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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. When you see an equation in factored form in a question?
(total distance) / (total time)
The probability of an event occurring plus the probability of the event not occurring = 1
Immediately UNFACTOR or vice versa
Any multiplication involving an even number creates an even product.

2. Prime Factorization to find Greatest Common Factor
16.6%
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
P(E)P(F)

3. To determine multiple-event probability where each individual event must occur in a certain way.
y2 - y1 / x2 - x1
1st Rule of Probability: Basic Rule is what?
Figure out the probability for each individual event. Multiply the individual probabilities together.
-b +- sq. rt(b^2 - 4ac) / 2a

4. Compound interest formula
Principal (1 + interest/number times compounded)^(t)(n)
(x-n(n)y-n)
-b +- sq. rt(b^2 - 4ac) / 2a
x - x - x(sq. rt 2)

5. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
12^3
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
D or E
(total distance) / (total time)

6. Set Problems formula
Odd
180(n-2)
(x-n(n)y-n)
Any multiplication involving an even number creates an even product.

7. Odd Factors
(sum of bases)(height) / 2
3-4-5 - 5-12-13 - 9-12-15
Odd numbers only have ___________
Principal (1 + interest/number times compounded)^(t)(n)

8. How to check whether a number is a multiple of 12.
gcd(m,n)*lcm(m,n) = mn
Sum of digits is multiple of 3 - last two digits multiple of 4.
always try to factor
Find simple interest then look for the answer that is a little bigger

9. The number of ways independent events can occur together.
16.6%
sum = (average)(number of terms)
Balancing
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

10. Trial Problems: look at the probability of NOT OCCURRING
1 - P(E)
The probability of an event occurring plus the probability of the event not occurring = 1
P(event NOT occurring) = 1 - P(event occurring)
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

11. Average Rate: Average A per B
D or E
x(sq. rt 3) - x - 2x
Group 1 + Group 2 + Neither - Both = Total
(total A) / (total B)

12. 3rd Rule of Probability: Conditional Probability
83.3%
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.
1st Rule of Probability: Basic Rule is what?
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

13. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
3-4-5 - 5-12-13 - 9-12-15
Gross Profit = Selling Price - Cost
347
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.

14. Inscribed Angle - Minor Arc
Find simple interest then look for the answer that is a little bigger
Minor arc = 2(inscribed angle)
s Sq. rt (x^r)
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)

15. Multiples of 3
3 - 6 - 9 - 12
P(E)P(F)
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
Purchase price

16. Permutations: Order Matters
n! / (n - r)!
Any multiplication involving an even number creates an even product.
Sum of digits is multiple of 3 - last two digits multiple of 4.
Even

17. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
Exterior angle d is equal to the sum of the two remote interior angles a and b
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.
Even
A = P(1 + r) ^n

18. 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.
1
(x-n(n)y-n)
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.

19. Price purchased for by wholesaler
Principal (1 + interest/number times compounded)^(t)(n)
(total A) / (total B)
Purchase price
347

20. 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?
12.5%
0.15n + 0.08(5) = 0.1(n+5)
(x-n(n)y-n)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

21. Properties of 0
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
1st Rule of Probability: Basic Rule is what?
Minor arc = 2(inscribed angle)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

22. Compound interest rule
P(E) + P(F) - P(E and F)
P(event NOT occurring) = 1 - P(event occurring)
Find simple interest then look for the answer that is a little bigger
(n-1)!

23. How to check whether number is multiple of 9
Sum of digits is multiple of 9
| A union B| = |A| + |B| - |A intersect B|
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.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

24. 1/8 = what %
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.
(# of favorable outcomes) / (# of possible outcomes)
12.5%
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

25. Sq. rt(2)
A = P(1 + r) ^n
P(E)P(F)
1.4
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

26. Think of averages as what? The average of 3 - 4 - 5 - and x is 5. What is x? 3 is 2 less than 5 4 is 1 less than 5 - 5 is the average - x = 5 + 3 = 8
Gross Profit = Selling Price - Cost
(n-1)!
Balancing
0.15n + 0.08(5) = 0.1(n+5)

27. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
22
(total distance) / (total time)
0.15n + 0.08(5) = 0.1(n+5)
y2 - y1 / x2 - x1

28. How to find all divisors of a number
(# of favorable outcomes) / (# of possible outcomes)
(total distance) / (total time)
Find all prime factors
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

29. Formula for Mixed Group problems (involving Both/Neither)
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
Group 1 + Group 2 + Neither - Both = Total
Sum of digits is multiple of 3 - last two digits multiple of 4.
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.

30. Gross
Find all prime factors
Odd
(sum of bases)(height) / 2
The total amount before any deductions

31. How do you multiply roots together.
Exterior angle d is equal to the sum of the two remote interior angles a and b
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
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
Find all prime factors

32. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
(x-n(n)y-n)
Immediately try factoring/simplifying when possible
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Principal (1 + interest/number times compounded)^(t)(n)

33. gcd(m,n)
Group 1 + Group 2 + Neither - Both = Total
principle (interest rate - in decimal form) (time - in years)
______ |m-n|
(amount of change) / (original amount)

34. Volume of a sphere
Sum of digits is multiple of 3
1st Rule of Probability: Basic Rule is what?
Figure out the probability for each individual event. Multiply the individual probabilities together.
4/3 TT r ^3

35. 45-45-90 triangle basic lengths of sides
p/100 = is/of
x - x - x(sq. rt 2)
If the outcome of one event affects the outcome of the other event.
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.

36. Probability and Geometry.
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
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

37. Price sold for by retailer (after markup)
always try to factor
Group 1 + Group 2 + Neither - Both = Total
market value
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

38. 5/6 = what %
83.3%
P(E) + P(F) - P(E and F)
The amount after deductions
n! / (n - r)!

39. Indistinguishable events how to find the number of permutations

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40. Triangle abc with d on the outside with a line. What does d = ?
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.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Exterior angle d is equal to the sum of the two remote interior angles a and b
(sum of bases)(height) / 2

41. What to do with equations that have fractions
at least 3 steps
347
Immediately try factoring/simplifying when possible
(x-n(n)y-n)

42. How to check whether a number is a multiple of 3.
n! / (n - r)!
Odd numbers only have ___________
sum = (average)(number of terms)
Sum of digits is multiple of 3

43. How to find the slope.
347
1.4
y2 - y1 / x2 - x1
Exterior angle d is equal to the sum of the two remote interior angles a and b

44. The average of consecutive numbers
Purchase price
2 steps
(total A) / (total B)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

45. Number added or deleted
3 - 6 - 9 - 12
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
1/16
Gross Profit = Selling Price - Cost

46. 2n - 2n+2 - 2n+4
(total distance) / (total time)
4/3 TT r ^3
Find simple interest then look for the answer that is a little bigger
Even

47. Gross Profit formula
Immediately UNFACTOR or vice versa
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
x(sq. rt 3) - x - 2x
Gross Profit = Selling Price - Cost

48. Work problem rule
(total A) / (total B)
market value
1st Rule of Probability: Basic Rule is what?
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.

49. Combined Events: E or F
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
3-4-5 - 5-12-13 - 9-12-15
1
P(E) + P(F) - P(E and F)

50. 2n+1 - 2n+3 - 2n+5
4/3 TT r ^3
P(E) + P(F) - P(E and F)
1.4
Odd