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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 12.
Sum of digits is multiple of 3 - last two digits multiple of 4.
22
0.15n + 0.08(5) = 0.1(n+5)
(sum of bases)(height) / 2

2. 30-60-90 triangle basic lengths of sides
| A union B| = |A| + |B| - |A intersect B|
x(sq. rt 3) - x - 2x
Immediately try factoring/simplifying when possible
1

3. Sum of consecutive numbers
Gross Profit = Selling Price - Cost
347
sum = (average)(number of terms)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

4. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
The probability of event occurring is...
Number is a multiple of 3 and 2
12^3
A = P(1 + r) ^n

5. 2n+1 - 2n+3 - 2n+5
14 liters
Odd
(total distance) / (total time)
The probability of event occurring is...

6. Indistinguishable events how to find the number of permutations

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7. Percent increase = ?
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
(amount of change) / (original amount)
(total distance) / (total time)
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

8. In general - difficult questions require how many steps to solve?
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.
at least 3 steps
The total amount before any deductions
1

9. Combined Events: Not E = P(not E) = ?
1 - P(E)
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.
principle (interest rate - in decimal form) (time - in years)

10. 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.
1.4
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
The probability of an event occurring plus the probability of the event not occurring = 1

11. Gross Profit formula
1.7
Gross Profit = Selling Price - Cost
(n-1)!
3-4-5 - 5-12-13 - 9-12-15

12. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
(total distance) / (total time)
D or E
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

13. 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.
always try to factor
Find simple interest then look for the answer that is a little bigger
12.5%
Organize into a grid.

14. 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
(# of favorable outcomes) / (# of possible outcomes)
Divide 4999 by 15 => 333 integers
1.4
Balancing

15. How to check whether number is multiple of 9
y2 - y1 / x2 - x1
Sum of digits is multiple of 9
x - x - x(sq. rt 2)
Even

16. x^r/s = ?
Odd
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Gross Profit = Selling Price - Cost
s Sq. rt (x^r)

17. 3^3 x 4^3 = ?
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
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
The probability of event occurring is...
12^3

18. The number of ways independent events can occur together.
Figure out the probability for each individual event. Multiply the individual probabilities together.
market value
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Odd

19. Volume of a sphere
12.5%
3-4-5 - 5-12-13 - 9-12-15
180(n-2)
4/3 TT r ^3

20. The average of consecutive numbers
12^3
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Minor arc = 2(inscribed angle)
x(sq. rt 3) - x - 2x

21. Inscribed Angle - Minor Arc
0.15n + 0.08(5) = 0.1(n+5)
x - x - x(sq. rt 2)
Minor arc = 2(inscribed angle)
Purchase price

22. Multiplication principle
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
Number is a multiple of 3 and 2
Figure out the probability for each individual event. Multiply the individual probabilities together.

23. Odd and Even rule.
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-1)!
Any multiplication involving an even number creates an even product.
A = P(1 + r) ^n

24. Average Rate: Average A per B
(total A) / (total B)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
1/16
always try to factor

25. 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?
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
14 liters
3 - 6 - 9 - 12
Organize into a grid.

26. In general - medium questions require how many steps to solve?
Balancing
0.15n + 0.08(5) = 0.1(n+5)
2 steps
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

27. Sq. rt(3)
gcd(m,n)*lcm(m,n) = mn
P(event NOT occurring) = 1 - P(event occurring)
1.7
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

28. To determine multiple-event probability where each individual event must occur in a certain way.
Organize into a grid.
Figure out the probability for each individual event. Multiply the individual probabilities together.
3-4-5 - 5-12-13 - 9-12-15
D or E

29. What to do with equations that have fractions
Immediately try factoring/simplifying when possible
(x-n(n)y-n)
Balancing
s Sq. rt (x^r)

30. 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
P(E) + P(F) - P(E and F)
Minor arc = 2(inscribed angle)
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.
Balancing

31. Permutations: Order Matters
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
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
n! / (n - r)!
0.15n + 0.08(5) = 0.1(n+5)

32. Prime Factorization to find Greatest Common Factor
$11 - 025
The total amount before any deductions
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
(# of favorable outcomes) / (# of possible outcomes)

33. gcd(m,n)
x(sq. rt 3) - x - 2x
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
______ |m-n|
Balancing

34. 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.
The probability of event occurring is...
Organize into a grid.
Number is a multiple of 3 and 2
1st Rule of Probability: Basic Rule is what?

35. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
(n-1)!
(total A) / (total B)
(total distance) / (total time)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

36. Always try to factor
Odd
x(sq. rt 3) - x - 2x
Balancing
always try to factor

37. Number added or deleted
Balancing
Group 1 + Group 2 + Neither - Both = Total
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

38. Properties of 0
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
market value
1
1st Rule of Probability: Basic Rule is what?

39. Three triangle length patterns
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
12.5%
3-4-5 - 5-12-13 - 9-12-15

40. Combined Events: E or F
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.
P(E) + P(F) - P(E and F)
Balancing

41. Compound interest formula
Group 1 + Group 2 + Neither - Both = Total
Number is a multiple of 3 and 2
A = P(1 + r) ^n
Principal (1 + interest/number times compounded)^(t)(n)

42. How to check for a prime number.

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43. Simple probability
1
(# of favorable outcomes) / (# of possible outcomes)
-b +- sq. rt(b^2 - 4ac) / 2a
Group 1 + Group 2 + Neither - Both = Total

44. Average Rate: Average speed
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
P(event NOT occurring) = 1 - P(event occurring)
(total distance) / (total time)
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.

45. Percent Formula
Divide 4999 by 15 => 333 integers
Sum of digits is multiple of 3
p/100 = is/of
(sum of bases)(height) / 2

46. gcd(m,n)*lcm(m,n)
1st Rule of Probability: Basic Rule is what?
gcd(m,n)*lcm(m,n) = mn
180(n-2)
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.

47. How to check whether a number is a multiple of 6
y2 - y1 / x2 - x1
Number is a multiple of 3 and 2
Sum of digits is multiple of 3
x(sq. rt 3) - x - 2x

48. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
347
1 - P(E)
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)

49. Multiples of 3
3 - 6 - 9 - 12
p/100 = is/of
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.
(amount of change) / (original amount)

50. Net
Group 1 + Group 2 + Neither - Both = Total
Exterior angle d is equal to the sum of the two remote interior angles a and b
The amount after deductions
16.6%