GMAT Math Mprep

Question 1

If a right triangle is inscribed in a circle, then the hypotenuse is the…

Answer 1

Diameter of the circle

Question 2

Problem Type: One-sixth of the attendees at a certain convention are female students, two-thirds of the attendees are female, and one-third of the attendees are students. If 150 of the attendees are neither female nor students, what is the total number of attendees at the convention?

Answer 2

Overlapping sets, create a table

Question 3

Problem Type: In a certain class of students, 25% received A’s on the final exam and 2/3 of these students received A’s in the class as a whole. If 15 students in the class received A’s on the final exam but did not receive an A in the class, how many students did not receive an A on the final exam?

Answer 3

Overlapping sets, create a table

Question 4

Perpendicular lines have slopes that are…

Answer 4

Opposite signs & reciprocals of each other

Question 5

What is the formula for speed/distance/time?

Answer 5

Distance = (rate or speed)*(time)

Question 6

Problem Type: An object with mass m is spinning in uniform circular motion in a circle perpendicular to the ground with radius r at a circular velocity of 2 m/s. At the height of its spin, the forces acting on it, f, can be calculated by summing the force due to change in direction and the force due to gravity. The force due to gravity is the mass of the object multiplied by 9.8 m/s2. The force due to change in direction is the product of the square of the velocity of the object, the mass of the object, and the reciprocal of the radius. What is m in terms of r and f?

Answer 6

This is simple algebra / substitution. You could also use SMART #s

Question 7

Problem type: If n is a non-negative integer such that 12n is a divisor of 3,176,793, what is the value of n12 – 12n?

Answer 7

Divisibility & Primes - notice that 12n will always be an even number, and 3,176,793 is ODD. therefore, the only way this is possible is if n is equal to 0

Question 8

Problem Type: The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Which of the following could be the greatest common factor of n and 210?

Answer 8

Divisibility - approach is to look at the factorization of 16 and 45. This tells you that n’s factorization has two 2s and one 3, but NO 5. Then, look at the factorization of 210 and note that it is 2 x 3 x 5 x 7 . then look at the answer choices and find the answer that has 2’s and 3’s but no 5s.

Question 9

the average of a set of consecutive integer is equal to…

Answer 9

the average of the first and last integers

Question 10

Mean = Sum / # of integers so….

Answer 10

Mean * # of integers = sum

Question 11

Problem Type: Cindy has her eye on a sundress but thinks it is too expensive. It goes on sale for 15% less than the original price. Before Cindy can buy the dress, however, the store raises the new price by 25%. If the dress cost $68 after it went on sale for 15% off, what is the difference between the original price and the final price?

Answer 11

FDP - use ratios to set up

Question 12

Problem Type: What is the ratio of r to s?

(1) r + s = 7
(2) r^2 – s^2 = 7

Answer 12

to find the ratio, we could find r/s, s/r or find r and s independently. This allows you to find r and s independently if you use both statements together

Question 13

Problem Type: What is the sum of the multiples of 7 from 84 to 140, inclusive?

Answer 13

Since we know the first and the last number in the set, all we have to do is find the number of integers in the set, and then use the formula Sum = (mean of the set) x (number of integers in the set)

The mean is the first plus the last divided by 2, and we know there are 9 different terms because there are 9 multiples of 7 between 84 and 140

Question 14

Problem Type: Pastries made out of filo dough are brushed with either olive oil or butter (but not both). Pastries made out of shortcrust dough are not brushed with anything. Rashid and Mikhail submitted a total of x pastries to a baking competition. Mikhail used filo dough for all of his pastries, Rashid used shortcrust dough for all of his pastries, and each pastry was made using only one kind of dough. If Rashid made 2/3 as many pastries as Mikhail, and 5/8 of the filo dough pastries were brushed with olive oil, then how many of the pastries submitted by Rashid and Mikhail, in terms of x, were brushed with butter?

Answer 14

Use smart numbers and choose something that is divisible by both 3 and 8 to avoid fractions

Question 15

Problem Type: Boomtown urban planners expect the city’s population to increase by 10% per year over the next two years. If that projection were to come true, the population two years from now would be exactly double the population of one year ago. Which of the following is closest to the percent population increase in Boomtown over the last year?

Answer 15

use smart numbers, start with 100 since this problem includes percents

Question 16

Problem Type: If x and y are positive and x^2y^2=18−3xy, then x^2=

Answer 16

Simply choose a value for y & x that satisfies the first equation, then test those values with the answer choices to see which of them yields the same number as x^2

Question 17

Problem Type: A student committee that must consist of 5 members is to be formed from a pool of 8 candidates. How many different committees are possible?

Answer 17

Combinatorics, use 8 choose 5 formula of 8!/5!3!

Question 18

Problem Type: Bag A contains red, white and blue marbles such that the red to white marble ratio is 1:3 and the white to blue marble ratio is 2:3. Bag B contains red and white marbles in the ratio of 1:4. Together, the two bags contain 30 white marbles. How many red marbles could be in bag A?

