which of the following\nvalues of p, does the company make a profit?\n3", "options": {"A": "4", "B": "5", "C": "6", "D": "7"}, "correct_answer": null, "solution_text": null}
|
| 84 |
+
{"id": "book 2_q_427_75", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 427, "topic_guess": "word_problems", "question_text": "6. Half an hour a er Car A started traveling from Newtown to\nOldtown, a distance of 62 miles, Car B started traveling along the\nsame road from Oldtown to Newtown. The cars met each other on\nthe road 15 minutes a er Car B started its trip. If Car A traveled at a\nconstant rate that was 8 miles per hour greater than Car B’s\nconstant rate, how many miles had Car B driven when they met?\n14", "options": {"A": "12", "B": "10", "C": "9", "D": "8"}, "correct_answer": null, "solution_text": null}
|
| 85 |
+
{"id": "book 2_q_428_76", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 428, "topic_guess": "fractions_decimals_percents", "question_text": "9. If y is 20% less than 90% of x and z is 25% more than 130% of y,\nthen z is what percent of x ?\n 72%", "options": {"A": "92.5%", "B": "108.5%", "C": "117%", "D": "135%"}, "correct_answer": null, "solution_text": null}
|
| 86 |
+
{"id": "book 2_q_429_77", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 429, "topic_guess": "number_theory", "question_text": "integers in set A is equal to the sum of the integers in set B, what is\nthe least number that could be a member of set A ?\n69", "options": {"A": "72", "B": "75", "C": "78", "D": "81"}, "correct_answer": null, "solution_text": null}
|
| 87 |
+
{"id": "book 2_q_433_78", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 433, "topic_guess": "general", "question_text": "Profit will be zero if p = 5 or p = 3, which eliminates answers", "options": {"A": "and", "C": ".", "B": "."}, "correct_answer": null, "solution_text": null}
|
| 88 |
+
{"id": "book 2_q_439_79", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 439, "topic_guess": "general", "question_text": "Try Working Backwards from the answers, starting with", "options": {"B": "is incorrect. Furthermore, a", "D": ".", "A": "14 56 64 48 62"}, "correct_answer": null, "solution_text": null}
|
| 89 |
+
{"id": "book 2_q_441_80", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 441, "topic_guess": "algebra", "question_text": "8. \n Since there are variables in the\nanswer choices, choose a smart number to solve. If k = 2, then\n,\nwhich is less than 1. Now, test the answer choices and try to match the\ntarget; stop if you can tell that an answer won’t equal the target.", "options": {"A": "2 Too high. Eliminate.", "B": "Too high. Eliminate.", "C": "Too high. Eliminate.", "D": "Too high. Eliminate.", "E": "Correct!"}, "correct_answer": null, "solution_text": null}
|
| 90 |
+
{"id": "book 2_q_445_81", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 445, "topic_guess": "general", "question_text": "Try the answer choices; since the problem asks for the least value, start\nwith answer", "options": {"A": "{69, 72, 75} sums to 3(72) = not a multiple of 5.", "B": "."}, "correct_answer": null, "solution_text": null}
|
| 91 |
+
{"id": "book 2_q_466_82", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 466, "topic_guess": "number_theory", "question_text": "21. Let f(x) equal the sum of all of the integers from 1 to x, inclusive,\nwhere x ≥ 1. If\n, which of\nthe following is true of g ?\n0 ≤ g < 5", "options": {"A": "5 ≤ g < 10", "B": "10 ≤ g < 15", "C": "15 ≤ g < 20", "D": "20 ≤ g < 25"}, "correct_answer": null, "solution_text": null}
|
| 92 |
+
{"id": "book 2_q_468_83", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 468, "topic_guess": "general", "question_text": "25. At a certain store, all notebooks have the same price and all pencils\nhave the same price. The price of four notebooks and three pencils\nis more than $12 and less than $13. The price of two notebooks and\nfive pencils is more than $8 and less than $9. If a notebook costs x\nmore than a pencil, which of the following could be the value of x ?\n$0.60", "options": {"A": "$1.05", "B": "$1.30", "C": "$2.20", "D": "$2.70"}, "correct_answer": null, "solution_text": null}
|
| 93 |
+
