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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. Lowest Common Multiple 60: 2 x 2 x 3 x 5 - 72: 2 x 2 x 2 x 3 x 3 - LCM: 2 x 2 x 2 x 3 x 3 x 5
Sum of digits is multiple of 9
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)
at least 3 steps

2. Combined Events: E or F
Sum of digits is multiple of 3
P(E) + P(F) - P(E and F)
Any multiplication involving an even number creates an even product.
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.

3. Prime Factorization to find Greatest Common Factor
The probability of event occurring is...
at least 3 steps
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
22

4. gcd(m,n)*lcm(m,n)
always try to factor
P(E) + P(F) - P(E and F)
gcd(m,n)*lcm(m,n) = mn
Immediately UNFACTOR or vice versa

5. To determine multiple-event probability where each individual event must occur in a certain way.
Figure out the probability for each individual event. Multiply the individual probabilities together.
(total A) / (total B)
at least 3 steps
x(sq. rt 3) - x - 2x

6. Trial Problems: look at the probability of NOT OCCURRING
The amount after deductions
P(event NOT occurring) = 1 - P(event occurring)
83.3%
14 liters

7. How to find the slope.
Find simple interest then look for the answer that is a little bigger
y2 - y1 / x2 - x1
347
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

8. How to find all divisors of a number
P(event NOT occurring) = 1 - P(event occurring)
Find all prime factors
0.15n + 0.08(5) = 0.1(n+5)
16.6%

9. How to check for a prime number.

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10. Combined Events: Not E = P(not E) = ?
Immediately UNFACTOR or vice versa
1 - P(E)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
at least 3 steps

11. Volume of a sphere
Divide 4999 by 15 => 333 integers
4/3 TT r ^3
Principal (1 + interest/number times compounded)^(t)(n)
s Sq. rt (x^r)

12. How to check whether a number is a multiple of 6
principle (interest rate - in decimal form) (time - in years)
Sum of digits is multiple of 3 - last two digits multiple of 4.
(sum of bases)(height) / 2
Number is a multiple of 3 and 2

13. 0! = ?
The amount after deductions
always try to factor
| A union B| = |A| + |B| - |A intersect B|
1

14. When you see an equation in factored form in a question?
(# of favorable outcomes) / (# of possible outcomes)
Immediately UNFACTOR or vice versa
Find all prime factors
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

15. What to do with equations that have fractions
Immediately try factoring/simplifying when possible
Organize into a grid.
(total A) / (total B)
Minor arc = 2(inscribed angle)

16. In general - difficult questions require how many steps to solve?
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.
at least 3 steps
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
P(E)P(F)

17. Compound interest rule
Find simple interest then look for the answer that is a little bigger
x(sq. rt 3) - x - 2x
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
at least 3 steps

18. (1/4)^2
180(n-2)
The amount after deductions
Group 1 + Group 2 + Neither - Both = Total
1/16

19. Always try to factor
at least 3 steps
0.15n + 0.08(5) = 0.1(n+5)
always try to factor
1

20. Formula for area of a Trapezoid
(total distance) / (total time)
(sum of bases)(height) / 2
(total A) / (total B)
If the outcome of one event affects the outcome of the other event.

21. 2n+1 - 2n+3 - 2n+5
sum = (average)(number of terms)
at least 3 steps
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.
Odd

22. 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.
Organize into a grid.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
12.5%
(n-1)!

23. Multiplication principle
gcd(m,n)*lcm(m,n) = mn
Immediately try factoring/simplifying when possible
if a first object may be chosen in m ways and a second object may be chosen in n ways - then there are mn ways of choosing both objects
P(E)P(F)

24. Compound interest formula
x(sq. rt 3) - x - 2x
Principal (1 + interest/number times compounded)^(t)(n)
(total distance) / (total time)
The amount after deductions

25. Sum of consecutive numbers
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
if a first object may be chosen in m ways and a second object may be chosen in n ways - then there are mn ways of choosing both objects
sum = (average)(number of terms)
22

