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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. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
D or E
y2 - y1 / x2 - x1
Last two digits are multiple of 4 or the number can be divided by 2 twice.
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)

2. 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?
-b +- sq. rt(b^2 - 4ac) / 2a
14 liters
12^3
market value

3. 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.
at least 3 steps
(# of favorable outcomes) / (# of possible outcomes)
Organize into a grid.
principle (interest rate - in decimal form) (time - in years)

4. 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
Group 1 + Group 2 + Neither - Both = Total
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.
347
Immediately UNFACTOR or vice versa

5. 0! = ?
Immediately UNFACTOR or vice versa
| A union B| = |A| + |B| - |A intersect B|
1
P(E)P(F)

6. Formula for area of a Trapezoid
1 - P(E)
principle (interest rate - in decimal form) (time - in years)
22
(sum of bases)(height) / 2

7. (1/4)^2
Immediately UNFACTOR or vice versa
x(sq. rt 3) - x - 2x
1/16
| A union B| = |A| + |B| - |A intersect B|

8. How to check whether a number is a multiple of 6
Number is a multiple of 3 and 2
______ |m-n|
sum = (average)(number of terms)
If the outcome of one event affects the outcome of the other event.

9. Simple probability
(# of favorable outcomes) / (# of possible outcomes)
83.3%
Figure out the probability for each individual event. Multiply the individual probabilities together.
3 - 6 - 9 - 12

10. 3^3 x 4^3 = ?
(sum of bases)(height) / 2
Find simple interest then look for the answer that is a little bigger
If the outcome of one event affects the outcome of the other event.
12^3

11. In general - difficult questions require how many steps to solve?
1
sum = (average)(number of terms)
at least 3 steps
1 - P(E)

12. 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?
0.15n + 0.08(5) = 0.1(n+5)
gcd(m,n)*lcm(m,n) = mn
Sum of digits is multiple of 3 - last two digits multiple of 4.
Figure out the probability for each individual event. Multiply the individual probabilities together.

13. Multiplication principle
Balancing
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
Even
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

14. The number of outcomes that result in A divided by the total number of possible outcomes.
The probability of event occurring is...
P(E) + P(F) - P(E and F)
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)
14 liters

15. To determine multiple-event probability where each individual event must occur in a certain way.
(total distance) / (total time)
Find simple interest then look for the answer that is a little bigger
Figure out the probability for each individual event. Multiply the individual probabilities together.
P(event NOT occurring) = 1 - P(event occurring)

16. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
(amount of change) / (original amount)
Organize into a grid.
principle (interest rate - in decimal form) (time - in years)
| A union B| = |A| + |B| - |A intersect B|

17. How to check whether number is multiple of 9
y2 - y1 / x2 - x1
| A union B| = |A| + |B| - |A intersect B|
Sum of digits is multiple of 9
Immediately UNFACTOR or vice versa

18. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
1st Rule of Probability: Basic Rule is what?
Divide 4999 by 15 => 333 integers
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
$11 - 025

19. Sum of consecutive numbers
gcd(m,n)*lcm(m,n) = mn
The amount after deductions
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.
sum = (average)(number of terms)

20. Net
(# of favorable outcomes) / (# of possible outcomes)
Figure out the probability for each individual event. Multiply the individual probabilities together.
The amount after deductions
(sum of bases)(height) / 2

21. 3rd Rule of Probability: Conditional Probability
2 steps
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
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 total amount before any deductions

22. Gross Profit formula
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.
Gross Profit = Selling Price - Cost
The probability of an event occurring plus the probability of the event not occurring = 1
2 steps

23. Prime Factorization to find Greatest Common Factor
Even
Exterior angle d is equal to the sum of the two remote interior angles a and b
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
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

24. Triangle abc with d on the outside with a line. What does d = ?
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Exterior angle d is equal to the sum of the two remote interior angles a and b
Sum of digits is multiple of 3
| A union B| = |A| + |B| - |A intersect B|

25. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
347
y2 - y1 / x2 - x1
Any multiplication involving an even number creates an even product.
Find simple interest then look for the answer that is a little bigger

26. Combined Events: E or F
Sum of digits is multiple of 3 - last two digits multiple of 4.
gcd(m,n)*lcm(m,n) = mn
Immediately try factoring/simplifying when possible
P(E) + P(F) - P(E and F)

27. Formula for Mixed Group problems (involving Both/Neither)
Group 1 + Group 2 + Neither - Both = Total
(# of favorable outcomes) / (# of possible outcomes)
-b +- sq. rt(b^2 - 4ac) / 2a
83.3%

28. Gross
Purchase price
Principal (1 + interest/number times compounded)^(t)(n)
The total amount before any deductions
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

29. Compound interest rule
Find simple interest then look for the answer that is a little bigger
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Even
(x-n(n)y-n)

30. How to check whether a number is a multiple of 12.
12^3
The probability of an event occurring plus the probability of the event not occurring = 1
Sum of digits is multiple of 3 - last two digits multiple of 4.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

31. Quadratic formula
Balancing
-b +- sq. rt(b^2 - 4ac) / 2a
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.
The probability of an event occurring plus the probability of the event not occurring = 1

32. Number added or deleted
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Gross Profit = Selling Price - Cost
(# of favorable outcomes) / (# of possible outcomes)
Purchase price

33. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
n! / (n - r)!
-b +- sq. rt(b^2 - 4ac) / 2a
A = P(1 + r) ^n
Exterior angle d is equal to the sum of the two remote interior angles a and b

34. How to check whether a number is a multiple of 3.
Figure out the probability for each individual event. Multiply the individual probabilities together.
The amount after deductions
Sum of digits is multiple of 3
(# of favorable outcomes) / (# of possible outcomes)

35. Odd Factors
Odd numbers only have ___________
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 average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

36. Odd and Even rule.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
P(event NOT occurring) = 1 - P(event occurring)
Any multiplication involving an even number creates an even product.
22

37. 1/8 = what %
p/100 = is/of
12.5%
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.
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.

38. 2n+1 - 2n+3 - 2n+5
Sum of digits is multiple of 3
83.3%
Odd
347

39. Permutations: Order Matters
1st Rule of Probability: Basic Rule is what?
12.5%
1
n! / (n - r)!

40. Dependent events: When are two events said to be dependent events?
If the outcome of one event affects the outcome of the other event.
Minor arc = 2(inscribed angle)
1.4
s Sq. rt (x^r)

41. Combined Events: Not E = P(not E) = ?
p/100 = is/of
22
0.15n + 0.08(5) = 0.1(n+5)
1 - P(E)

42. gcd(m,n)*lcm(m,n)
(sum of bases)(height) / 2
gcd(m,n)*lcm(m,n) = mn
12^3
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.

43. In general - medium questions require how many steps to solve?
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
Balancing
2 steps

44. Average Rate: Average A per B
always try to factor
n! / (n - r)!
Immediately UNFACTOR or vice versa
(total A) / (total B)

45. Three triangle length patterns
347
Immediately UNFACTOR or vice versa
principle (interest rate - in decimal form) (time - in years)
3-4-5 - 5-12-13 - 9-12-15

46. Probability and Geometry.
Principal (1 + interest/number times compounded)^(t)(n)
x - x - x(sq. rt 2)
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
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

47. Always try to factor
Group 1 + Group 2 + Neither - Both = Total
always try to factor
(total A) / (total B)
The amount after deductions

48. Trial Problems: look at the probability of NOT OCCURRING
y2 - y1 / x2 - x1
Sum of digits is multiple of 3 - last two digits multiple of 4.
Exterior angle d is equal to the sum of the two remote interior angles a and b
P(event NOT occurring) = 1 - P(event occurring)

49. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
(total distance) / (total time)
2 steps
22
P(E)P(F)

50. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
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.
(n-1)!
x - x - x(sq. rt 2)
always try to factor