GRE Math

Question 1

Answer 1

1) Simplify! Reduce to primes when possible. 2) Cross out common values across the invisible divide.

Question 2

Answer 2

1. Recognize that the right side (B) is a little less then 0.
2. Recognize that the left side (A) is 1/# that is a little less than 0. This value will be >1. Thus, A is bigger.

Question 3

Answer 3

1. Do not compute! Cheat off of B. Pretend B (150) is the starting value.
2. 30% of 150 = 45….150 -45 = 105.
3. However, this^ number is bigger than 99, the value we know we end up at… Therefore, our starting number has to be LESS than 150 and B is bigger.

Question 4

Answer 4

1. Do not assume that X = 90. Upfront info does not say that. Angle could be bigger OR smaller than 90. “Can i make it really big? Can i make it really small??”
2. Yes^. Given the angle could either be huge or VERY small, we can make the height of this triange teeny tiny. 1/2(b)h can then be smaller than 1.5 or close to 0 (ie if the triangle is basically flat).

Question 5

Answer 5

1. Notice that everything here is positive.
2. On the left, we have a number over a BIGGER number.
3. On the right, we have a BIGGER number over a smaller number. This will always be larger than option A.

Question 6

Answer 6

1. Notice that both sides could be equal if Z = 2.5.
2. Notice that A could be bigger than B (z = 3) OR B could be bigger than A (z = 2).

Therefore, answer is D.

Question 7

Answer 7

Notice: Quantity B is exactly in the middle of 60 and 70. Means that if both divisions were exactly EQUAL, this is the number we would get.

BUT:

• We know that there are more people in the 60,000 side of the spectrum, meaning the AVG is closer to 60 than 65. Therefore, 65 is bigger!

Question 8

Answer 8

1. Simplify across the hidden inequality (ie factor out what you can).
2. A is bigger.

Question 9

Answer 9

1. Cancel out ACROSS both sides of the hidden inequality.
2. NOTE: to simplify .5%, write as (0.5)/(100). Be consistent!

Question 10

Answer 10

1. Simplify both sides by canceling out with common denominator (15!)
2. Get rid of Xs and Ys from across both sides so that you end up with just comparing A = y and B = x.

Question 11

Answer 11

1. Note that slope = rise/run = change in y/change in x
2. Therefore, slope of the line = 0- (-b)/(c-0) = b/c
3. Therefore, slope m = b/c and the 2 values are EQUAL.

Question 12

Answer 12

1. Be CAREFUL to note which angles you are being asked to compare.
2. Note that all angles must equal 180. Calculating for X gives you X = 30.
3. Therefore, ratio of Q:R = 130:30 = 4 and 1/3
4. Notice that 1/3 is less than 1/2 so B (4.5) is bigger!

Question 13

Answer 13

1. Simplify by adding n^3 to both sides. Notice that n can be any number between 0 and 1 OR negative.
2. If positive (ex. 1/2), A is bigger because N will be greater than N^2.
3. However, if n is negative (ex. -1/2), B will be bigger bc (-)^2 = +.
4. Therefore, the answer is D.

Question 14

Answer 14

1. Setup 2 equations. 1) J = B + 400 AND 2) B+.2J = ⅔ (.8)J
2. NOTE that for the second equation, because Jennifer has given B money, her total is not 100 but instead 80% of her original.
3. Calculating out, you should get 200.

Question 15

Answer 15

1. To solve, recognize that: “the length of a side of a triangle must always be less than the sum of the lengths of the two other sides.”
2. Therefore, BC < AB + AC
3. Substituting, we get 2AB < AB + AC
4. Therefore, AB < AC so the answer is B.

Question 16

Answer 16

1. Note: do NOT just add up all the rates and divide by the number of days. Need to take into account the TIME that was spent at each of these speeds.
2. Pick an easy number for D (i.e. 60) and calculate out the times. Can see that she spent 6 hours at both rates!
3. Therefore, her average speed is 25 and B is bigger.

Question 17

Answer 17

1. Note that a side of the smaller square = sqrt(1/2). This can be simplified to 1/sqrt2.
2. Then, sqrt2(1/sqrt2) = 1.
3. The difference of sqrt2 (diagonal of longer sq) and 1 = 0.4. Therefore, B is bigger.

*be careful: sqrt(2) = 1.14!

Question 18

Answer 18

1. First, arrange numbers in order. Note that 3+8 as the middle numbers get you the correct median of 5.5.
2. Calculating for x+7, we know that x+y = 18.
3. Because X
4. In order not to change the median, the max number X could be is 3! This would make the numbers {2, 3, 3, 8, 11, 15}

Question 19

Answer 19

1. Simplify the fractions with a common demon of 12. multiply 0.416*12 to get ~5.
2. 4a-3b = 5. Substitute b=17-a into the equation.
3. Therefore, a = 8

Question 20

Answer 20

1. The problem states that when x is divided by y the remainder is 6. In general, the divisor (y in this case) will always be greater than the remainder. For example, x/y with remainder 6, y will be >6.
2. Similarly, a/b remainder 9, b will be > 9.
3. Therefore, y+b = >6 + >9 = >15, so the answer cannot be 15!

Question 21

Answer 21

1. Note that to simplify a radical in the denominator, you want to multiply by something that will get rid of the denom!
2. Multiply the denominator 2+sqrt(3) by its conjugate (2-sqrt(3)).
3. This will simplify to 6-3(sqrt3).