{"id": "book 2_q_468_84", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 468, "topic_guess": "sequences_patterns", "question_text": "26. A certain sequence is defined by the following rule: Sn = k(Sn − 1),\nwhere k is a constant. If S1 = 2 and S13 = 72 , what is the value of S7 ?\n 6", "options": {"A": "12", "B": "24", "C": "36", "D": "37"}, "correct_answer": null, "solution_text": null}
|
| 94 |
+
{"id": "book 2_q_469_85", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 469, "topic_guess": "sequences_patterns", "question_text": "28. In a certain sequence, each term a er the first is twice the previous\nterm. If the first term of the sequence is 3, what is the sum of the\n14th, 15th, and 16th terms in the sequence?\n3(216)", "options": {"A": "9(215)", "B": "21(214)", "C": "9(214)", "D": "21(213)"}, "correct_answer": null, "solution_text": null}
|
| 95 |
+
{"id": "book 2_q_485_86", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 485, "topic_guess": "general", "question_text": "The correct answer will yield a value of z = 30 mph when x = 40 and y =\n40 are plugged in.", "options": {"A": "is a fraction that is significantly less", "B": ", which", "C": "Correct!", "D": "is much greater than 30.", "E": "is not an integer, so it cannot equal 30. Eliminate. "}, "correct_answer": null, "solution_text": null}
|
| 96 |
+
{"id": "book 2_q_487_87", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 487, "topic_guess": "general", "question_text": "32. If Sn = 5n + 94 and K = (S80 + S82 + S84) − (S81 + S83 + S85), what is the\nvalue of K ?\n−282", "options": {"A": "−84", "B": "−30", "C": "−15", "D": "−3"}, "correct_answer": null, "solution_text": null}
|
| 97 |
+
{"id": "book 2_q_488_88", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 488, "topic_guess": "general", "question_text": "34. If y ≠ x, then \n is the equivalent of\nwhich of the following?\n(x − 1)2y", "options": {"A": "(x + 1)2", "B": "x2 + x + 1", "C": "(x2 + x + 1)y", "D": "(x2 + x + 1)(x − y)"}, "correct_answer": null, "solution_text": null}
|
| 98 |
+
{"id": "book 2_q_490_89", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 490, "topic_guess": "number_theory", "question_text": "39. In a certain sequence, the term Sn is given by the formula Sn = (n +\n1)! for all integers n ≥ 1. Which of the following is equivalent to the\ndifference between S100 and S99 ?\n101!", "options": {"A": "100!", "B": "992(98!)", "C": "1002(99!)", "D": "(100!)2"}, "correct_answer": null, "solution_text": null}
|
| 99 |
+
{"id": "book 2_q_496_90", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 496, "topic_guess": "strategy", "question_text": "Alternatively, you could choose smart numbers. If x = 2 and y = 3, then.\nPlug the selected values into the choices. The choice that equals 7 is the\ncorrect", "options": {}, "correct_answer": null, "solution_text": null}
|
| 100 |
+
{"id": "book 2_q_512_91", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 512, "topic_guess": "strategy", "question_text": "Alternatively, choose smart numbers. For example, if x = 2 and y = 3, then\nthe final answer x + y = 5.\nFor values to plug into the choices, first compute a and b.\nNext, test each answer choice; the one that equals 5 is the correct", "options": {}, "correct_answer": null, "solution_text": null}
|
| 101 |
+
{"id": "book 2_q_521_93", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 521, "topic_guess": "coordinate_geometry", "question_text": "52. Three of the four vertices of a rectangle in the xy-coordinate plane\nare (–5, 1), (–4, 4), and (8, 0). What is the fourth vertex?\n(–4.5, 2.5)", "options": {"A": "(–4, 5)", "B": "(6, –2)", "C": "(7, –3)", "D": "(10, 1)"}, "correct_answer": null, "solution_text": null}
|
| 102 |
+
{"id": "book 2_q_522_94", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 522, "topic_guess": "statistics", "question_text": "55. What is the average (arithmetic mean) of these numbers: 12; 13; 14;\n510; 520; 530; 1,115; 1,120; and 1,125 ?\n419", "options": {"A": "551", "B": "601", "C": "620", "D": "721"}, "correct_answer": null, "solution_text": null}
|
| 103 |
+
{"id": "book 2_q_523_95", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 523, "topic_guess": "statistics", "question_text": "element in the set. If the median of the set equals the mean, what is\nthe greatest possible value in the set?\n85", "options": {"A": "87", "B": "88", "C": "92", "D": "93"}, "correct_answer": null, "solution_text": null}