Answer 18

Looks like ratios, but its actually about divisibility. The ratios tell us that the numbers of marbles must be multiples of different numbers based on the ratios provided, use this to figure out possible values

Question 19

Problem Type: Miguel is mixing up a salad dressing. Regardless of the number of servings, the recipe requires that 5/8 of the finished dressing mix be olive oil, 1/4 vinegar, and the remainder an even mixture of salt, pepper and sugar. If Miguel accidentally doubles the vinegar and forgets the sugar altogether, what proportion of the botched dressing will be olive oil?

Answer 19

Choose a smart number for the total dressing volume based on common denominator. The best # to use is 24

Question 20

Problem Type: For every integer n ≥ 3, the function g(n) is defined as the product of all the odd integers from 1 to n, inclusive. What is the value of g(100) – g(99)?

Answer 20

Look for a pattern and test cases. If you start with small numbers for n, you notice that for any odd n, the result equals the same as n+1, therefore the answer to the question is 0

Question 21

Problem Type: Barry walks from one end to the other of a 30-meter long moving walkway at a constant rate in 30 seconds, assisted by the walkway. When he reaches the end, he reverses direction and continues walking with the same speed, but this time it takes him 120 seconds because he is traveling against the direction of the moving walkway. If the walkway were to stop moving, how many seconds would it take Barry to walk from one end of the walkway to the other?

Answer 21

Rates & Work, set up a table where work = rate x time
remember that you can add rates, so when barry is moving with the walkway, use b+w = r, and when he goes against it, use b-w=r

Question 22

Problem Type: What percent of the students at Jefferson High School study French but not Spanish?

(1) 30% of all students at Jefferson High School study French.
(2) 40% of all students at Jefferson High School do not study Spanish.

Answer 22

Overlapping sets, set up a table

Question 23

Problem Type: If n is an integer between 10 and 100, is the tens digit of n even?

(1) The remainder when n is divided by 4 is equal to the remainder when n is divided by 5.
(2) The only prime factor of n is 3.

Answer 23

Test Cases

Question 24

Same exponent means you can

Answer 24

multiply the bases, keep exponent the same

Question 25

|x-5| < 8 means…

Answer 25

x-5<8 or -(x-5)

Question 26

“x is div by y”, “x is a mult of y”, “y is a factor of x”, “x/y is an integer” all mean that…

Answer 26

x’s prime factorization contains all of what is in y’s

Question 27

How do you find the GCF of 2 numbers?

Answer 27

Compute both prime factorizations, everything they have in common is the GCF

Question 28

How do you find the LCM of 2 numbers?

Answer 28

compute both prime factorizations, find the smallest number that has the minimum primes of both. If a prime repeats, you only need to include it 1 time

Question 29

Shortcut to finding the number of factors a number has

Answer 29

add the exponents of its prime factorization

Question 30

How do you know the # of degrees inside a polygon?

Answer 30

Triangles have 180, every time you add another side, you add another 180

Question 31

Area of a trapezoid =

Answer 31

average of the parallel sides (bases) multiplied times height

Question 32

Rhombus facts

Answer 32

all sides equal, opposite sides parallel, area = 1/2*(product of diagonals)

Question 33

Diagonal of a rectangular solid with sides a/b/c

Answer 33

a^2+b^2 +c^2 =d^2

Question 34

What special right triangle side lengths should I know?

Answer 34

3:4:5 (sometimes 6:8:10), 5:12:13

Question 35

30 - 60 - 90 right triangle sides

Answer 35

x:x root 3:2x, root 3 is approx 1.7 or 3/17

Question 36

45 - 45 - 90 right triangle side ratios

Answer 36

x:x: x root 2 , root 2 is approx 1.4 or 2/14

Question 37

Arclength =

Answer 37

angle/360 * circumference

Question 38

Area of a Sector =

Answer 38

angle/360 * area

Question 39

Rectangle inscribed in a circle means that…

Answer 39

the diagonal of that rectangle is the diameter

Question 40

Any triangle inscribed in a semi circle (aka a half circle) is a ….

Answer 40

right triangle

Question 41

To find the distance between 2 points in a plane…

Answer 41

make a right triangle where the distance is the hypotenuse

Question 42

powers of numbers with units digit 4 end in…

Answer 42

4 or 6

Question 43

Powers of numbers with units digit 9 end in…

Answer 43

9 or 1, depending on if the power is odd or even. 1 = even powers, 9 = odd powers

Question 44

Powers of numbers that end in 0,1,5,and 6

Answer 44

will always end in those respective #s

Question 45

Powers of numbers with units digit 2,3,7, or 8 end in…

Answer 45

a cycle of 4 numbers
2 - (2,4,8,6)
3 - (3,9,7,1)
7 - (7,9,3,1)
8 - (8,4,2,6)

You can figure out the last digit by figuring out how far the exponent is from a multiple of 4

Question 46

percent change =

Answer 46

(new - old) / old