![\"Manhattan](\"https:\/\/www.manhattanprep.com\/gmat\/wp-content\/uploads\/sites\/18\/2018\/07\/memorizable-list-gmat-quant-content-quantent-patrick-tyrrell.png\")
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Even though there\u2019s no \u201cnew math\u201d on GMAT Quant, there is still a <\/span>ton <\/span><\/i>of content to keep on our radar. And just like the tragic studying for a vocab test, we\u2019ll have to learn 200 different things, even though the test is going to only ask us 31 of those things (because we don\u2019t know which 31 things we\u2019ll get asked on our test day).<\/span><\/p>\n How are we going to keep all that stuff in our brain at once? It takes most students at least a couple weeks to cycle through 200 different GMAT Quant problems, so by the time you\u2019re doing the 200<\/span>th<\/span> problem, it\u2019s usually been a few weeks since you\u2019ve seen the content on the first 10 problems. <\/span><\/p>\n In order to take quicker laps around the GMAT Quant universe, you want to make some of your practice feel like you\u2019re studying for a vocab test. We can take a lap through 200 vocab flashcards much more quickly than we can through 200 GMAT Quant problems.<\/span><\/p>\n Instead of having vocab flashcards with Word on one side and Definition on the other, we\u2019ll have GMAT Quant flashcards that have Topic\/Stimulus on one side, and First Move\/First Thought on the other.<\/span><\/p>\n If Pavlov can get dogs to salivate in response to a bell, we can get ourselves to break a number down to primes in response to \u2018divisibility language.\u2019 But we\u2019ll have to outdo Pavlov, or at least outdo his dogs, by learning way more than just one stimulus\/response pairing. Are you all ready to outdo Pavlov\u2019s certain-to-be-dead-by-now dogs?!<\/span><\/p>\n (Moment of silence: I hope in doggy heaven, every time the bell rings, you really <\/span>do <\/span><\/i>get a treat.)<\/span><\/p>\n In the rest of Part 1 (of this 2-part post), I\u2019ll get you started with a baker\u2019s dozen topics. Next month, we\u2019ll finish off the list.<\/span><\/p>\n Your job: if you see anything you don\u2019t already know with the ease\/certainty of a famous actor\u2019s name\/face, then commit that fact to flashcard. Quiz yourself on those flashcards at least three times a week. Add your own flashcards as you review problems you\u2019ve tried and see moves you wish you had made, or number properties you wish you would have inferred.<\/span><\/p>\n Let us know if you have any questions.<\/span><\/p>\n #1 Move: If we see <\/span>x is <\/span><\/i>divisible<\/i><\/b> by y, x is a <\/span><\/i>multiple<\/i><\/b> of y, y is a <\/span><\/i>factor<\/i><\/b> of x, x\/y <\/span><\/i>is an integer<\/i><\/b>, <\/span><\/i>then we <\/span>break these numbers down to primes.<\/b><\/p>\n Divisibility <\/b>means \u201cthe numerator has <\/span>at least <\/span><\/i>the primes in the denominator.\u201d<\/span><\/p>\n \u201cx is divisible by 45\u201d = x has at least 3 * 3 * 5 in it.<\/span><\/p>\n \u201cx is not a multiple of 12\u201d = x either has fewer than two 2\u2019s or doesn\u2019t have a 3, or both.<\/span><\/p>\n \u201c36 is a factor of 8x\u201d =\u00a02*2*2*x<\/sup>2*2*3*3<\/sub> = #2 Move: If we see a <\/span>multiplication cluster + integer<\/span><\/i>, then we think about <\/span>the logic of multiples<\/b> and ask, \u201cWhat are both quantities divisible by?\u201d<\/span><\/p>\n If we see 14x + 35, we think \u201cboth 14x and 35 are divisible by 7,\u201d so 14x +35 is divisible by 7.<\/span> If we see 7! + 15, we think \u201cboth 7! and 15 are divisible by 5,\u201d so 7! + 15 is divisible by 5.<\/span><\/p>\n If we\u2019re talking <\/span>median,<\/b><\/p>\n If we\u2019re talking average,<\/b><\/p>\n If we\u2019re talking <\/span>standard deviation,<\/b><\/p>\n #1 Thought: <\/span>even * anything = even<\/b><\/p>\n #2 Thought: Remember or derive the E\/O rules for addition\/subtraction\/multiplication<\/span> Usual #1 Move: Take anything with an even coefficient and translate that quantity into E.