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Question

# When I see ... ... triangle in triangle ...

Answer 1

I will ... understand they want to testing similarity | **read this example** ## Footnote Review similariry

Answer 2

I will ... 1. Write any rates **especially when they are unusual rates** (med cunsumprion per day during a 2 days trip) 2. write down the table ## Footnote 2 days : <4 /over 5>

Answer 3

I will ... In a round-trip problem when only the total time traveled is provided, consider letting the time to a destination equal some variable t and the time back equal (total trip time - t)

Answer 4

I will ... 1. Think of the lines of plugging in that is testing values. 2. if I have fractions **Try to use int values** by **plugging** in a common multiple of the denominators. 3. Plug in **more than once if required** 4. **Analyze** the answer choices and try to figure out why the remaining four answer choices are incorrect. 5. if i have percentages, **plug in 100**

Answer 5

I will ... 1. backsolving 2. start from **C** 3. decide whether go up or doown

Answer 6

I will ... Write down that ç could be 1,2,3,-1,-3 **or 1/3, 1/7 or ...**

Answer 7

I will ... * **Always** make a list * Make list of values based on the conditions of statements * When combining statements the list will come in handy as I can use the values in the list which **overlap** * Also try to find **more than 2 items in overlap list**

Answer 8

I will ... Consider LCM ***even in numinators***

Answer 9

I will ... * Try to find the multiplication relation between denominator and nominator. If I can not select other than select **OTHER THAN obvious** rounding ## Footnote **21/16 x 127/5 → 21/5 x 127/16 → 4.2 x almost 8 → 33.6**

Answer 10

I will ... consider numbers with ***1 difference***. Except the questions stem make a clear difference

Answer 11

A merchant purchased a jacket for $60 and then determined **a selling price that equaled the purchase price of the jacket plus a markup that was 25 percent of the selling price**. During a sale, the merchant discounted the selling price by 20 percent and sold the jacket. What was the merchant’s gross profit on this sale? → selling price = 60 + 25% selling price → selling price = 80 → 80 * 0.8 = 64 → profit = $4 **Tip: Read carefully. Usually, markup is a percent of the purchase price, but in this problem, it is a percent of the selling price.**

Answer 12

I will ... ... be cautious about boundries. Two times I mistakenly assumed for this equation the min is 200. Instead, it should be consider 225. Also the max is 225. | **Min ↑ and Max ↓**

Answer 13

I will ... Assume the price is $x, since it could cross of in %profit

Answer 14

I will ... ... sketch a number line to help keep the details straight. ## Footnote Ten years ago, scientists predicted that the animal Z would become extinct in t years. What is the value of t ? (1) Animal Z became extinct 4 years ago. (2) If the scientists had extended their extinction prediction for animal Z by 3 years, their prediction would have been incorrect by 2 years.

Answer 15

I will ... Asume the possibility of y by itself could be a perfect square ## Footnote If x, y, z, and a are integers greater than zero and x, y, and z are consecutive integers such that x < y < z and x²y³z²y^a is a perfect square, what is the value of a? 1) z = 4 2) a² < 9

Answer 16

I will ... Use mean x number of elements instead of over calculation of factoring 2 and so on .... ## Footnote After rearrangment, Mean is 300, and # elements is 101. So the answer is 101 x 300 = 30300

Answer 17

I will ... Use allegation method. | **The resulted ratio will use to calculate quantities** ## Footnote Caution: it could be used for problems involved **"per"**: percentage, km/h, $/lit , ...

Answer 18

I will ... note than it is not necessary that the set is equally spaced: {1,2,3,4,5} → mean=3 and median=3 {1,2,4,5} → mean=3 and median=3 ## Footnote equaly spaced → mean=median mean=median ✗→ equaly spaced

Answer 19

I will ... Check both extremes | **Especially for DS** ## Footnote In a recent survey, twenty families reported their incomes for 2012. Was the range of reported incomes for these families greater than $60,000? 1) Thirteen families reported incomes were between $20,000 and $35,000 2) Seven families reported incomes were between $80,000 and $95,000 It is obvious that AD are out for C consider these two set: {20,20,20 ..... , 95,95,95} → Yes {35,35,35, ... , 80,80,80} → No So the answer is E

Answer 20

I will ... Use 2/3 venn diagram | مثلا یکی می‌تونه هم پیتزا بخوره هم همبرگر هم گاو نباشه