|
| 104 |
+
{"id": "book 2_q_524_96", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 524, "topic_guess": "general", "question_text": "60. Four different children have jelly beans: Aaron has 5, Bianca has 7,\nCallie has 8, and Dante has 11. How many jelly beans must Dante\ngive to Aaron to ensure that each child has within 1 jelly bean of all\nthe other children?\n2", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": null, "solution_text": null}
|
| 105 |
+
{"id": "book 2_q_534_98", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 534, "topic_guess": "general", "question_text": "Similarly, point B can be anywhere on the line from point A to point C.\nMaximize E by minimizing B, so make B = A.\nTherefore, E = 5 + 3A = 5 + 3(29) = 5 + 87 = 92.\nThe correct answer is", "options": {"D": "."}, "correct_answer": null, "solution_text": null}
|
| 106 |
+
{"id": "book 2_q_539_99", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 539, "topic_guess": "general", "question_text": "62. A group of friends charters a boat for $540 and each person\ncontributes equally to the cost. They determine that if they can get\nthree more of their friends to join them, every person in the group\nwill pay $9 less. If they find three more friends to join them, what is\nthe total number of people renting the boat?\n 6", "options": {"A": "9", "B": "15", "C": "18", "D": "21"}, "correct_answer": null, "solution_text": null}
|
| 107 |
+
{"id": "book 2_q_540_100", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 540, "topic_guess": "number_theory", "question_text": "64. The sum of the interior angle measures for any n-sided polygon\nequals 180(n − 2). If Polygon A has interior angle measures that\ncorrespond to a set of consecutive integers, and if the median angle\nmeasure for Polygon A is 140°, what is the least angle measure in\nthe polygon?\n130°", "options": {"A": "135°", "B": "136°", "C": "138°", "D": "140°"}, "correct_answer": null, "solution_text": null}
|
| 108 |
+
{"id": "book 2_q_541_101", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 541, "topic_guess": "number_theory", "question_text": "66. If a and b are odd integers, a ∆ b represents the product of all odd\nintegers between a and b,inclusive. If y is the least prime factor of (3\n∆ 47) + 2, which of the following must be true?\ny > 50", "options": {"A": "30 ≤ y ≤ 50", "B": "10 ≤ y < 30", "C": "3 ≤ y < 10", "D": "y = 2"}, "correct_answer": null, "solution_text": null}
|
| 109 |
+
{"id": "book 2_q_541_102", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 541, "topic_guess": "number_theory", "question_text": "67. Set S is the set of all prime integers between 0 and 20. If three\nnumbers are chosen randomly from set S, and no number is chosen\nmore than once, what is the probability that the sum of all three\nnumbers is odd?", "options": {}, "correct_answer": null, "solution_text": null}
|
| 110 |
+
{"id": "book 2_q_558_104", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 558, "topic_guess": "statistics", "question_text": "71. \nEnergy usage (units) 11 10 8 7\nNumber of days 4 5 n 3\nThe table above shows daily energy usage for an office building and\nthe number of days that amount of energy was used. If the average\n(arithmetic mean) daily energy usage was greater than the median\ndaily energy usage, what is the least possible value for n ?\n2", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": null, "solution_text": null}
|
| 111 |
+
{"id": "book 2_q_560_105", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 560, "topic_guess": "number_theory", "question_text": "75. If (s × 10q) − (t × 10r) = 10r, where q, r, s, and t are positive integers\nand q > r, then what is the units digit of t ?\n0", "options": {"A": "1", "B": "5", "C": "7", "D": "9"}, "correct_answer": null, "solution_text": null}
|
| 112 |
+
{"id": "book 2_q_561_106", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 561, "topic_guess": "fractions_decimals_percents", "question_text": "78. A decimal is called a “shrinking number” if its value is between 0\nand 1 and each digit to the right of the decimal is not less than the\ndigit to its immediate right. For instance, 0.86553221 is a shrinking\nnumber. If x is a shrinking number, which of the following must be\ntrue?\n is a shrinking number.I.\n is a shrinking number.II.\n is a shrinking number. III.\nI only", "options": {"A": "II only", "B": "I and II only", "C": "III only", "D": "I, II, and III"}, "correct_answer": null, "solution_text": null}
