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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. How to check whether a number is a multiple of 3.
Sum of digits is multiple of 3
1 - P(E)
s Sq. rt (x^r)
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

2. Three triangle length patterns
at least 3 steps
3-4-5 - 5-12-13 - 9-12-15
P(E)P(F)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

3. Gross Profit formula
Principal (1 + interest/number times compounded)^(t)(n)
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
Gross Profit = Selling Price - Cost

4. How to check whether number is multiple of 9
Sum of digits is multiple of 9
sum = (average)(number of terms)
principle (interest rate - in decimal form) (time - in years)
| A union B| = |A| + |B| - |A intersect B|

5. gcd(m,n)*lcm(m,n)
1.7
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.
gcd(m,n)*lcm(m,n) = mn
Number is a multiple of 3 and 2

6. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
-b +- sq. rt(b^2 - 4ac) / 2a
The probability of event occurring is...
(n-1)!
principle (interest rate - in decimal form) (time - in years)

7. 0! = ?
1.7
1
P(E) + P(F) - P(E and F)
Gross Profit = Selling Price - Cost

8. How to find the slope.
Odd numbers only have ___________
The probability of an event occurring plus the probability of the event not occurring = 1
-b +- sq. rt(b^2 - 4ac) / 2a
y2 - y1 / x2 - x1

9. Triangle abc with d on the outside with a line. What does d = ?
s Sq. rt (x^r)
(x-n(n)y-n)
Exterior angle d is equal to the sum of the two remote interior angles a and b
1/16

10. 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.
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
Number is a multiple of 3 and 2
2 steps

11. Quadratic formula
1.4
Number is a multiple of 3 and 2
-b +- sq. rt(b^2 - 4ac) / 2a
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.

12. 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. 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.
P(E) + P(F) - P(E and F)
1st Rule of Probability: Basic Rule is what?
(total A) / (total B)

13. 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?
Sum of digits is multiple of 9
0.15n + 0.08(5) = 0.1(n+5)
Purchase price
D or E

14. Percent Formula
p/100 = is/of
Gross Profit = Selling Price - Cost
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

15. 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.
Immediately try factoring/simplifying when possible
gcd(m,n)*lcm(m,n) = mn
-b +- sq. rt(b^2 - 4ac) / 2a

16. To determine the number of integers less than 5000 that are evenly divisible by 15...?
P(E)P(F)
A = P(1 + r) ^n
Figure out the probability for each individual event. Multiply the individual probabilities together.
Divide 4999 by 15 => 333 integers

17. Average Rate: Average A per B
(total A) / (total B)
Sum of digits is multiple of 9
Any multiplication involving an even number creates an even product.
Odd numbers only have ___________

18. Simple probability
1/16
12.5%
p/100 = is/of
(# of favorable outcomes) / (# of possible outcomes)

19. 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
Balancing
A = P(1 + r) ^n
(amount of change) / (original amount)
The probability of event occurring is...

20. x^r/s = ?
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
s Sq. rt (x^r)
Immediately try factoring/simplifying when possible
1.4

21. Compound interest rule
Immediately UNFACTOR or vice versa
D or E
1.7
Find simple interest then look for the answer that is a little bigger

22. Work problem rule
12^3
Number is a multiple of 3 and 2
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.
180(n-2)

23. (1/4)^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.
P(E) + P(F) - P(E and F)
1/16
gcd(m,n)*lcm(m,n) = mn

24. Sq. rt(3)
Sum of digits is multiple of 3
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Group 1 + Group 2 + Neither - Both = Total
1.7

25. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
Find all prime factors
12^3
3-4-5 - 5-12-13 - 9-12-15
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

26. Average Rate: Average speed
(# of favorable outcomes) / (# of possible outcomes)
at least 3 steps
(total distance) / (total time)
2 steps

27. Price purchased for by wholesaler
Principal (1 + interest/number times compounded)^(t)(n)
Exterior angle d is equal to the sum of the two remote interior angles a and b
-b +- sq. rt(b^2 - 4ac) / 2a
Purchase price

28. Price sold for by retailer (after markup)
2 steps
market value
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.

29. Trial Problems: look at the probability of NOT OCCURRING
-b +- sq. rt(b^2 - 4ac) / 2a
n! / (n - r)!
| A union B| = |A| + |B| - |A intersect B|
P(event NOT occurring) = 1 - P(event occurring)

30. In general - difficult questions require how many steps to solve?
at least 3 steps
Immediately try factoring/simplifying when possible
x(sq. rt 3) - x - 2x
1/16

31. 45-45-90 triangle basic lengths of sides
1
at least 3 steps
If the outcome of one event affects the outcome of the other event.
x - x - x(sq. rt 2)

32. To determine multiple-event probability where each individual event must occur in a certain way.
3 - 6 - 9 - 12
s Sq. rt (x^r)
Figure out the probability for each individual event. Multiply the individual probabilities together.
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.

33. 2n+1 - 2n+3 - 2n+5
Odd
Immediately try factoring/simplifying when possible
Sum of digits is multiple of 3 - last two digits multiple of 4.
Find simple interest then look for the answer that is a little bigger

34. Probability and Geometry.
4/3 TT r ^3
Number is a multiple of 3 and 2
(n-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

35. 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)
1st Rule of Probability: Basic Rule is what?
P(event NOT occurring) = 1 - P(event occurring)
sum = (average)(number of terms)

36. How to check whether a number is a multiple of 4.
Gross Profit = Selling Price - Cost
Last two digits are multiple of 4 or the number can be divided by 2 twice.
347
3-4-5 - 5-12-13 - 9-12-15

37. How to check for a prime number.

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38. Odd and Even rule.
______ |m-n|
Last two digits are multiple of 4 or the number can be divided by 2 twice.
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.

39. Volume of a sphere
n! / (n - r)!
P(E) + P(F) - P(E and F)
4/3 TT r ^3
(total A) / (total B)

40. Combined Events: Not E = P(not E) = ?
principle (interest rate - in decimal form) (time - in years)
The probability of event occurring is...
1 - P(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.

41. What to do with equations that have fractions
Immediately try factoring/simplifying when possible
Group 1 + Group 2 + Neither - Both = Total
Sum of digits is multiple of 3 - last two digits multiple of 4.
s Sq. rt (x^r)

42. Number added or deleted
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)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Sum of digits is multiple of 3

43. Sum of consecutive numbers
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.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
sum = (average)(number of terms)

44. Formula for Mixed Group problems (involving Both/Neither)
Purchase price
Group 1 + Group 2 + Neither - Both = Total
16.6%
P(event NOT occurring) = 1 - P(event occurring)

45. The number of outcomes that result in A divided by the total number of possible outcomes.
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)
(total distance) / (total time)
The probability of event occurring is...

46. When you see an equation in factored form in a question?
Immediately UNFACTOR or vice versa
gcd(m,n)*lcm(m,n) = mn
1/16
(amount of change) / (original amount)

47. Compound interest formula
Figure out the probability for each individual event. Multiply the individual probabilities together.
Principal (1 + interest/number times compounded)^(t)(n)
-b +- sq. rt(b^2 - 4ac) / 2a
y2 - y1 / x2 - x1

48. 3^3 x 4^3 = ?
always try to 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
The amount after deductions
12^3

49. Odd Factors
p/100 = is/of
$11 - 025
Odd numbers only have ___________
2 steps

50. 1/6 = what %
p/100 = is/of
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
16.6%
(x-n(n)y-n)