<\/span><\/p>\n 3x + <\/span>4y<\/b> is odd \u2192 3x + <\/span>E<\/b> = O \u2192 3x = O \u2013 E \u2192 3x = O \u2192 x = O <\/span><\/p>\n Dealing with division facts: If we see \u201cx\/y is even,\u201d we write,\u00a0x<\/sup>y\u00a0<\/sub><\/span>= Even, and then multiply y to the other side to get \u00a0x = Even (y).\u00a0<\/span>This tells us that x is even (we know nothing about y).<\/span><\/p>\n Useful Shortcut:<\/b> If something has an even coefficient, we won\u2019t learn whether that variable is even or odd. The even coefficient will \u201chide\u201d which type it is.<\/span><\/p>\n #1 Thought: <\/span>Keep track<\/b> of possible words with <\/span>\u201cpos, neg\u201d or \u201c+, -\u201d<\/b><\/p>\n #1 Move: Use the pos\/neg properties of addition, subtraction, multiplication, and division to eliminate possible words.<\/span><\/p>\n x+y > 0 (at least one positive \u2026 eliminate neg\/neg) \u00a0\u00a0\u00a0\u00a0<\/span> Useful Shortcut:<\/b> If something has an even exponent, we won\u2019t learn whether that variable is positive or negative. The even exponent will \u201chide\u201d which type it is.<\/span><\/p>\n #1 Move: Clean it up by<\/span> multiplying by a power of 10.<\/b><\/p>\n If we see 0.0045, we write \u00a045 * 10-4<\/sup><\/span><\/p>\n #2 Move: Line up the decimals, add zeros where necessary, then remove the decimal.<\/span><\/p>\n If we see 1.2\/.03, we write 1.2<\/span>0<\/b>\/<\/span>0<\/b>.03 = 120\/3 = 40.<\/span><\/p>\n #1 Move: <\/span>Write out the pattern<\/b> for that units digit.<\/span> Example: <\/b>What\u2019s the units digit of 6345<\/sup><\/span>?<\/span><\/p>\n Write out the pattern for powers of 3 (the patterns are either a constant digit, a cycle of 2, or a cycle of 4).<\/span><\/p>\n 3\u00b9<\/span>\u00a0ends in 3 Since every power that\u2019s a multiple of 4 will end in 1, 344<\/sup><\/span>\u00a0= ends in a 1.<\/span><\/p>\n So 345<\/sup><\/span>\u00a0= ends in a 3, so the units digit of 6345<\/sup><\/span>\u00a0<\/span>is 3.<\/span><\/p>\n #1 Move: If any of the bases aren\u2019t currently prime, <\/span>break the bases down to primes.<\/b><\/b><\/p>\n If we see 14x<\/sup><\/span>\u00a0* 10y<\/sup><\/span>\u00a0* 85<\/sup><\/span>\u00a0= 2\u00b3\u00b2<\/span>\u00a0* 5z+1<\/sup><\/span>\u00a0* 74<\/sup><\/span><\/p>\n Then our next move is: 2x\u00a0<\/sup><\/span>7x<\/sup><\/span>\u00a0* 2y<\/sup><\/span>\u00a05y<\/sup><\/span>\u00a0* (2\u00b3<\/span>)5<\/sup><\/span>DIVISIBILITY on GMAT Quant<\/strong><\/h4>\n
2*2<\/del>*2*x<\/sup>2*2<\/del>*3*3<\/sub> = 2x<\/sup>3*3\u00a0<\/sub><\/span>= x has at least 3*3 in it.<\/p>\n
\n<\/span>a multiple of 7 + a multiple of 7 = a multiple of 7<\/span><\/i><\/p>\nSTATISTICS on GMAT Quant<\/strong><\/h4>\n
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ODDS\/EVENS on GMAT Quant<\/strong><\/h4>\n
\n<\/span>E +\/- E = E \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0E * E = E <\/span>
\n<\/span>E +\/- O = O \u00a0\u00a0\u00a0\u00a0E * O = E <\/span>
\n<\/span>O +\/- O = E \u00a0\u00a0\u00a0\u00a0O * O = O <\/span><\/p>\nPOSITIVE\/NEGATIVE on GMAT Quant<\/strong><\/h4>\n
\n<\/span>x+y < 0 (at least one negative \u2026 eliminate pos\/pos)<\/span>
\n<\/span>x-y > 0 (x > y \u00a0\u2026 eliminate neg\/pos)<\/span>
\n<\/span>x-y < 0 (x < y \u00a0\u2026 eliminate pos\/neg)<\/span>
\n<\/span>xy > 0 or x\/y > 0 (same sign \u2026 must be pos\/pos or neg\/neg)<\/span>
\n<\/span> xy < 0 or x\/y < 0 (opposite signs \u2026 must be pos\/neg or neg\/pos)<\/span><\/p>\nDECIMALS on GMAT Quant<\/strong><\/h4>\n
UNITS DIGITS on GMAT Quant<\/strong><\/h4>\n
\n<\/span>3\u00b2<\/span>\u00a0ends in 9
\n<\/span>3\u00b3<\/span>\u00a0ends in 7<\/span>
\n<\/span>34<\/sup><\/span>\u00a0ends in 1<\/span>
\n<\/span>—————- <\/span>
\n<\/span>35<\/sup><\/span>\u00a0ends in 3
\n<\/span>36<\/sup><\/span>\u00a0ends in 9
\n<\/span>37<\/sup><\/span>\u00a0ends in 7<\/span>
\n<\/span>38<\/sup><\/span>\u00a0ends in 1<\/span><\/p>\nEXPONENTS\/ROOTS on GMAT Quant<\/strong><\/h4>\n