|
| 113 |
+
{"id": "book 2_q_562_107", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 562, "topic_guess": "coordinate_geometry", "question_text": "80. An (x, y) coordinate pair is to be chosen at random from the xy-\nplane. What is the probability that y ≥ |x| ?", "options": {}, "correct_answer": null, "solution_text": null}
|
| 114 |
+
{"id": "book 2_q_567_108", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 567, "topic_guess": "word_problems", "question_text": "20 houses painted at a rate of 4 houses/week = 5 weeks\n60 houses painted at a rate of 5 houses/week = 12 weeks\nTotal time for 80 houses = 5 + 12 = 17 weeks\nThe correct answer is", "options": {"B": "Not an integer.", "A": "Correct!", "C": "Not an integer.", "D": "Eliminate."}, "correct_answer": null, "solution_text": null}
|
| 115 |
+
{"id": "book 2_q_575_109", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 575, "topic_guess": "fractions_decimals_percents", "question_text": "number is relatively easy to do math with, start by using x = 0.1 to test\ncases.\nI. As a fraction, \n , so\n. However, this is not a\nshrinking number, since 9 is greater than 0. So statement I is not\nnecessarily true. Eliminate choices", "options": {"A": ",", "C": ", and", "E": ".", "D": ".", "B": "."}, "correct_answer": null, "solution_text": null}
|
| 116 |
+
{"id": "book 2_q_578_110", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 578, "topic_guess": "geometry", "question_text": "81. \nAs shown in the figure, square ABCD is inscribed in a circle with\ncircumference \n . What is the area of the shaded region in the\ndiagram above?\n2x", "options": {}, "correct_answer": null, "solution_text": null}
|
| 117 |
+
{"id": "book 2_q_594_113", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 594, "topic_guess": "general", "question_text": "If B started out with 80 sheets, then a 20-sheet increase would still be\nless than 30% of the starting number, and again B would end up with\nmore sheets than", "options": {"A": "Algebraically, use a for the original number of sheets in Printer A and use", "B": "A er the transfer, A has a – 0.2a = 0.8a sheets. B has b + 0.2a sheets."}, "correct_answer": null, "solution_text": null}
|
| 118 |
+
{"id": "book 2_q_597_114", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 597, "topic_guess": "fractions_decimals_percents", "question_text": "93. A cylinder of height h is \n full of water. When all of the water is\npoured into an empty cylinder whose radius is 25% larger than that\nof the original cylinder, the new cylinder is \n full. The height of the\nnew cylinder is what percent of h ?\n 25%", "options": {"A": "50%", "B": "60%", "C": "80%", "D": "100%"}, "correct_answer": null, "solution_text": null}
|
| 119 |
+
{"id": "book 2_q_598_115", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 598, "topic_guess": "general", "question_text": "In valid codes, the second digit in the code is exactly twice the first\ndigit. How many valid codes are there?\n 42", "options": {"A": "120", "B": "210", "C": "360", "D": "840"}, "correct_answer": null, "solution_text": null}
|
| 120 |
+
{"id": "book 2_q_616_119", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 616, "topic_guess": "algebra", "question_text": "As an alternative to testing all five choices, you could use a hybrid\napproach to determine the formula using variables.\nThe number of possible groups was \n , but remember that this\nformula took Sally into account.\nThe 3 came from the difference between these numbers: 7 − 4 = (x − 1) − (y\n− 1) = (x − y).", "options": {}, "correct_answer": null, "solution_text": null}
|
| 121 |
+
{"id": "book 2_q_620_120", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 620, "topic_guess": "geometry", "question_text": "104. \nIn the figure above, the trapezoid ABCD is inscribed in a circle.\nParallel sides AB and CD are 7 inches apart and 6 and 8 inches long,\nrespectively. What is the radius of the circle in inches?\n4", "options": {"A": "5", "B": "7"}, "correct_answer": null, "solution_text": null}
