Test your basic knowledge |

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. Volume of a sphere
Last two digits are multiple of 4 or the number can be divided by 2 twice.
4/3 TT r ^3
-b +- sq. rt(b^2 - 4ac) / 2a
The amount after deductions

2. The number of ways independent events can occur together.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
12.5%
Purchase price
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

3. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
180(n-2)
1st Rule of Probability: Basic Rule is what?
1/16
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

4. 1/8 = what %
12.5%
(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.
Even

5. gcd(m,n)*lcm(m,n)
D or E
gcd(m,n)*lcm(m,n) = mn
P(E)P(F)
-b +- sq. rt(b^2 - 4ac) / 2a

6. 2n+1 - 2n+3 - 2n+5
1.4
1 - P(E)
Odd
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

7. Set Problems formula
(amount of change) / (original amount)
1.4
(x-n(n)y-n)
D or E

8. Intersecting Sets
1/16
| A union B| = |A| + |B| - |A intersect B|
sum = (average)(number of terms)
Divide 4999 by 15 => 333 integers

9. Prime Factorization to find Greatest Common Factor
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.
(n-1)!
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

10. x^r/s = ?
(x-n(n)y-n)
Exterior angle d is equal to the sum of the two remote interior angles a and b
Any multiplication involving an even number creates an even product.
s Sq. rt (x^r)

11. 5/6 = what %
83.3%
Find all prime factors
12^3
Last two digits are multiple of 4 or the number can be divided by 2 twice.

12. Combined Events: Not E = P(not E) = ?
Balancing
at least 3 steps
1 - P(E)
83.3%

13. 4th rule of Probability
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)
P(E)P(F)
(amount of change) / (original amount)
Organize into a grid.

14. Triangle abc with d on the outside with a line. What does d = ?
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
| A union B| = |A| + |B| - |A intersect B|
1.7
Exterior angle d is equal to the sum of the two remote interior angles a and b

15. How to find the slope.
y2 - y1 / x2 - x1
(x-n(n)y-n)
22
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

16. Percent Formula
gcd(m,n)*lcm(m,n) = mn
p/100 = is/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
4/3 TT r ^3

17. Percent increase = ?
(amount of change) / (original amount)
at least 3 steps
1.4
12.5%

18. The number of outcomes that result in A divided by the total number of possible outcomes.
Sum of digits is multiple of 3
1.4
The probability of event occurring is...
______ |m-n|

19. The average 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.
1.7
(total A) / (total B)
| A union B| = |A| + |B| - |A intersect B|

20. How to find all divisors of a number
2 steps
Odd
Exterior angle d is equal to the sum of the two remote interior angles a and b
Find all prime factors

21. 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?
gcd(m,n)*lcm(m,n) = mn
0.15n + 0.08(5) = 0.1(n+5)
x - x - x(sq. rt 2)
180(n-2)

22. Odd and Even rule.
Odd
Any multiplication involving an even number creates an even product.
Balancing
The probability of event occurring is...

23. When you see an equation in factored form in a question?
| A union B| = |A| + |B| - |A intersect B|
The probability of event occurring is...
Immediately UNFACTOR or vice versa
83.3%

24. Combined Events: E or F
1 - P(E)
P(E) + P(F) - P(E and F)
A = P(1 + r) ^n
______ |m-n|

25. What to do with equations that have fractions
(total distance) / (total time)
Immediately try factoring/simplifying when possible
market value
Group 1 + Group 2 + Neither - Both = Total

26. 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
Exterior angle d is equal to the sum of the two remote interior angles a and b
Sum of digits is multiple of 9
Principal (1 + interest/number times compounded)^(t)(n)

27. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
P(E) + P(F) - P(E and F)
D or E
1st Rule of Probability: Basic Rule is what?

28. Formula for area of a Trapezoid
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
n! / (n - r)!
(sum of bases)(height) / 2
Principal (1 + interest/number times compounded)^(t)(n)

29. Sq. rt(3)
A = P(1 + r) ^n
1/16
Odd numbers only have ___________
1.7

30. Average Rate: Average speed
sum = (average)(number of terms)
Number is a multiple of 3 and 2
Find all prime factors
(total distance) / (total time)

31. Multiplication principle
Principal (1 + interest/number times compounded)^(t)(n)
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
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
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.

32. Dependent events: When are two events said to be dependent events?
Figure out the probability for each individual event. Multiply the individual probabilities together.
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
If the outcome of one event affects the outcome of the other event.
A = P(1 + r) ^n

33. Work problem rule
Immediately try factoring/simplifying when possible
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.
Sum of digits is multiple of 3
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

34. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
22
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.
The probability of an event occurring plus the probability of the event not occurring = 1
1

35. Price sold for by retailer (after markup)
market value
The probability of event occurring is...
Immediately try factoring/simplifying when possible
1.4

36. In general - difficult questions require how many steps to solve?
Divide 4999 by 15 => 333 integers
1 - P(E)
The probability of event occurring is...
at least 3 steps

37. Compound interest rule
Find simple interest then look for the answer that is a little bigger
sum = (average)(number of terms)
Sum of digits is multiple of 3 - last two digits multiple of 4.
83.3%

38. Net
347
Any multiplication involving an even number creates an even product.
2 steps
The amount after deductions

39. Odd Factors
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
A = P(1 + r) ^n
Odd numbers only have ___________
Odd

40. Inscribed Angle - Minor Arc
P(E) + P(F) - P(E and F)
Minor arc = 2(inscribed angle)
2 steps
The probability of an event occurring plus the probability of the event not occurring = 1

41. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
Even
2 steps
$11 - 025
principle (interest rate - in decimal form) (time - in years)

42. 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.
If the outcome of one event affects the outcome of the other event.
The probability of event occurring is...
market value

43. Permutations: Order Matters
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.
n! / (n - r)!
(total distance) / (total time)
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

44. Average Rate: Average A per B
(total A) / (total B)
Any multiplication involving an even number creates an even product.
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
12^3

45. 2n - 2n+2 - 2n+4
The probability of event occurring is...
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
p/100 = is/of
Even

46. Three triangle length patterns
Balancing
3-4-5 - 5-12-13 - 9-12-15
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
p/100 = is/of

47. How to check for a prime number.

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183

48. How do you multiply roots together.
-b +- sq. rt(b^2 - 4ac) / 2a
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.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
1.4

49. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
Find all prime factors
A = P(1 + r) ^n
Odd numbers only have ___________
2 steps

50. Gross
Find simple interest then look for the answer that is a little bigger
x - x - x(sq. rt 2)
The total amount before any deductions
2 steps