Practice Questions & Answers Flashcards

Question

What is possibly a better way of solving this question rather than going straight to the equations to solve for r?

Answer 1

Simply use the possible answers given to you to plug in values and see what gives you the right outcome.

Answer 2

D The change in the area is equal to the change of the sides squared: x²

Answer 3

We know two angles are the same, there we can conclude that the side AB is equal to BC.

Answer 4

You need to indentify the second equation which can be formed using the triangle DEC. Using this equation you can tranpose the equation into the other one through y.

Answer 5

The answer is D.

Answer 6

You need to use the fact that the smaller inner triangle is indentical to the larger whole triangle expect for proportion.

Answer 7

You could have gone for the precise approach using variavles and the 3,4,5 triangle, but the most effective approach is the logical one.

Answer 8

You can also anwer the question by concluding that the smaller triangle can fit three more times into the larger triangle, i.e. four of the ADE fit in ABC.

Answer 9

√7 This goes for any value. √7/7 = 1/√7

Answer 10

We're picking 5 out of 7, so there are 7\*6\*5\*4\*3 ways to do so. However, since order doesn't matter, there are 5\*4\*3\*2\*1 ways of picking the same balls (that is, in a different order). We then divide one by the other and get (7\*6\*5\*4\*3)/(5\*4\*3\*2\*1) = 42/2 = 21

Answer 11

You can't just average it, you need to use total\_distance/(t₁+t₂) and replace total time with the individual rate equations D/r where D is distance r is rate.

Answer 12

The answer is 19. The key here is remember the 5^x \* 2^y relaionship to make trailing zeros. Knowing that makes these seemingly complicated question a lot easier to solve.

Answer 13

This is a trick question and the answer is A. Just because you get an equation that has two unkowns doesn't mean it automatically rules out the one option alone, you need to consider logically if the expression can take multiple different values or if it in fact limits one of the variables to one value due to logic.

Answer 14

The main equation you need to remember here is that: work_total = work_jason + work_john Where work is equal to rate\*time. The individual rates of the Jason and John come out to 1/6 and 1/4. Which comes out to: 1 = (1/6)t + (1/4)t

Answer 15

Create a table and test out both possibilities separately and then together. The answer is C.

Answer 16

Multiplying an inquality by a negative flips the sign, therefore we need to know whether a,b,c,d are negative or not. The answer is C.

Answer 17

Look to make the decimals easier to deal with, convert them to 'integers' using scientific notation. The handling of the values and 10s becomes a lot easier once you do that.

Answer 18

The answer is 18. The key thing here is remember the equation: nC_k = n! / K!(n-K)! Where n is the number of possible choices and K represents the number of choices in a combination.

Answer 19

Don't overthink this one. You simply need to right down the equations for each year up to 8 and then solve the equation knowing the 5/4 relation.

Answer 20

The relations and equations you need use: 30-60-90 triangles has the following relation x:x√3:2x Arc length: 2pi\*r\*(θ/360) Also importantly you need to remember that the central angle is 2 times the angle at YXZ, which you can then use to calculate the arc YZ.

Answer 21

Remember in this case for the average you divide by the quantity of tickets. Also, in these questions focus on writing down the equation and then solving for the unkown.

Answer 22

The thing you here is you need to remember the cyclicity of 7^x. The units digit of the first for power is: 7¹ =\> 7 7² =\> \_9 7³ =\> \_3 7⁴ =\> \_1 and the pattern repeats from here.

Answer 23

That if a line doesn't intersect another said line, that means that their slopes are equal...

Answer 24

Just because the P is there doesn't mean we can't consider 2) to answer the question.

Answer 25

You cannot divide an inequality by an unkown variable (in this case dividing out z) because we don't know whether it is -ve or not. Answer is E

Answer 26

'At least' problems normally require the addition of outcomes.

Answer 27

You need to remember to clearly read what they're saying, underline key words in the question. In this case they're saying the markup was 40% of the _selling price_. Purchase price = 150 Selling price = x 150 + 0.4\*x = x 0.6\*x = 150 x = 250 Profit = 250 - 150 = 100 (E)

Answer 28

Learnt that it is really important to use the distance = rate \* time equation with these problems, you cannot just average. --- (1) Avg speed \> 16fps So distance covered \> 16\*1800 feet = 28800feet or about 5.45miles So distance \> 5.45 miles Not sufficient (2) average speed \< 18fps So distance \< 18\*1800 feet or about 6.14miles So distance \< 6.14miles Not sufficient (1)+(2) Distance is between 5.45 and 6.14 miles Not sufficient to say if it is \> 6 miles Answer = E

Answer 29

There are some number of boards stacked. 20th board from the top is immediately below the 16th board from the bottom: 1 2 3 . . . **16** **20** 15 14 13 . . . 3 2 1 As you can see 20th board from the top is immediately below the 16th board from the bottom. The total number of boards 20(red)+14(blue)=34. Answer: D.

Answer 30

The answer is A. 1. t is less than 0 T is negative and K is to the left of T so K is negative as well negative\*negative = positive and any positive will be to the right of t when it's negative A is sufficient 2. k is less than 1 if T is 10 K could be 1/2 and kt would be to the left of T if T is -1 K could be -2 and kt would be to the right of T Insufficient The mistakere here was that you did not consider that K could be a fraction, i.e. 1/2. Unless they say you're only dealing with integers, consider fractions as well.

Answer 31

You need to consider each statement independently. You need to test them by themselves first. Remove the other statement of your mind temporarily when you're working on one. This is realy important because you've consistently chosen C when it was either A or B.

Answer 32

We are given that each of the students in a certain class received a single grade of P, F, or I. We can let p = the number of students who received P, f = the number of students who received F, and i = the number of students who received I. Thus, the total number of students in the class is p + f + i. We need to determine the percentage of students who were females. Statement One Alone: Of those who received a P, 40 percent were females. This means 0.4p students are females. However, since we know neither the values of p, f, and i nor the percentage of students who received an F or I, statement one alone is not sufficient to answer the question. Statement Two Alone: Of those who received either an F or I, 80 percent were males. This means 20 percent of the students who received either an F or I were females. In other words, 0.2(f + i) students are females. However, since we know neither the values of p, f, and i nor the percentage of students who received a P, statement two alone is not sufficient to answer the question. Statements One and Two Together: From the two statements, we can say that the percentage of students in the class who were females is: (0.4p + 0.2(f + i))/(p + f + i) x 100 However, since we don’t know the values of p, f, and i, we can’t determine the numerical value of the expression above. Statements one and two together are still not sufficient. Answer: E **The key thing here is too many unknown variables.**

Answer 33

We are told that n!=990∗k=2∗5∗32∗11∗kn!=990∗k=2∗5∗32∗11∗k --\> n!=2∗5∗32∗11∗kn!=2∗5∗32∗11∗k which means that n!n! must have all factors of 990 to be the multiple of 990, hence must have 11 too, so the least value of nn is 11 (notice that 11! will have all other factors of 990 as well, otherwise the least value of n would have been larger).. Answer: B. So to be a multiple it must have all the factors of 990, this is only achieved if n is at least 11.

Answer 34

The key here is to remember the logic of Vladimir having travelled 2/3 of the distance by 10mins, and thus the time to reach the house can be determined.

Answer 35

In this case tom's time gets 1/2 hour more to the time, as thats the extra amount of time he travels.

Answer 36

You glanced over the first statement and missed that it said greater than 50. Always read the questions properly and don't glance over!

Answer 37

_Question Stem Analysis:_ We want to know whether he can drive 550 miles on the full take of gas. From the initial information given, we don't know the fuel capacity nor the fuel efficiency of the car.