|
| 122 |
+
{"id": "book 2_q_621_121", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 621, "topic_guess": "number_theory", "question_text": "107. For how many values of x from 1 to 300, inclusive, is the sum of the\nintegers from 1 to x, inclusive, divisible by 3 ?\n 30", "options": {"A": "99", "B": "100", "C": "199", "D": "200"}, "correct_answer": null, "solution_text": null}
|
| 123 |
+
{"id": "book 2_q_622_122", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 622, "topic_guess": "number_theory", "question_text": "110. If p = (22)(3x) and r = (22)(3y), where x and y are prime numbers and\nx ≠ y, which of the following represents the least common multiple\nof p and r ?\n12xy", "options": {"A": "6xy", "B": "xy", "C": "12", "D": "6"}, "correct_answer": null, "solution_text": null}
|
| 124 |
+
{"id": "book 2_q_628_123", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 628, "topic_guess": "geometry", "question_text": "Since (x + y)(x − y) = 7, (x − y) = 1.\nSolve for x and y.\nThe radius of the circle is 5, because r2 = 32 + 42 = 25.\nThe correct answer is", "options": {"B": ".", "E": ".", "A": ": First, translate the question stem: Is πr2 ≥ r ? Simplify."}, "correct_answer": null, "solution_text": null}
|
| 125 |
+
{"id": "book 2_q_635_124", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 635, "topic_guess": "algebra", "question_text": "111. \nWhich of the following equations represents a line parallel to line ℓ in the\nfigure above?\n2y − 3x = 0", "options": {"A": "2y + 3x = 0", "B": "2y − 3x = 6", "C": "3y + 2x = 6", "D": "3y − 2x = 9"}, "correct_answer": null, "solution_text": null}
|
| 126 |
+
{"id": "book 2_q_638_125", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 638, "topic_guess": "sets_probability_counting", "question_text": "117. Three boys are ages 4, 6, and 7, respectively. Three girls are ages 5, 8, and\n9, respectively. If two of the boys and two of the girls are randomly\nselected and the sum of the selected children’s ages is z, what is the\ndifference between the probability that z is even and the probability that\nz is odd?", "options": {}, "correct_answer": null, "solution_text": null}
|
| 127 |
+
{"id": "book 2_q_639_126", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 639, "topic_guess": "number_theory", "question_text": "119. Positive integers a and b are less than or equal to 9. If a and b are\nassembled into the six-digit number ababab, which of the following must\nbe a factor of ababab ?\n3", "options": {"A": "4", "B": "5", "C": "6", "D": "None of the above"}, "correct_answer": null, "solution_text": null}
|
| 128 |
+
{"id": "book 2_q_653_128", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 653, "topic_guess": "general", "question_text": "3. On the test, stop here and select answer", "options": {"A": "4: An integer is divisible by 4 if its last two digits represent a two-digit", "B": "5: An integer is divisible by 5 if the last digit is 0 or 5. It is uncertain"}, "correct_answer": null, "solution_text": null}
|
| 129 |
+
{"id": "book 2_q_656_129", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 656, "topic_guess": "number_theory", "question_text": "121. If x and y are positive integers such that x2 – y2 = 48, how many\ndifferent values of y are possible?\nTwo", "options": {"A": "Three", "B": "Four", "C": "Five", "D": "Six"}, "correct_answer": null, "solution_text": null}
|
| 130 |
+
{"id": "book 2_q_656_130", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 656, "topic_guess": "number_theory", "question_text": "122. If the number 200! is written in the form p × 10q, where p and q are\nintegers, what is the maximum possible value of q ?\n40", "options": {"A": "48", "B": "49", "C": "55", "D": "64"}, "correct_answer": null, "solution_text": null}
|
| 131 |
+
{"id": "book 2_q_658_131", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 658, "topic_guess": "algebra", "question_text": "127. \nWhich of the following equations represents a line perpendicular to\nline k in the figure above?\n3y + 2x = −12", "options": {"A": "2y + x = 0", "B": "2y − x = 0", "C": "y + 2x = 12", "D": "y − 2x = 12"}, "correct_answer": null, "solution_text": null}
|