26. Percent increase = ?
Balancing
3 - 6 - 9 - 12
3-4-5 - 5-12-13 - 9-12-15
(amount of change) / (original amount)

27. Price sold for by retailer (after markup)
1.4
(# of favorable outcomes) / (# of possible outcomes)
D or E
market value

28. Triangle abc with d on the outside with a line. What does d = ?
D or E
1
Exterior angle d is equal to the sum of the two remote interior angles a and b
Group 1 + Group 2 + Neither - Both = Total

29. Multiples of 3
A = P(1 + r) ^n
3 - 6 - 9 - 12
16.6%
sum = (average)(number of terms)

30. 3^3 x 4^3 = ?
4/3 TT r ^3
If the outcome of one event affects the outcome of the other event.
-b +- sq. rt(b^2 - 4ac) / 2a
12^3

31. Dependent events: When are two events said to be dependent events?
market value
4/3 TT r ^3
If the outcome of one event affects the outcome of the other event.
Exterior angle d is equal to the sum of the two remote interior angles a and b

32. 45-45-90 triangle basic lengths of sides
Group 1 + Group 2 + Neither - Both = Total
1 - P(E)
x - x - x(sq. rt 2)
Principal (1 + interest/number times compounded)^(t)(n)

33. Net
Gross Profit = Selling Price - Cost
22
The amount after deductions
Organize into a grid.

34. Three triangle length patterns
Any multiplication involving an even number creates an even product.
n! / (n - r)!
-b +- sq. rt(b^2 - 4ac) / 2a
3-4-5 - 5-12-13 - 9-12-15

35. 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
1st Rule of Probability: Basic Rule is what?
1/16
Minor arc = 2(inscribed angle)

36. In general - medium questions require how many steps to solve?
2 steps
12.5%
347
1st Rule of Probability: Basic Rule is what?

37. How do you multiply roots together.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
3-4-5 - 5-12-13 - 9-12-15
The probability of an event occurring plus the probability of the event not occurring = 1
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

38. How to check whether a number is a multiple of 4.
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.
x(sq. rt 3) - x - 2x
(total distance) / (total time)
Last two digits are multiple of 4 or the number can be divided by 2 twice.

39. 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?
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
p/100 = is/of
0.15n + 0.08(5) = 0.1(n+5)
x(sq. rt 3) - x - 2x

40. Sq. rt(2)
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.
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
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
1.4

41. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
The total amount before any deductions
p/100 = is/of
P(E) + P(F) - P(E and F)
22

42. 1/6 = what %
1st Rule of Probability: Basic Rule is what?
The total amount before any deductions
16.6%
x - x - x(sq. rt 2)

43. Price purchased for by wholesaler
16.6%
| A union B| = |A| + |B| - |A intersect B|
P(E) + P(F) - P(E and F)
Purchase price

44. Average Rate: Average speed
(total distance) / (total time)
Check each prime number up to the approximate square root of the number. If you haven't found a number less than or equal to the square root of the number - then the number is prime.
Divide 4999 by 15 => 333 integers
Balancing

45. 2nd Rule of Probability: P(E) = 1 - P(not E)
P(event NOT occurring) = 1 - P(event occurring)
The probability of event A OR B occurring is the probability of event A occurring plus the probability of event B occurring minus the probability of both events occurring. P(A or B) = P(A) +P(B) - P(A and B)
The probability of an event occurring plus the probability of the event not occurring = 1
3 - 6 - 9 - 12

46. Formula for Mixed Group problems (involving Both/Neither)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Group 1 + Group 2 + Neither - Both = Total
The probability of an event occurring plus the probability of the event not occurring = 1
12.5%

47. x^r/s = ?
1/16
if a first object may be chosen in m ways and a second object may be chosen in n ways - then there are mn ways of choosing both objects
n! / (n - r)!
s Sq. rt (x^r)

48. What does the Sum of the angles in a Regular Polygon formula look like?
1/16
12^3
180(n-2)
D or E

49. Set Problems formula
______ |m-n|
-b +- sq. rt(b^2 - 4ac) / 2a
(x-n(n)y-n)
x - x - x(sq. rt 2)

50. Indistinguishable events how to find the number of permutations

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