Answer 21

I will ... Table method

Answer 22

I will ... Consider whether the arrangement is given or not: * P(A and B) = P(A) x P(B) but if the arrangemtn doesn't given * P(A and B) = P(A) x P(B) x arrangement

Answer 23

I will ... First understand whether they are mutually exclusive or not ## Footnote اگر P(A and B) = 0 باشه mutually exclusive هستن

Answer 24

I will .... 1. Draw a line instead of calculation 2. Consider both possible orders like these: * x₁ → John → y₁ → Mary → z₁ And * x₂ → Mary → y₂ → John → z₂

Answer 25

I will ... * write down step by step for each interval * "at the end of third hour Bran's height was **1/4 less than his height at** the end of the ninth hour." interpretation is: **A+3k = 3/4(A+9k)** ## Footnote Note: ✘ A+3k = (A+9k) - 1/4

Answer 26

I will ... Consider a vertical line in order to visualize the boundries

Answer 27

I will ... try to solve it backward. ## Footnote Rita and Sam play the following game with n sticks on a table. Each must remove 1, 2, 3, 4 or 5 sticks at a time on alternate turns, and no stick that is removed is put back on the table. The one who removes the last stick (or sticks) from the table wins. If Rita goes first, which of the following is a value of n such that Sam can always win no matter how Rita plays? A. 7 B. 10 C. 11 D. 12 E. 16 Sam is me I've to force her to remain with 6 sticks Next Since she start the game, by having 7,8,9,10,11 sticks I can force her to remain with 6. So the answer is 12

Answer 28

I will ... 1. find the difference 2. by adding/subtracting a constant try to create a secuence multiple of **A** ## Footnote For example, to determine the number of terms in the sequence 13, 19, 25, 31, 37, 43, …, 301, we first observe that consecutive differences are equal to 6, so we subtract from each term a number chosen so that the first term becomes (1)(6) = 6. Thus, we subtract 7 from each term and obtain the sequence 6, 12, 18, 24, 30, 36, …, 294, which has the same number of terms as the original sequence. The number of terms in this new sequence is now easy to find—divide each term of this new sequence by 6, and it will be clear that the number of terms is 49.

Answer 29

I will ... In order to prevent loosing data, use variable method instead of drawing graph.

Answer 30

I will ... Look all around the whole question stem and answer choices to get clues. ## Footnote Can the positive integer n be written as the sum of two different positive prime numbers? 1. n is greater than 3. 2. n is odd. I Didn't comprehend the question If I interpreted the question correctly I would understand that, in order to get an odd number, the only way is odd+even. Thus one of them should be 2.

Answer 31

I will ... Assume they want to fool me to assume somthing that is not stated. | **use variables** ## Footnote If cubical blocks in a display are stacked one on top of the other on a flat surface, what is the volume of the stack of blocks in cubic centimeters? 1.The volume of the top block is 8 cubic centimeters. 2. The height of the stack of blocks is 10 centimeters. **Tip: Do not assume anything that is not explicitly stated in the problem. In this problem, it is tempting to assume that all of the blocks are identical, in which case there would be five blocks, each with height 2 cm to give the whole stack a height of 10 cm and a volume of 40 cubic centimeters. Under the assumption that all of the blocks are identical, the correct answer would be C.**

Answer 32

I will ... Consider both: 1. For any positive integers x and y, y is a **factor/divisor** of x if and only if x/y is an integer. and 2. Furthermore, 1 < y < x.

Answer 33

I will ... 1. Pay attention to answer choices’ order. 2. Consider test value. 3. **Do Not *insist*** just with test values. Consider solving inequalities.

Answer 34

I will ... Stop the URGE to consider "r" as an integer **"r" could be non-integer** | **e.g. (2√3)⁵** ## Footnote S is a sequence in which each term after the first is equal to r times the previous term, where r is a nonzero constant. What is the value of r? (1) The second term of S is 6. (2) The sixth term of S is 96.

Answer 35

I will ... Notice Each of the following is necessary & sufficient for a sequence to be an AP: * *a*_*i* - *a*_*i-1* = Constant * If you pick any 3 consecutive terms, the middle one is the mean of the other two * For all i,j > k >= 1

Answer 36

* (*a*_*i*) ÷ (*a*_*i-1*) = Constant * If you pick any 3 consecutive terms, the middle one is the geometric mean of the other two * For all i,j > k >= 1 :

Answer 37

* *a*_*1* = 0 **&** * *d*=0

Answer 38

absolute value of r < 1 |r| < 1

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