| 132 |
+
{"id": "book 2_q_659_132", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 659, "topic_guess": "number_theory", "question_text": "129. K-numbers are positive integers with only 2’s as their digits. For\nexample, 2, 22, and 222 are K-numbers. The K-weight of a number n\nis the minimum number of K-numbers that must be added together\nto equal n.For example, the K-weight of 50 is 5, because 50 = 22 + 22\n+ 2 + 2 + 2. What is the K-weight of 600 ?\n10", "options": {"A": "11", "B": "12", "C": "13", "D": "14"}, "correct_answer": null, "solution_text": null}
|
| 133 |
+
{"id": "book 2_q_668_134", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 668, "topic_guess": "algebra", "question_text": "Thus, the slope of a line perpendicular to k is −2.\nUse the desired slope to create a slope-intercept equation and look for a match among\nthe answers.\nOnly answer", "options": {"D": "offers a match for the le side of the equation."}, "correct_answer": null, "solution_text": null}
|
| 134 |
+
{"id": "book 2_q_671_135", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 671, "topic_guess": "general", "question_text": "Plug x = 3 into the answers, and find the one that equals \n .\nThe correct answer is", "options": {"A": "x2 − x = An integer. Eliminate.", "B": "2x − 1 = An integer. Eliminate.", "C": "Eliminate.", "D": "Correct."}, "correct_answer": null, "solution_text": null}
|
| 135 |
+
{"id": "book 2_q_672_136", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 672, "topic_guess": "sequences_patterns", "question_text": "131. The sequence A is defined as follows: A1 = 1, and An = An − 1 + (−1)n +\n1(n2) for all integer values n > 1. What is the value of A15 − A13 ?\n 14", "options": {"A": "29", "B": "169", "C": "196", "D": "421"}, "correct_answer": null, "solution_text": null}
|
| 136 |
+
{"id": "book 2_q_673_137", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 673, "topic_guess": "sets_probability_counting", "question_text": "134. A chain is comprised of 10 identical links, each of which\nindependently has a 1% chance of breaking under a certain load. If\nthe failure of any individual link means the failure of the entire\nchain, what is the probability that the chain will fail under the load?\n(0.01)10", "options": {"A": "10(0.01)10", "B": "1 − (0.10)(0.99)10", "C": "1 − (0.99)10", "D": "1 − (0.99)(10 × 9)"}, "correct_answer": null, "solution_text": null}
|
| 137 |
+
{"id": "book 2_q_674_138", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 674, "topic_guess": "general", "question_text": "138. If f(x) = (x + 6)2 and g(x) = 9x, which of the following specifies all the\npossible values of x for which f(g(x)) < g(f(x)) ?\n–2 < x < 2", "options": {"A": "x > 2", "B": "0 < x < 3", "C": "–4 < x < 2", "D": "6 < x < 9"}, "correct_answer": null, "solution_text": null}
|
| 138 |
+
{"id": "book 2_q_675_139", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 675, "topic_guess": "general", "question_text": "139. \nIn the figure above, ABCD is a rectangle, and each of AP and CQ is\nperpendicular to BD. If DP = PQ = QB = 1, what is the length of AB ?", "options": {}, "correct_answer": null, "solution_text": null}
|
| 139 |
+
{"id": "book 2_q_676_140", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 676, "topic_guess": "coordinate_geometry", "question_text": "140. \nIn the rectangular coordinate system above, point A is not shown. If\nthe area of triangle OAB is at least 16, which of the following could\nNOT be the coordinates of point A ?\n(1, 8)", "options": {"A": "(4, 14)", "B": "(5, −4)", "C": "(8, −1)", "D": "(14, 4)"}, "correct_answer": null, "solution_text": null}
|
| 140 |
+
{"id": "book 2_q_689_141", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 689, "topic_guess": "general", "question_text": "Finally, use the Pythagorean theorem to determine the length of AB.\nAlternatively, since the diagram is drawn to scale, you can try to estimate. Side\nAB appears to be longer than BP, but shorter than BD. Its length should be\nbetween 2 and 3. Estimate the values of the answer choices.\nOnly answers", "options": {"C": "= between 2 and 3.", "D": "= More than 3. Eliminate.", "A": "(1, 8): First, identify any answer choices that will be easy to eliminate before", "B": "and", "E": "are symmetrical;"}, "correct_answer": null, "solution_text": null}