Question 22

Answer 22

1. Remember that these numbers could be negative or fractions! Don’t assume they are positive integers.

Question 23

Answer 23

1. Be careful with terminology. This looks simple if we pick a simple number (ie 3). Factors of A will be (7*3)= 21 –> 1,21,7,3. Factors of B will be (11*3) = 22 –> 1, 33, 11, 3.
2. However, if we pick 7:

A = 7*7. Factors are now: 1,49,7

B = 11*7. Factors are now 1,77,11,7. B will have more factors!

Answer is therefore D.

Question 24

Answer 24

1. Don’t just test numbers! Remember that there is a hidden inequality.
2. SIMPLIFY both sides so that n is compared with 7/3 (~2 1/3).
3. Knowing that n <3, n could be greater or less than 7/3, making the answer here D!

Question 25

Answer 25

Be sure to take 30% of 30%! Pick a number (i.e. 100). 30% of $30 left is 9, meaning $21 (or 21%) is leftover.

Question 26

Answer 26

1. Don't solve, estimate! Imagine if there were 2 wendy's. Would take half the amount of time it currently takes her to build a birdhouse (~7.5). 2. If there were 2 miguel's, would also take him half the time (~5 hours). 3. Therefore, working together, it should take them somewhere between 5-7.5 hours to complete the house. Answer choice B.

Question 27

Answer 27

``` Micheal = x Norman = x + 12 ``` After 6 years, 2(x+6) = x+12 + 6 2x + 12 = x + 18 x = 6. Thus the best answer is B.

Question 28

Answer 28

First way to solve: Algebra! * Create 2 equations * N = M + 12 * N + 6 = 2(M+6). * Solve for M and get 6. Alternative way: use answer key! (see screenshot). * Acknowledge that current answers are Michael's age NOW. * Create a column for Norman, who is 12 years older. * Add 6 to both columns until N = 2M (answer choice B).

Question 29

Answer 29

* Simplify both sides so that they are in the same format. * 21%x = 0.0021x. * x/21 = 0.0476x. * X has to be negative and note that becasue 0.0021x is closer to 0, the number will always be bigger! Therefore, the answer is A.

Question 30

Answer 30

* Remember that a UNITS digit is in the one's place. * Use the calculator to get 3^5 = 243. * Now, calculating 243^5 will not be possible in the calculator. Just focus on the one's digit (which is the same as 3^5). So, the units digit should be the same as 3^5. * The answer is 3.

Question 31

Answer 31

* Pick good numbers for this problem! If A can travel 3/4 as many miles as B, let's assume B can travel 4 miles and A can travel 3. * Then, if A can hold 25% more fuel then B, set B's fuel to 4 and A's fuel to 5. * 3\*5 = 15 for A * 4\*4 = 16 for B * X is therefore 15/16.

Question 32

Answer 32

* Remember that for it to not rain on ANY day, it means that all 'will not rain' probabilities for each individual day need to be multiplied together. * The chain it will NOT rain on Monday = .7, Tues = .8, Wed = .75, Thurs = .65 * Multipled together, that is .273 = 27.3%

Question 33

Answer 33

* Given Bruce can lay 200 bricks in 1 hour, it will take him 3.5 hours to lay 700 (ie Quant A). * To find Quant B, we can use the combined work formula. Their combined Rates (200+300)\*T = 1700 bricks. T= 3.4 * Therefore, Quant A is bigger.

Question 34

Answer 34

* The trick here is knowing that you can ADD both equations together because the inequalities point in the same direction. This simplifies the equation and allows crossing out. * Adding them together results in ab^2 \> b^2c * Canceling out b^2 yields a \> c, so A is bigger.

Question 35

Answer 35

* Since water is filling into the tank at 22 meters per hour, we can set the volume of the tank = 22. * And, since the water level rises at 0.7 meters/hour, we can set the height to 0.7. * To find volumen of a cycler, we just need: 22=Pi(R^2)(0.7) * r^2 = about 10 so r is about sqrt(10).

Question 36

Answer 36

* RT = D. In the setup, we know that R(5)=5 for 5 robots. Therefore, together these 5 robots work at a rate of 1 cup per second. Each individual robot therefore works at a pace of 1/5 cup per second. * When multiple workers are working together, their rates get added. In this case, there are 25 robots each working at a pace of 1/5. Therefore, their combined pace is 25/5 = 5. * RT=D. So 5T = 25 and the time it takes these robots is 5 seconds.

Question 37

Answer 37

1. First, you know that 1/3 of vehicles have to be black. Cross out numbers that are not divisible by 3 (A, C, E). 2. Then, remainder has to be divisible by 5! If answer is 12, 4 are black. Remainder = 8 which is not divisible by 5. For E, 1/3 = 10, remainder is 20, and that IS divisible by 5. So, the answer is D.

Question 38

Answer 38

1. Make this real! Assign a number to the old studio (100). If 20% are not going to the new studio, then 80 ARE going to new studio. 2. New studio can hold 145 total. 145-80 = 65 who will be new. 65/145 reduces to 13/29 (answer D)!

Question 39

Answer 39

1. Draw a picture to make this real! If she spends 5/8 and then 1/3 of the remainder, this leaves 2/8 left, which we know = $40. 2. 2/8x = 40 making x = 160.

Question 40

Answer 40

* fgh = EVEN and fg = odd. for fg to be odd, both numbers have to be odd. therefore, g = odd and f = odd. this means that h = even. * F/2 (odd/2) will leave a remainder of 1. H/2 (even/2) if H = 2 will leave a remainder of 0. * Therefore, A is bigger.

Question 41

Answer 41

* For ab+ c = odd, abc could be the following: EE + O, EO + O, OO + E, OE + O. * Working through the answer choices, we can see that only C will be always be true.