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GMAT Concepts > Word Problems > Flashcards

Word Problems Flashcards

1
Q

What is the equation to calculate total cost?

A

Total cost = unit price x quantity purchased

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2
Q

What is the equation for profit?

A

Profit = revenue x cost

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3
Q

What is the equation for total earnings?

A

Total earnings = wage rate x hours worked

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4
Q

What is the equation for miles when you have the miles per hour and the time?

A

Miles = miles per hour x hours

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5
Q

What is the process of the working backwards strategy?

A

Plug the answers into a problem to see which makes the math work.

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6
Q

Which answer choices do you choose to work backwards from?

A

1) When numerical answer choices
2) “Nice” answer choices - small or with 0s at the end
3) When the question asks for a definite number, like a total or a single variable

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7
Q

When do you not use working backwards strategy?

A

When the question is asking for a combination of variables (eg. the difference between Person A and Person B)

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8
Q

What is a relative rate?

A

When two bodies are traveling at the same time

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9
Q

If the object spends more time traveling at a slower rate, the average will always be closer to the ___ of the two rates than to the __.

A

If the object spends more time traveling at a slower rate, the average will always be closer to the slower of the two rates than to the faster.

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10
Q

What is the equation of speed?

A

Speed = total distance / total time

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11
Q

When 2+ workers are performing the same task, their rates can be ___ together.

A

Their rates can be added together.

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12
Q

If one worker is undoing the work of the other, ___ the rates.

A

Subtract the rates if one worker is undoing the work of the others.

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13
Q

When work involves completing a task, treat completing the task as ___ unit.

A

Treat completing a task as one unit of work.

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14
Q

When you know the rate of every worker, __ the rates of workers who work together to complete the same task.

A

Add the the rates if the workers are completing a task together.

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15
Q

When would you choose smart numbers?

A

To replace variables in questions where they are asking for relationships between variables. Especially used in questions where variables are used throughout, including the answer choices.

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16
Q

How do you choose a smart number?

A

1) Pick numbers with different characteristics (even vs. odd)
2) Follow constraints of the problem (eg. distance is not negative)
3) Choose numbers that work in the problem

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17
Q

You can/cannot replace variables in answer choices wtih smart numbers.

A

You can do this.

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18
Q

Smart numbers are used in questions with variables, but can also be used in __.

A

Can be used in questions asking for percentages or fractions, and in hard questions.

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19
Q

What types of smart numbers should you avoid choosing?

A
  1. Numbers where you may get the same numerical answers at different points in the problem
  2. 0 or 1 or a number used elsewhere in the problem
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20
Q

For percentages, which smart number should you use?

A

Use 100 if possible, unless it appears elsewhere in the problem.

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21
Q

How do you calculate 5% of a number quickly?

A

Find 10% of the desired number, then halve that answer to get 5%.

22
Q

What is an overlapping set?

A

A problem that involves 2+ sets of data that partially intersect with each other.

23
Q

What is the best way to deal with overlapping sets?

A

Use a double-set matrix, for problems with 2 categorizations of decisions.

24
Q

When does the double set matrix work?

A

Mutually exclusive options (you have A or you don’t have A)

25
Q

Can you use a double set matrix with percentages?

A

Yes, if you choose smart numbers, but no actual numbers can appear in the problem or else totals are pre-determined…. if there are numbers available, then you have to solve, not use a smart number.

26
Q

What is the equation for average?

A

Average = sum / # of terms

27
Q

The median exists as a value in a set if there is an odd/even number of values.

A

Odd; does not exist in set with even number of values unless the middle two values are the same.

28
Q

What is the definition of standard deviation?

A

How far from the average the data points fall.

29
Q

What does a small standard deviation mean?

A

A set is clustered around the average value

30
Q

What does a large standard deviation mean?

A

A set is spread widely from the mean.

31
Q

When is the standard deviation 0?

A

When all the values in the set are the same.

32
Q

If every absolute difference from the mean is equal, then the standard deviation is __ that difference.

A

The standard deviation is equal to that difference.

33
Q

If a problem asks about changes in standard deviation, check __.

A

Check whether there are changes in how the data moves compared to the mean (closer, farther or neither).

34
Q

If a problem asks to compare standard deviations, ask __.

A

Ask which set is more spread out from the mean.

35
Q

What is the equation for weighted averages?

A

Weighted average = component 1 (weight 1) x component 2 (weight 2)

36
Q

What are evenly spaced sets?

A

Values of numbers in a set go up / down by the same increment.

37
Q

What are consecutive multiples?

A

Special cases of evenly spaced sets - all values in a set are multiples of the same increment.

38
Q

What are consecutive integers?

A

Consecutive multiples but all values increase by 1 and all integers are multiples of 1.

39
Q

When counting the number of integers in a group, add ___ to the difference between the first and last numbers in the group.

A

Add 1. The equation is (last - first) + 1

40
Q

What is the equation for counting consecutive multiples?

A

(last - first) / increment + 1

A bigger increment means smaller number of consecutive integers because there are less numbers to count.

41
Q

What are the properties of evenly spaced sets?

A

1) The mean and median are equal to each other.

2) The mean and median are equal to the average of the first and last terms

42
Q

What are the steps to find the sum of a bunch of consecutive integers?

A

1) Find the average of the set. (first + last ) / 2
2) Count the number of terms (last - first) + 1
3) Sum = average x number of terms

43
Q

The average of an even/odd number of consecutive integers will also be an integer.

A

Odd. The average of an even number of integers will never be an integer.

44
Q

What questions are ideal for drawing out?

A

Rate and work problems, problem with slots

45
Q

What should you remember when working on problems with where there are slots and you don’t have the actual numbers?

A

1) Test extreme cases

2) If there is information about the median of the numbers, then the list should be evaluated from least to greatest.

46
Q

What is the hidden integer constraint?

A

The idea is to assume that numbers are whole beacuse some things can’t be split, like people.

47
Q

What is the best way to draw out sets, where there are multiple choices involved?

A

You can use double-set matrix for more choices, as long as there is no overlap.

48
Q

What is the best way to draw out overlapping sets?

A

Venn diagrams

49
Q

The product of k consecutive integers is always divislbe by…

A

…divisible by k factorial (k!)

eg. the product of 3 consecutive integers is always divislbe by 3, 2, and 1, which means 3 x 2 x 1 = 3! = 6

50
Q

For any set of consecutive integers with an ODD number of terms, the sum of the integers is always…

A

…is always a multiple of the number of items.

If the set has an EVEN number of items, the sum of the integers is is not a multiple of the number of items.

this is due to the average formula

51
Q

What is the best way to approach solving scheduling problems?

A

Always consider the extreme possibilities, such as the earliest and the latest possible time slots for events being scheduled.

GMAT Concepts (2 decks)

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