|
| 141 |
+
{"id": "book 2_q_692_142", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 692, "topic_guess": "number_theory", "question_text": "141. If \n , where a and b are integers and a\ndoes not equal 1 or −2, which of the following could be the value of\nb ?\n1I.\n2II.\n3III.\nI only", "options": {"A": "II only", "B": "I and II only", "C": "I and III only", "D": "I, II, and III"}, "correct_answer": null, "solution_text": null}
|
| 142 |
+
{"id": "book 2_q_693_143", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 693, "topic_guess": "number_theory", "question_text": "144. Each digit 1 through 5 is used exactly once to create a five-digit\ninteger. If the 3 and the 4 cannot be adjacent digits in the integer,\nhow many five-digit integers are possible?\n48", "options": {"A": "66", "B": "72", "C": "78", "D": "90"}, "correct_answer": null, "solution_text": null}
|
| 143 |
+
{"id": "book 2_q_694_144", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 694, "topic_guess": "general", "question_text": "146. A soccer competition consisted of two rounds. In each round, the 20\nteams competing were divided randomly into 10 pairs, and each\npair played a single game. None of the games resulted in a tie, and\nof the teams that lost in the first round, 7 also lost in the second\nround. How many teams won both of their games?\n3", "options": {"A": "4", "B": "5", "C": "6", "D": "7"}, "correct_answer": null, "solution_text": null}
|
| 144 |
+
{"id": "book 2_q_711_145", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 711, "topic_guess": "fractions_decimals_percents", "question_text": "rate of y milligrams per hour, how many hours will it take for the\nconcentration of salt to reach (x + 10)%, in terms of x and y ?", "options": {}, "correct_answer": null, "solution_text": null}
|
| 145 |
+
{"id": "book 2_q_715_146", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 715, "topic_guess": "geometry", "question_text": "160. An unpainted wall with a total area of 100 square feet needed to be\npainted with three coats of paint. Nelson began the job by painting\nan area of 60 square feet. Then, Jamaica painted a total area of 70\nsquare feet. Finally, Bryan painted a total area of 80 square feet.\nA er Bryan finished painting, an area of q square feet of the wall\nwas covered in three coats of paint. If the entire surface area of the\nwall had received at least one coat of paint, which of the following\nspecifies all the possible values of q ?\n0 ≤ q ≤ 50", "options": {"A": "0 ≤ q ≤ 60", "B": "10 ≤ q ≤ 50", "C": "10 ≤ q ≤ 55", "D": "10 ≤ q ≤ 60"}, "correct_answer": null, "solution_text": null}
|
| 146 |
+
{"id": "book 2_q_722_148", "source_name": "Manhattan Prep GMAT Advanced Quant", "source_file": "book 2.pdf", "page": 722, "topic_guess": "number_theory", "question_text": "Thus, if set A contains the integers from 1 to 5, set B consists of 1, 2, 3, 4, 5, 6, 7, 8,\nand 9. The question asks for the greatest integer in set", "options": {"B": "(1) SUFFICIENT: The range of a set is the difference between the greatest and the", "A": "Those numbers are x + 3 and x + 4, and their sum is 2x + 7."}, "correct_answer": null, "solution_text": null}
|
gmat_topic_index.json
ADDED
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| 1 |
+
{
|
| 2 |
+
"general": {
|
| 3 |
+
"chunk_count": 128,
|
| 4 |
+
"question_count": 53,
|
| 5 |
+
"sources": [
|
| 6 |
+
"GMAT Club Math Book 2024 v8.pdf",
|
| 7 |
+
"GMAT QUANT.pptx",
|
| 8 |
+
"book 2.pdf"
|
| 9 |
+
]
|
| 10 |
+
},
|
| 11 |
+
"word_problems": {
|
| 12 |
+
"chunk_count": 133,
|
| 13 |
+
"question_count": 8,
|
| 14 |
+
"sources": [
|
| 15 |
+
"GMAT Club Math Book 2024 v8.pdf",
|
| 16 |
+
"GMAT Math Flashcards from GMAT Prep Now.pdf",
|
| 17 |
+
"GMAT QUANT.pptx",
|
| 18 |
+
"book 2.pdf"
|
| 19 |
+
]
|
| 20 |
+
},
|
| 21 |
+
"number_theory": {
|
| 22 |
+
"chunk_count": 190,
|
| 23 |
+
"question_count": 25,
|
| 24 |
+
"sources": [
|
| 25 |
+
"GMAT Club Math Book 2024 v8.pdf",
|
| 26 |
+
"GMAT QUANT.pptx",
|
| 27 |
+
"book 2.pdf"
|
| 28 |
+
]
|
| 29 |
+
},
|
| 30 |
+
"fractions_decimals_percents": {
|
| 31 |
+
"chunk_count": 72,
|
| 32 |
+
"question_count": 13,
|
| 33 |
+
"sources": [
|
| 34 |
+
"GMAT Club Math Book 2024 v8.pdf",
