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GMAT Quantitative General

Subjects : gmat, math

Instructions:

Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can study here.
Match each statement with the correct term.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.

1. In general - difficult questions require how many steps to solve?
22
p/100 = is/of
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
at least 3 steps

2. Formula for Mixed Group problems (involving Both/Neither)
To find the number of distinct permutations of a set of items with indistinguishable ('repeat') items - divide the factorial of the items in the set by the product of the factorials of the number of indistinguishable elements.
2 steps
Group 1 + Group 2 + Neither - Both = Total
1st Rule of Probability: Basic Rule is what?

3. Percent increase = ?
x(sq. rt 3) - x - 2x
the probability of event A AND event B occurring is the probability of event A times the probability of event B - given that A has already occurred.
1 - P(E)
(amount of change) / (original amount)

4. How many liters of a solution that is 15% salt must be added to 5 liters of a solution that is 8% salt so that the resulting mixture is 10% salt?
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
0.15n + 0.08(5) = 0.1(n+5)
1. Start by writing each number as product of primes. 2. Write so that each new prime factor begins in the same place. 3. Greatest Common Factor is found by multiplying all factors appearing in BOTH lists
4/3 TT r ^3

5. How to check whether a number is a multiple of 4.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
If the outcome of one event affects the outcome of the other event.
1/16
Balancing

6. How to check whether number is multiple of 9
12^3
Sum of digits is multiple of 9
12.5%
180(n-2)

7. 2nd Rule of Probability: P(E) = 1 - P(not E)
the probability of event A AND event B occurring is the probability of event A times the probability of event B - given that A has already occurred.
The probability of an event occurring plus the probability of the event not occurring = 1
(amount of change) / (original amount)
Gross Profit = Selling Price - Cost

8. Trial Problems: look at the probability of NOT OCCURRING
P(event NOT occurring) = 1 - P(event occurring)
p/100 = is/of
Number is a multiple of 3 and 2
3-4-5 - 5-12-13 - 9-12-15

9. Sq. rt(3)
1.7
always try to factor
2 steps
12.5%

10. Some GMAT word problems involve groups with distinct 'either/or' categories (male/female - blue collar/white collar - etc.) The key is to do what with the information? 1. Find total number of possible outcomes. 2. Find the number of desired outcomes.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
D or E
1/16
Organize into a grid.

11. What to do with equations that have fractions
22
1
(x-n(n)y-n)
Immediately try factoring/simplifying when possible

12. Volume of a sphere
the probability of event A AND event B occurring is the probability of event A times the probability of event B - given that A has already occurred.
Exterior angle d is equal to the sum of the two remote interior angles a and b
4/3 TT r ^3
Consider work done in one hour. Inverse of the time it takes everyone working together = Sum of the inverse of the times it would take each person working individually.

13. How to check whether a number is a multiple of 3.
Minor arc = 2(inscribed angle)
at least 3 steps
Sum of digits is multiple of 3
22

14. Permutations: Order Matters
1
n! / (n - r)!
Sum of digits is multiple of 3 - last two digits multiple of 4.
3-4-5 - 5-12-13 - 9-12-15

15. Multiples of 3
12^3
3 - 6 - 9 - 12
Any multiplication involving an even number creates an even product.
(total A) / (total B)

16. Average Rate: Average A per B
(total A) / (total B)
14 liters
180(n-2)
Immediately try factoring/simplifying when possible

17. 3rd Rule of Probability: Conditional Probability
Find simple interest then look for the answer that is a little bigger
0.15n + 0.08(5) = 0.1(n+5)
Minor arc = 2(inscribed angle)
the probability of event A AND event B occurring is the probability of event A times the probability of event B - given that A has already occurred.

18. How do you multiply roots together.
Group 1 + Group 2 + Neither - Both = Total
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
always try to factor

19. Intersecting Sets
| A union B| = |A| + |B| - |A intersect B|
1st Rule of Probability: Basic Rule is what?
180(n-2)
Organize into a grid.

20. Combined Events: E and F
P(E)P(F)
4/3 TT r ^3
16.6%
(x-n(n)y-n)

21. When you see an equation in factored form in a question?
83.3%
Find simple interest then look for the answer that is a little bigger
Immediately UNFACTOR or vice versa
x(sq. rt 3) - x - 2x

22. 1. A and B < A or B 2. A or B > Individual probabilities of A - B 3. P(A and B) = P(A) x P(B) <-- 'fewer options' 4. P(A or B) = P(A) + P(B) <-- 'more options' - Probability of multiple events rules.
1.7
principle (interest rate - in decimal form) (time - in years)
1st Rule of Probability: Basic Rule is what?
(sum of bases)(height) / 2

23. 0! = ?
-b +- sq. rt(b^2 - 4ac) / 2a
s Sq. rt (x^r)
1
P(E) + P(F) - P(E and F)

24. 45-45-90 triangle basic lengths of sides
Find all prime factors
P(event NOT occurring) = 1 - P(event occurring)
Any multiplication involving an even number creates an even product.
x - x - x(sq. rt 2)

25. Quadratic formula
Any multiplication involving an even number creates an even product.
(x-n(n)y-n)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
-b +- sq. rt(b^2 - 4ac) / 2a

26. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
Even
A = P(1 + r) ^n
The total amount before any deductions
If the outcome of one event affects the outcome of the other event.

27. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
347
Sum of digits is multiple of 3 - last two digits multiple of 4.
The amount after deductions
Last two digits are multiple of 4 or the number can be divided by 2 twice.

28. x^r/s = ?
Exterior angle d is equal to the sum of the two remote interior angles a and b
1.7
y2 - y1 / x2 - x1
s Sq. rt (x^r)

29. Percent Formula
D or E
p/100 = is/of
Minor arc = 2(inscribed angle)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

30. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
If the outcome of one event affects the outcome of the other event.
-b +- sq. rt(b^2 - 4ac) / 2a
22
3 - 6 - 9 - 12

31. Always try to factor
3 - 6 - 9 - 12
1. Start by writing each number as product of primes. 2. Write so that each new prime factor begins in the same place. 3. Greatest Common Factor is found by multiplying all factors appearing in BOTH lists
Balancing
always try to factor

32. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
12.5%
1
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Gross Profit = Selling Price - Cost

33. Dependent events: When are two events said to be dependent events?
n! / (n - r)!
1. Start by writing each number as a product of primes. 2. Write so that each new prime factor begins in the same place. 3. Lowest common multiple is found by multiplying all factors in either list.
If the outcome of one event affects the outcome of the other event.
The amount after deductions

34. To determine the number of integers less than 5000 that are evenly divisible by 15...?
(total distance) / (total time)
3 - 6 - 9 - 12
Odd
Divide 4999 by 15 => 333 integers

35. Three triangle length patterns
Group 1 + Group 2 + Neither - Both = Total
3-4-5 - 5-12-13 - 9-12-15
Any multiplication involving an even number creates an even product.
Purchase price

36. To determine multiple-event probability where each individual event must occur in a certain way.
22
P(E) + P(F) - P(E and F)
(n-1)!
Figure out the probability for each individual event. Multiply the individual probabilities together.

37. Compound interest formula
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
The probability of event occurring is...
Principal (1 + interest/number times compounded)^(t)(n)
12.5%

38. Indistinguishable events how to find the number of permutations

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39. How to find the slope.
2 steps
y2 - y1 / x2 - x1
If a point is chosen at random within a space with an area - volume - or length of Y and a space with a respective area - volume - or length of X lies within Y - the probability of choosing a random point within Y is the area - volume - or length of
1. Start by writing each number as product of primes. 2. Write so that each new prime factor begins in the same place. 3. Greatest Common Factor is found by multiplying all factors appearing in BOTH lists

40. Prime Factorization to find Greatest Common Factor
1. Start by writing each number as product of primes. 2. Write so that each new prime factor begins in the same place. 3. Greatest Common Factor is found by multiplying all factors appearing in BOTH lists
p/100 = is/of
1.7
Number is a multiple of 3 and 2

41. What does the Sum of the angles in a Regular Polygon formula look like?
180(n-2)
12.5%
A = P(1 + r) ^n
12^3

42. Inscribed Angle - Minor Arc
The amount after deductions
P(event NOT occurring) = 1 - P(event occurring)
The probability of event occurring is...
Minor arc = 2(inscribed angle)

43. 1/8 = what %
gcd(m,n)*lcm(m,n) = mn
Sum of digits is multiple of 3
12.5%
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

44. Formula for area of a Trapezoid
(sum of bases)(height) / 2
$11 - 025
(n-1)!
market value

45. gcd(m,n)*lcm(m,n)
Sum of digits is multiple of 9
gcd(m,n)*lcm(m,n) = mn
y2 - y1 / x2 - x1
If the outcome of one event affects the outcome of the other event.

46. Gross
1.4
Odd
The total amount before any deductions
The probability of an event occurring plus the probability of the event not occurring = 1

47. 30-60-90 triangle basic lengths of sides
1. Start by writing each number as product of primes. 2. Write so that each new prime factor begins in the same place. 3. Greatest Common Factor is found by multiplying all factors appearing in BOTH lists
x(sq. rt 3) - x - 2x
180(n-2)
Sum of digits is multiple of 9

48. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
(total distance) / (total time)
180(n-2)
D or E
Group 1 + Group 2 + Neither - Both = Total

49. How many liters of a solution that is 10% alcohol by volume must be added to 2 liters of a solution that is 50% alcohol by volume to create a solution that is 15% alcohol by volume?
14 liters
Consider work done in one hour. Inverse of the time it takes everyone working together = Sum of the inverse of the times it would take each person working individually.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Even

50. Odd Factors
Odd numbers only have ___________
1. Start by writing each number as a product of primes. 2. Write so that each new prime factor begins in the same place. 3. Lowest common multiple is found by multiplying all factors in either list.
(x-n(n)y-n)
0.15n + 0.08(5) = 0.1(n+5)