|
| 35 |
+
"GMAT QUANT.pptx",
|
| 36 |
+
"book 2.pdf"
|
| 37 |
+
]
|
| 38 |
+
},
|
| 39 |
+
"sequences_patterns": {
|
| 40 |
+
"chunk_count": 88,
|
| 41 |
+
"question_count": 6,
|
| 42 |
+
"sources": [
|
| 43 |
+
"GMAT Club Math Book 2024 v8.pdf",
|
| 44 |
+
"GMAT QUANT.pptx",
|
| 45 |
+
"book 2.pdf"
|
| 46 |
+
]
|
| 47 |
+
},
|
| 48 |
+
"statistics": {
|
| 49 |
+
"chunk_count": 81,
|
| 50 |
+
"question_count": 13,
|
| 51 |
+
"sources": [
|
| 52 |
+
"GMAT Club Math Book 2024 v8.pdf",
|
| 53 |
+
"GMAT QUANT.pptx",
|
| 54 |
+
"book 2.pdf"
|
| 55 |
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|
| 56 |
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|
| 57 |
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|
| 58 |
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|
| 59 |
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|
| 60 |
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|
| 61 |
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"GMAT Club Math Book 2024 v8.pdf",
|
| 62 |
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"GMAT Math Flashcards from GMAT Prep Now.pdf",
|
| 63 |
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"GMAT QUANT.pptx",
|
| 64 |
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"book 2.pdf"
|
| 65 |
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|
| 66 |
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|
| 67 |
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| 68 |
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|
| 69 |
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|
| 70 |
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|
| 71 |
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"GMAT Club Math Book 2024 v8.pdf",
|
| 72 |
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"GMAT QUANT.pptx",
|
| 73 |
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"book 2.pdf"
|
| 74 |
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]
|
| 75 |
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|
| 76 |
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|
| 77 |
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|
| 78 |
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|
| 79 |
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|
| 80 |
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"GMAT Club Math Book 2024 v8.pdf",
|
| 81 |
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"GMAT QUANT.pptx",
|
| 82 |
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"book 2.pdf"
|
| 83 |
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|
| 84 |
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|
| 85 |
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|
| 86 |
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|
| 87 |
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|
| 88 |
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|
| 89 |
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"GMAT Club Math Book 2024 v8.pdf",
|
| 90 |
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"GMAT QUANT.pptx",
|
| 91 |
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"book 2.pdf"
|
| 92 |
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|
| 93 |
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|
| 94 |
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|
| 95 |
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|
| 96 |
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|
| 97 |
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|
| 98 |
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"book 2.pdf"
|
| 99 |
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|
| 100 |
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| 101 |
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|
| 102 |
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|
| 103 |
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|
| 104 |
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|
| 105 |
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"GMAT Math Flashcards from GMAT Prep Now.pdf"
|
| 106 |
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]
|
| 107 |
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}
|
| 108 |
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}
|